Linda's response regarding homework, and how it is often too difficult for the students (making them feel like failures) reminded me of a conversation I had with my father, who lives in Wyoming and who is a part-time substitute teacher (as is my mom).
He said that my nieces school had taken up some kind of "inquiry" approach. Immediately, when he said it, I thought of CMP; he could not verify that this was the exact name of the program, but said it sounded as though they at least are similar. The problem with it, in his mind, is that this is being implemented at the elementary level. Rather than teaching times tables and making sure that students can do simple arithmetic, the questions ask that students come up with multiple answers to questions; for example, "show 3 ways to add 2+2" (not an exact question from the book, but what I took from my father's speech). Now, anyone who has taken educational psychology has some idea about cognitive stages. I believe that small children (elementary age) are at what Piaget would identify as the concrete-operational stage. This is not the stage of abstract thinking. Some students will do very well with this approach; others will not. I assert that I would have probably fallen into the group that could not--indeed , it is only as an adult that I suddenly see all kinds of overlapping connections in math that I did not see when I was young. Anyhow, the school's new approach means that my niece, who is a very smart young lady and who works very hard to do well in school, finds herself crying over her math homework. Why on earth should a fourth grade student be crying over math homework? And I don't suggest that she is smart merely because she is related to me--you can just ask me about some of my other nieces and I will verify that they are not smart. My dad said it sounded like a load of "poo" to him that fourth grade students were still learning basic arithmetic as part of this new approach. He said that he learned long division in second grade when he was in England and that when he came back to the states the next year the teachers were worried that he might be behind. HAH!
I guess what I am saying is that it is hard for me to believe that the approach is going to cure our problem of scoring low in math as a nation. Perhaps I will see in a decade whether or not that approach is working with my niece . . . until then, I will remain skeptical.
Saturday, December 10, 2011
CMP Inquiry-Middle Grade Interview
Linda Beardsley at Adam Stevens Middle School was kind enough to answer the following interview questions for me. My thanks to her for completing these with such short notice.
Q: How does the CMP curriculum align with the national Common Core and NCTM standards?
Linda: For many years now, Salem-Keizer has modified the order and level of the CMP books from what the authors originally wrote. With that being said, it seems like it was not aligned very well to the state standards. With the upcoming national standards the district and the authors are working hard to find some alignment. Last summer the authors of CMP held a workshop to introduce supplementary units which will patch up the curriculum to fit the new national standards. However, I find the units a little disjointed. The authors have begun a third addition of CMP to match the national standards.
Q: Numerous students are a year or more behind in the basics. How does one address the needs of these students on a daily basis so they can get up to grade level and also experience success in the inquiry to investigation philosophy of the CMP?
Linda: The best way is to have a support class which helps the kids fill in during another period. However, that is not always possible. So the teachers spend a lot of time looking at the material the kids should have learned before and building those skills into warm-ups or 5 minute drills. In my class, I am lucky to have 15 computers which can be used to differentiate the classroom. I have used them to do Math workshop which is basically different stations. The lower kids are with me in a group and the higher kids are on the computer doing Math whizz or manga high as fun extensions. In a perfect world I would like to do this once a week but I tend to get behind in my implementation plan if I do that. After school tutoring also helps. Our special education department holds a mandatory special education help session twice a week. Students get individual support on class work.
Q: What is the role of homework (and accountability) in the CMP?
Linda: CMP has three levels of homework for each investigation. The first are application, the second, connection and the last, extensions. I believe that homework is practice of what the student has a beginning understand of. However, the constructivist approach that CMP uses often follows through on the homework assignments making them a huge challenge for the kids. I know we are trying to increase rigor with the work but we don't want to deflate the kids.
Because homework is practice, I count it very little in my grade book. I ask the students to try at home so that they connect to the problem and can find their mistake easier. Since I stopped grading homework, I have less accountability from the students so this is still a place I struggle. I have thought of doing all work in the room but there are not enough hours to do the teaching and practice of all of the standards.
Q: CMP Investigations compose of small-groups (pair-share, teamwork, cooperative learning). Describe several classroom management techniques that ensure all students are actively engaged. Eg, how are individual roles established? Accountability (Group, individual)? Ongoing assessment(s) and checking for understanding?
Linda: I like using partners and then I ask who wants to share and pick the partner instead of the volunteer. In groups of 4 I have assigned roles for the 4 students (recorder, time keeper, supply person, drill Sargent) and they have to do their roles. One student is responsible for asking group questions so I will not talk to the whole group. When groups are stuck or off task, I ask one member to huddle with me to get some questions answered and take the answers back to the group. To establish roles, I have used cards that they pick or have them number off and all 1's are recorders, all 2's are time keepers…).
Accountability is hard. I ask each student to turn in work rather than group work. I have done partner tests but I will also do individual tests. I want to know what each student understands.
I often do formative exit quizzes on skill based questions. Very simple 5 minute questions and I record these at 2 points or “not yet” in my grade book. We circle back to make sure the students have a chance to show me that they understand.
Q: How does the CMP curriculum align with the national Common Core and NCTM standards?
Linda: For many years now, Salem-Keizer has modified the order and level of the CMP books from what the authors originally wrote. With that being said, it seems like it was not aligned very well to the state standards. With the upcoming national standards the district and the authors are working hard to find some alignment. Last summer the authors of CMP held a workshop to introduce supplementary units which will patch up the curriculum to fit the new national standards. However, I find the units a little disjointed. The authors have begun a third addition of CMP to match the national standards.
Q: Numerous students are a year or more behind in the basics. How does one address the needs of these students on a daily basis so they can get up to grade level and also experience success in the inquiry to investigation philosophy of the CMP?
Linda: The best way is to have a support class which helps the kids fill in during another period. However, that is not always possible. So the teachers spend a lot of time looking at the material the kids should have learned before and building those skills into warm-ups or 5 minute drills. In my class, I am lucky to have 15 computers which can be used to differentiate the classroom. I have used them to do Math workshop which is basically different stations. The lower kids are with me in a group and the higher kids are on the computer doing Math whizz or manga high as fun extensions. In a perfect world I would like to do this once a week but I tend to get behind in my implementation plan if I do that. After school tutoring also helps. Our special education department holds a mandatory special education help session twice a week. Students get individual support on class work.
Q: What is the role of homework (and accountability) in the CMP?
Linda: CMP has three levels of homework for each investigation. The first are application, the second, connection and the last, extensions. I believe that homework is practice of what the student has a beginning understand of. However, the constructivist approach that CMP uses often follows through on the homework assignments making them a huge challenge for the kids. I know we are trying to increase rigor with the work but we don't want to deflate the kids.
Because homework is practice, I count it very little in my grade book. I ask the students to try at home so that they connect to the problem and can find their mistake easier. Since I stopped grading homework, I have less accountability from the students so this is still a place I struggle. I have thought of doing all work in the room but there are not enough hours to do the teaching and practice of all of the standards.
Q: CMP Investigations compose of small-groups (pair-share, teamwork, cooperative learning). Describe several classroom management techniques that ensure all students are actively engaged. Eg, how are individual roles established? Accountability (Group, individual)? Ongoing assessment(s) and checking for understanding?
Linda: I like using partners and then I ask who wants to share and pick the partner instead of the volunteer. In groups of 4 I have assigned roles for the 4 students (recorder, time keeper, supply person, drill Sargent) and they have to do their roles. One student is responsible for asking group questions so I will not talk to the whole group. When groups are stuck or off task, I ask one member to huddle with me to get some questions answered and take the answers back to the group. To establish roles, I have used cards that they pick or have them number off and all 1's are recorders, all 2's are time keepers…).
Accountability is hard. I ask each student to turn in work rather than group work. I have done partner tests but I will also do individual tests. I want to know what each student understands.
I often do formative exit quizzes on skill based questions. Very simple 5 minute questions and I record these at 2 points or “not yet” in my grade book. We circle back to make sure the students have a chance to show me that they understand.
Monday, November 28, 2011
Inquiry & CMP Research
Inquiry based instruction is supposedly student-centered (rather than teacher centered) and focuses less on learning the answer to a problem and more on learning various strategies for solving a problem. Proponents of the model suggest that traditional methods of instruction treat the teacher as the one and only source of knowledge in the classroom and that the teacher is supposedly only telling students about what has been learned (an abstract set of facts) rather than helping students learn (creating knowledge on their own). I believe that I detect a little bit of Vygotsky and in this supposition; if we learn through interactions with our peers and use cultural tools (language, books, and other resources) to build our pools of knowledge, then we must become adept at utilizing those tools (and persons) more than in simply memorizing facts (which in themselves are bits of knowledge, but which were not necessarily learned by the learner but given to them in the hopes that the knowledge would stick).
There are some problems with the approach, however, in as much as we can implement it in our current school systems. Students are taking tests in which they are being asked to show knowledge of a great deal of “facts”—instructors see that list of things the students “need” to know and realize that limited time means that memorization is the only way to get it all done. The other problem is that neither students nor teachers are accustomed to using this model. Students left to ponder how to solve problems might fail to generate any solutions (instead saying “but we’ve never done problems like this before!”) and teachers, who are accustomed to being the experts (and who themselves were taught that the teacher is the expert), are willing to present solutions to get the students moving forward. If too much time is spent on a single inquiry, then other time must be being wasted, perhaps?
The CMP model is designed to be a type of inquiry-based model of instruction. Believing that “math” is about strategies rather than facts, the creators have worked to make a program that presents students with engaging problems for which there are a number of “correct” solutions or a number of methods for reaching the solution. They suggest that their program moves students through a variety of inquiries that are interconnected, allowing students to build the skills necessary for solving more complex situations over time. Moreover, technology (computers and calculators, in particular) are recognized for the ways that they have changed our view of math and the usage of both is promoted rather than prohibited.
Personally, I think that while CMP has some excellent goals in mind, the actual implementation of their strategies in a classroom is not as easy as it sounds. Although I have not been an observer in many math classrooms outside my own education, I was able to observe one 8th grade classroom in the Salem-Keizer district which uses the CMP. In NO way did it strike me as being different from my own junior high experience (which occurred over ten years ago in a different state). CMP suggests that their questions are engaging, and yet, the probability question involving marbles, for example, still continues to be irrelevant to today’s middle school students. Do the 12-year old kids of today actually know what marbles are? Do they know how to play marbles? How on earth is a question about marbles engaging to students? The other problem with the approach, which I suggested somewhere in my first paragraph, is that sometimes students themselves are unable to see how to solve problems and will resort to whining. “But we’ve never done this kind of problem before!” was the one complaint I heard over and over (even though I had personally witnessed them doing similar problems previously—they apparently did not have the “self-help” skill of being able to look at previous work and to search their textbook for similar problems). This is a problem within itself—if you cannot see similarities between different problems, then you cannot possibly be expected to use the resources you have to solve the problem (i.e. transfer of skills or external tools). To me, this means that there needs to be a balance of memorization AND exploration (e.g. direct instruction and inquiry-based instruction).
Wednesday, November 9, 2011
Anticipatory Sets and Closure
Closure and Anticipatory Sets—what is the purpose of?
Anticipatory sets are designed as “hooks” for a lesson or unit (McTighe & Wiggins, 2005). Thus the reason for the term “anticipatory” (i.e. anticipation) in the name. They are designed to catch the student’s interest the activities that are about to transpire. There are multiple purposes for including an anticipatory set in a lesson (and at the beginning of the unit): 1. It supposedly gets the student’s attention (i.e. used as a way to generate curiosity in what is about to occur). 2. It tells students about the topic of the unit or lesson. 3. It can be used to reference previous learning experiences and student knowledge (activating prior knowledge) as a way to bridge learning from one day to the next (providing continuity); and finally, 4. It can (and should) be used by the teacher as a guide for “where to go” today—or in other words, can act as a pre-assessment. When students, during an anticipatory set activity such as brainstorming, demonstrate more knowledge than the teacher thought them previous in possession of, the teacher should adjust plans to avoid covering already-learned material in more than a “brief” fashion (so as to not bore anyone).
It isn’t always easy, of course, to “hook” students when what you are about to teach is as boring as watching water erosion in slow motion. It is particularly important, at these times, to activate prior knowledge and to try to present what is about to take place in a way that demonstrates that even if it is not exciting, that it will be of benefit to students even outside of the content class.
Take poetry, for example, in an 8th grade level Language Arts class. When a teacher opens the day by telling students, “alright, little pumpkins, this next six weeks we will be starting a poetry unit!”—no matter how much excitement he/she has in her voice (and no matter how many exclamation marks he/she adds to it on the objective on the board)—students will immediately begin groaning and moaning and wishing for death. It is, admittedly, often difficult for students to access poetry. Thick with figures of speech, and not adhering to the conventions that students have been forced to follow since the day they picked up a pencil in school (using capitals at the beginning of a sentence, proper punctuation, etc.), poetry presents students with little familiarity (or proficiency) with a challenge. Even worse, they have spent at least half of their school experience learning that poetry rhymes. Give them a poem that doesn’t rhyme and that doesn’t have punctuation and that contains figures of speech and archaic language forms, and it is certain that eyes will glaze over immediately. Thus, anticipatory sets for poetry have to occur over time—that is, the teacher needs to start the beginning of the year by slipping poetry here and there without making a big deal of it (aside from having students engaging in a class discussion about what it contains) and then when the poetry unit begins, the enthusiasm that the teacher worked to generate should squelch some of the groans. Also, students will have been spoon-fed poetry without having to do assignments on it, thus paving the way for the real “anticipatory statement” at the beginning of the unit for poetry.
Anticipatory sets can also include review of vocabulary, brainstorming, KWL charts (DomNwachukwu, 2005), and/or sharing of homework or classwork from previous day.
- McTighe, J. & Wiggins, G. (2005). Understanding by design (2nd ed). New Jersey: Prentice Hall.
- DomNwachukwu, C. (2005). Standards-Based Planning and Teaching in Multicultural Classroom. Multicultural Education, 13(1), 40-4. Retrieved from Education Full Text database.
Closure, as should be obvious by the very name, is a way to conclude the lesson and give students a feeling of finality. It is considered to be the most direct way to remind students about what they should have learned (what they hopefully DID learn) and can also be used to preview what will be happening tomorrow, particularly if tomorrow’s lesson will be an extension of the project or activity.
Closure for single lessons often takes place in the form of exit slips, whole-class discussions or sharing of findings of the day, presentation of work completed. Closure for units might involve self-reflection in addition to those used for daily lessons; because self-reflection is not typically utilized in the classroom, students rarely know how to complete the activity in a meaningful manner and time should be spent teaching students how to evaluate their own learning beyond the directionless “what did I learn today” question that is often presented.
Yet, the secondary purpose of closure is not as apparent as the name itself. If closure involves more than the teacher merely summarizing “what we learned today” and students are asked for input, then the teacher should be utilizing information gleaned during closure for informal assessment purposes. The teacher will learn not only what students were able to accomplish, but will be able to see misunderstanding that pop up or insights that were not previously anticipated. This knowledge will guide subsequent planning for the class—does something need to be re-taught? Should students be allowed a second day of class to complete an assignment? Do students obviously know the information and thus we should move on? Which students are struggling? Which students are more advanced than others and might be able to help lead group discussions as “experts”? When a teacher takes a second or two to utilize closure for more than just gathering assignments and summarizing information, informal assessment takes place.
Source previewed but not directly referenced:
- Johnson, A. (2000). It's time for Madeline Hunter to go: a new look at lesson plan design. Action in Teacher Education, 22(1), 72-8. Retrieved from Education Full Text database.
Anticipatory sets are designed as “hooks” for a lesson or unit (McTighe & Wiggins, 2005). Thus the reason for the term “anticipatory” (i.e. anticipation) in the name. They are designed to catch the student’s interest the activities that are about to transpire. There are multiple purposes for including an anticipatory set in a lesson (and at the beginning of the unit): 1. It supposedly gets the student’s attention (i.e. used as a way to generate curiosity in what is about to occur). 2. It tells students about the topic of the unit or lesson. 3. It can be used to reference previous learning experiences and student knowledge (activating prior knowledge) as a way to bridge learning from one day to the next (providing continuity); and finally, 4. It can (and should) be used by the teacher as a guide for “where to go” today—or in other words, can act as a pre-assessment. When students, during an anticipatory set activity such as brainstorming, demonstrate more knowledge than the teacher thought them previous in possession of, the teacher should adjust plans to avoid covering already-learned material in more than a “brief” fashion (so as to not bore anyone).
It isn’t always easy, of course, to “hook” students when what you are about to teach is as boring as watching water erosion in slow motion. It is particularly important, at these times, to activate prior knowledge and to try to present what is about to take place in a way that demonstrates that even if it is not exciting, that it will be of benefit to students even outside of the content class.
Take poetry, for example, in an 8th grade level Language Arts class. When a teacher opens the day by telling students, “alright, little pumpkins, this next six weeks we will be starting a poetry unit!”—no matter how much excitement he/she has in her voice (and no matter how many exclamation marks he/she adds to it on the objective on the board)—students will immediately begin groaning and moaning and wishing for death. It is, admittedly, often difficult for students to access poetry. Thick with figures of speech, and not adhering to the conventions that students have been forced to follow since the day they picked up a pencil in school (using capitals at the beginning of a sentence, proper punctuation, etc.), poetry presents students with little familiarity (or proficiency) with a challenge. Even worse, they have spent at least half of their school experience learning that poetry rhymes. Give them a poem that doesn’t rhyme and that doesn’t have punctuation and that contains figures of speech and archaic language forms, and it is certain that eyes will glaze over immediately. Thus, anticipatory sets for poetry have to occur over time—that is, the teacher needs to start the beginning of the year by slipping poetry here and there without making a big deal of it (aside from having students engaging in a class discussion about what it contains) and then when the poetry unit begins, the enthusiasm that the teacher worked to generate should squelch some of the groans. Also, students will have been spoon-fed poetry without having to do assignments on it, thus paving the way for the real “anticipatory statement” at the beginning of the unit for poetry.
Anticipatory sets can also include review of vocabulary, brainstorming, KWL charts (DomNwachukwu, 2005), and/or sharing of homework or classwork from previous day.
- McTighe, J. & Wiggins, G. (2005). Understanding by design (2nd ed). New Jersey: Prentice Hall.
- DomNwachukwu, C. (2005). Standards-Based Planning and Teaching in Multicultural Classroom. Multicultural Education, 13(1), 40-4. Retrieved from Education Full Text database.
Closure, as should be obvious by the very name, is a way to conclude the lesson and give students a feeling of finality. It is considered to be the most direct way to remind students about what they should have learned (what they hopefully DID learn) and can also be used to preview what will be happening tomorrow, particularly if tomorrow’s lesson will be an extension of the project or activity.
Closure for single lessons often takes place in the form of exit slips, whole-class discussions or sharing of findings of the day, presentation of work completed. Closure for units might involve self-reflection in addition to those used for daily lessons; because self-reflection is not typically utilized in the classroom, students rarely know how to complete the activity in a meaningful manner and time should be spent teaching students how to evaluate their own learning beyond the directionless “what did I learn today” question that is often presented.
Yet, the secondary purpose of closure is not as apparent as the name itself. If closure involves more than the teacher merely summarizing “what we learned today” and students are asked for input, then the teacher should be utilizing information gleaned during closure for informal assessment purposes. The teacher will learn not only what students were able to accomplish, but will be able to see misunderstanding that pop up or insights that were not previously anticipated. This knowledge will guide subsequent planning for the class—does something need to be re-taught? Should students be allowed a second day of class to complete an assignment? Do students obviously know the information and thus we should move on? Which students are struggling? Which students are more advanced than others and might be able to help lead group discussions as “experts”? When a teacher takes a second or two to utilize closure for more than just gathering assignments and summarizing information, informal assessment takes place.
Source previewed but not directly referenced:
- Johnson, A. (2000). It's time for Madeline Hunter to go: a new look at lesson plan design. Action in Teacher Education, 22(1), 72-8. Retrieved from Education Full Text database.
Sunday, October 23, 2011
Practicum - Sharing a Lesson
Admittedly, my area of experience is not in teaching. I have often trained employees at the various restaurants where I have been employed. Lesson objectives? Learn how to use the computer and learn to multi-task. Certainly, it is easy to wait tables once you get the hang of it, but it is mostly just overwhelming out first. We once had “tip a cop” night at one of my restaurants….at the end of the night, the officer who had “worked” with me said to his friends, “she ran my a--- off! I had no idea you guys did so much work.” Strategy of implementation? I typically just throw them in and tell them to do it (no following me around for three days “watching”—I consider that to be a waste of time). Checks for understanding? Well, I simply watched over their shoulders to make sure they weren’t ringing in the orders incorrectly and I would sometimes say, “what do you need to do now?” What might I change? I really am not sure….most people either catch on right away or they don’t.
I did, however, begin teaching my unit at the middle school last week. For the first day, there were only two goals: take a pre-assessment (I think the kids were thrilled by how short it was) and create a booklet for using over the next two weeks. My mentor teacher had suggested that the booklet creating might take most of the hour, so I had not planned for anything else beyond that, which turned out to be a mistake on my part. Next time I will make sure to bring a book to read aloud while they are working on their booklets, because although I think it is nice to let students talk while they are working (they were decorating the covers of their booklets and coming up with pseudonyms), it would have been a better use of time for me to start getting them interested in reading (also, reading aloud is beneficial at every grade level, and it usually catches student’s attention). I walked them through the activity one step at a time, walking from one table to the next holding my model and watching to make sure that at least one person at each table started in the correct direction before walking to the next table. Incidentally, only three people made theirs “incorrectly” and it was because they jumped ahead. I had no problem with that, given that what they ended up with will work just as well as what I was aiming for. Parts to change? Again, always have something else planned. Other changes? 1) making a more clear explanation of “nom de plume” so that students understand that the reason to have one is to make sure that they aren’t uncomfortable sharing their poetry (most of them started shouting out their fake names immediately, which told me that I had not made it clear that I was letting them create a fake name for the purpose of the poetry evaluation at the end, where they would have to share what they wrote—I know that people often feel very uncomfortable about writing poems); 2) I would consider using a longer pre-assessment. The reason I did not use a longer pre-assessment in this case is that the students have already taken 7 days of tests since the start of the semester. I think that the consistent failure (taking tests for things you have not yet learned) creates a negative attitude and causes students to not try as hard (some do not even bother reading the questions—they simply write “IDK”—which is a waste of everyone’s time, in my opinion). Also, I think I was just as tired of the tests as they were since I’d been sitting through every class period of tests.
But I digress.
The pre-assessment showed me, however, that my initial goals needed to change. I had originally been simply planning to concentrate on teaching the students figurative devices, symbolism, and tone, but it turns out that the students are perfectly competent in these areas, having had these things drilled down their throats since 5th or 6th grade. What they are unable to do, however, is make explicit references to the text to show how they know what they know. They were also unable to read beyond the literal meaning of the metaphor in the poem that I used for the assessment. I attempted to change my lessons that night, staying up quite late, but the results of my next day activity revealed that the students had not completely understood what I was trying to teach (I was attempting a modified “close reading” exercise, which I can’t really explain without drawing it by hand). Thusly, what I would change in the future is: 1) I would make sure to not go over my 10-12 minute limit for the mini lesson at the beginning of class and 2) I would break the activity into 2 parts so that it would not be so difficult to understand. I did try guiding the students through one poem as an example, but I believe half of the students were not listening.
Therefore, the final thing I am going to try my hand at changing is “how” I teach the lesson. First, I have decreased the difficulty of the activity so that it should fit more easily into a 45 minute time frame (I only have 10 lessons in all, can’t go about wasting time). This will not only mean that the assignment is more likely to be completed but also means that it shouldn’t take me 25 minutes to explain it. Second, I will not be using technology with which I am still unfamiliar—this should help decrease my personal stress and help create a more calm atmosphere (students can really sense nervousness, I discovered). Moreover, currently, the students desks are grouped, and I find myself talking to their backs for half of the lesson—or constantly asking them to turn around. It is not my classroom, or I would shift those desks around to ALWAYS be facing the front. Instead, I have purchased a white-board and I will bring the students to the back area of the classroom to sit around me on the floor. Admittedly, there is not very much room in the back (there are just as many students as desks), but this method should guarantee that I can see every students face and will not be shouting across the room to people who are in the back. I believe that my stress level will decrease (students not having their backs to me, me not feeling like I am shouting) will result in an increase in my ability to pay attention to the students faces to make sure they are listening and comprehending. Lastly, I am going to try out a “quiet” prompt to see if it helps me quiet down the students in a more timely fashion. The code word is “high five” and my sister (who is also a teacher) advises me to say it in a normal tone of voice and assures me that students will catch on quickly and will quiet down without you having to shout over them. I believe her, of course, because I happen to have the most intelligent and wise sisters in the entire universe.
I will be trying this tomorrow, and will determine whether the strategy is successful or not. I am sure you (the only person reading this Blog other than myself) are greatly eager to hear an update. (hah!)
;)
I did, however, begin teaching my unit at the middle school last week. For the first day, there were only two goals: take a pre-assessment (I think the kids were thrilled by how short it was) and create a booklet for using over the next two weeks. My mentor teacher had suggested that the booklet creating might take most of the hour, so I had not planned for anything else beyond that, which turned out to be a mistake on my part. Next time I will make sure to bring a book to read aloud while they are working on their booklets, because although I think it is nice to let students talk while they are working (they were decorating the covers of their booklets and coming up with pseudonyms), it would have been a better use of time for me to start getting them interested in reading (also, reading aloud is beneficial at every grade level, and it usually catches student’s attention). I walked them through the activity one step at a time, walking from one table to the next holding my model and watching to make sure that at least one person at each table started in the correct direction before walking to the next table. Incidentally, only three people made theirs “incorrectly” and it was because they jumped ahead. I had no problem with that, given that what they ended up with will work just as well as what I was aiming for. Parts to change? Again, always have something else planned. Other changes? 1) making a more clear explanation of “nom de plume” so that students understand that the reason to have one is to make sure that they aren’t uncomfortable sharing their poetry (most of them started shouting out their fake names immediately, which told me that I had not made it clear that I was letting them create a fake name for the purpose of the poetry evaluation at the end, where they would have to share what they wrote—I know that people often feel very uncomfortable about writing poems); 2) I would consider using a longer pre-assessment. The reason I did not use a longer pre-assessment in this case is that the students have already taken 7 days of tests since the start of the semester. I think that the consistent failure (taking tests for things you have not yet learned) creates a negative attitude and causes students to not try as hard (some do not even bother reading the questions—they simply write “IDK”—which is a waste of everyone’s time, in my opinion). Also, I think I was just as tired of the tests as they were since I’d been sitting through every class period of tests.
But I digress.
The pre-assessment showed me, however, that my initial goals needed to change. I had originally been simply planning to concentrate on teaching the students figurative devices, symbolism, and tone, but it turns out that the students are perfectly competent in these areas, having had these things drilled down their throats since 5th or 6th grade. What they are unable to do, however, is make explicit references to the text to show how they know what they know. They were also unable to read beyond the literal meaning of the metaphor in the poem that I used for the assessment. I attempted to change my lessons that night, staying up quite late, but the results of my next day activity revealed that the students had not completely understood what I was trying to teach (I was attempting a modified “close reading” exercise, which I can’t really explain without drawing it by hand). Thusly, what I would change in the future is: 1) I would make sure to not go over my 10-12 minute limit for the mini lesson at the beginning of class and 2) I would break the activity into 2 parts so that it would not be so difficult to understand. I did try guiding the students through one poem as an example, but I believe half of the students were not listening.
Therefore, the final thing I am going to try my hand at changing is “how” I teach the lesson. First, I have decreased the difficulty of the activity so that it should fit more easily into a 45 minute time frame (I only have 10 lessons in all, can’t go about wasting time). This will not only mean that the assignment is more likely to be completed but also means that it shouldn’t take me 25 minutes to explain it. Second, I will not be using technology with which I am still unfamiliar—this should help decrease my personal stress and help create a more calm atmosphere (students can really sense nervousness, I discovered). Moreover, currently, the students desks are grouped, and I find myself talking to their backs for half of the lesson—or constantly asking them to turn around. It is not my classroom, or I would shift those desks around to ALWAYS be facing the front. Instead, I have purchased a white-board and I will bring the students to the back area of the classroom to sit around me on the floor. Admittedly, there is not very much room in the back (there are just as many students as desks), but this method should guarantee that I can see every students face and will not be shouting across the room to people who are in the back. I believe that my stress level will decrease (students not having their backs to me, me not feeling like I am shouting) will result in an increase in my ability to pay attention to the students faces to make sure they are listening and comprehending. Lastly, I am going to try out a “quiet” prompt to see if it helps me quiet down the students in a more timely fashion. The code word is “high five” and my sister (who is also a teacher) advises me to say it in a normal tone of voice and assures me that students will catch on quickly and will quiet down without you having to shout over them. I believe her, of course, because I happen to have the most intelligent and wise sisters in the entire universe.
I will be trying this tomorrow, and will determine whether the strategy is successful or not. I am sure you (the only person reading this Blog other than myself) are greatly eager to hear an update. (hah!)
;)
Thursday, October 13, 2011
Warm-ups in Math Education
Interviewer (looks at Sarah over her glasses): “Based on your research and personal philosophy, what is the purpose of warm-ups in your classroom?”
Sarah (taps her lip thoughfully before replying, then leans forward a touch): "Funny you should ask, madam. Indeed, using warm-ups at the beginning of a class period are useful for a number of reasons. For one, having students work on some problems as soon as they enter class gives the teacher a few minutes in which to take roll and complete other “housekeeping” duties. This is doubly beneficial, because rather than talking and not settling down, the students are almost immediately engaged (in other words, none of their time is wasted) and the teacher will be more quickly able to move onto the lesson for the day.
Moreover, warm-ups are appropriate for daily classwork because they are designed to meet at least one of the following targets: activate prior knowledge, review material from the day before (repeat and reinforce learning), introduce new material, check for understanding or lack thereof, and/or get students ready for jumping into the next set of activities. An activity, for instance, that references a concept that students should have learned the previous year, will ensure that students are better able to remember it (we “learn” through repetition) and will help the teacher check for any instances of lack of knowledge (so that he/she can scaffold those students who are lacking in an area). An activity that reviews material from the day before creates a sense of continuity from one day to the next and ensures that students are less likely to forget material from lack of exposure to it. Also, students have had the night to process new information overnight and are better able to tackle any misunderstandings. Because the work time on warm-ups is short, it helps get students settled into the correct frame of mind for beginning the next lesson or activity or for getting back into a lesson that has spilled over from the day before—in other words, it makes students think about math before listening to the teacher lecture again.
(brief pause, as though considering whether to say more)
However, I do argue that the most important of the above stated reasons is the one regarding repetition and reinforcement. We cannot expect students to internalize new knowledge in one day. Our brains need time to process and store that information, but if it is not “activated” within a short period of time, the likelihood of retaining that knowledge is greatly lessened. Not only for their own general benefit, but also for passing tests, this repetition is the key to the students’ success. Students must be able to remember things that they were taught at the beginning of a semester when they are taking tests, and if the teacher was unkind enough only to teach it once and never reference it again, it is quite possible that a high number of students will not recall that information. If I had only spent one day learning the alphabet when I was a child, it would be unlikely that, four months hence, I could tell you it in its entirety. It would even be possible that I forgot all of it. By extension, we can easily assume that most children will not run home after math or science class and eagerly do problems for entertainment, so we have to address all learning as it happens in the classroom. As a result, repetition and reinforcement are the primary reasons for having warm-ups in a classroom to begin with.
Sarah (taps her lip thoughfully before replying, then leans forward a touch): "Funny you should ask, madam. Indeed, using warm-ups at the beginning of a class period are useful for a number of reasons. For one, having students work on some problems as soon as they enter class gives the teacher a few minutes in which to take roll and complete other “housekeeping” duties. This is doubly beneficial, because rather than talking and not settling down, the students are almost immediately engaged (in other words, none of their time is wasted) and the teacher will be more quickly able to move onto the lesson for the day.
Moreover, warm-ups are appropriate for daily classwork because they are designed to meet at least one of the following targets: activate prior knowledge, review material from the day before (repeat and reinforce learning), introduce new material, check for understanding or lack thereof, and/or get students ready for jumping into the next set of activities. An activity, for instance, that references a concept that students should have learned the previous year, will ensure that students are better able to remember it (we “learn” through repetition) and will help the teacher check for any instances of lack of knowledge (so that he/she can scaffold those students who are lacking in an area). An activity that reviews material from the day before creates a sense of continuity from one day to the next and ensures that students are less likely to forget material from lack of exposure to it. Also, students have had the night to process new information overnight and are better able to tackle any misunderstandings. Because the work time on warm-ups is short, it helps get students settled into the correct frame of mind for beginning the next lesson or activity or for getting back into a lesson that has spilled over from the day before—in other words, it makes students think about math before listening to the teacher lecture again.
(brief pause, as though considering whether to say more)
However, I do argue that the most important of the above stated reasons is the one regarding repetition and reinforcement. We cannot expect students to internalize new knowledge in one day. Our brains need time to process and store that information, but if it is not “activated” within a short period of time, the likelihood of retaining that knowledge is greatly lessened. Not only for their own general benefit, but also for passing tests, this repetition is the key to the students’ success. Students must be able to remember things that they were taught at the beginning of a semester when they are taking tests, and if the teacher was unkind enough only to teach it once and never reference it again, it is quite possible that a high number of students will not recall that information. If I had only spent one day learning the alphabet when I was a child, it would be unlikely that, four months hence, I could tell you it in its entirety. It would even be possible that I forgot all of it. By extension, we can easily assume that most children will not run home after math or science class and eagerly do problems for entertainment, so we have to address all learning as it happens in the classroom. As a result, repetition and reinforcement are the primary reasons for having warm-ups in a classroom to begin with.
Monday, October 3, 2011
Khan Academy
The delightful and intelligent Salman Khan, the creative mind behind “Khan Academy,” has become a fairly powerful force in some classrooms. Working as a hedge-fund analyst (and yes, I had to look up that job), Khan evidently generated his first Youtube videos for his cousins, to sort of supplement their learning as he was tutoring them remotely. He was surprised when they told him that they really preferred the videos over listening to him in person, and was more surprised when other people—YouTube viewers—started making comments about how well they understood new concepts simply from watching his videos. For them, it was easier to view these clips online and in the privacy of their own home. Teachers said they were using it in classrooms, in place of homework. The feedback he (Khan) was getting for his videos prompted him to create Khan Academy, the online video experience. The general idea now? To create a global classroom.
What is great about it? You can pause, rewind, watch it again at a later time, and—and this is key—if you fall asleep, your teacher isn’t there to tap you on the back or smack a ruler on your desk. That is, you can take care of your own learning in your own way. Maybe you have to watch it ten times, but at least you can still get it without having to ask questions (which might embarrass a student). You don’t have to put on a face and pretend that you understand it all.
The other benefit? Khan suggests that it can be used to “humanize” the classroom. To make it so that the students watch the lectures at home (and can watch it multiple times) and then will get to spend the class time working together, rather than having to work alone and silently.
Could Khan Academy do something for me for language arts???
Main problem? Computer access AND technology problems! One of the complaints that I have heard from teachers in my practicum school is that the technology is lagging and that when there is a problem, it takes too long to fix. “We need a technology person!” they exclaim. When the teachers are using computers that are running on a system that is 10 years old, you probably are not going to see an abundance of other computers that are running well enough to maintain a computerized classroom experience. But can you get around that? Somewhat—at least at the high school level. If a teacher were to assign the Khan Academy videos as homework, then class time (as he suggested) could be centered around focusing on one-on-one instruction. The likelihood that students at a low-income middle school will be able to access computers is much lower, however, than the likelihood around any high school (even a low-income one) because mobility is greatly increased in the upper grades (due to relaxation of parental rules and students reaching the legal age to drive).
I believe I suddenly just realized that Khan is talking about something that in Language Arts is called the workshop model. Well, more like a modified workshop model.
What is great about it? You can pause, rewind, watch it again at a later time, and—and this is key—if you fall asleep, your teacher isn’t there to tap you on the back or smack a ruler on your desk. That is, you can take care of your own learning in your own way. Maybe you have to watch it ten times, but at least you can still get it without having to ask questions (which might embarrass a student). You don’t have to put on a face and pretend that you understand it all.
The other benefit? Khan suggests that it can be used to “humanize” the classroom. To make it so that the students watch the lectures at home (and can watch it multiple times) and then will get to spend the class time working together, rather than having to work alone and silently.
Could Khan Academy do something for me for language arts???
Main problem? Computer access AND technology problems! One of the complaints that I have heard from teachers in my practicum school is that the technology is lagging and that when there is a problem, it takes too long to fix. “We need a technology person!” they exclaim. When the teachers are using computers that are running on a system that is 10 years old, you probably are not going to see an abundance of other computers that are running well enough to maintain a computerized classroom experience. But can you get around that? Somewhat—at least at the high school level. If a teacher were to assign the Khan Academy videos as homework, then class time (as he suggested) could be centered around focusing on one-on-one instruction. The likelihood that students at a low-income middle school will be able to access computers is much lower, however, than the likelihood around any high school (even a low-income one) because mobility is greatly increased in the upper grades (due to relaxation of parental rules and students reaching the legal age to drive).
I believe I suddenly just realized that Khan is talking about something that in Language Arts is called the workshop model. Well, more like a modified workshop model.
Appropriate Use of Technology
Khan Academy Videos
• Probability: Part 1, Part 2, Part 3 . . . Part 6 (I would not go as far as Parts 7 or 8 for middle school students as I believe Bayes Thrm. would simply drive myself and them to tears)
1. Part 1—simply introduces probability and explains how we can calculate the likelihood of predictable, equally likely events, such as flipping a “fair-sided” coin.
2. Part 2—explains the use of the probability tree for figuring out the “fair sided coin” problems (what is the likelihood of getting a heads out of 8 throws…)
3. Part 3—uses another event, free-throw percentages, to explain the concept
4. Part 4—more on free-throws
5. Part 5—using die (monopoly)
6. Part 6—an introduction to conditional probability (at which point I began to get lost; also, I ran out of time).
• What math does it teach or reinforce? Well, the obvious answer is “probability.” However, what it mainly covers is the probability of mutually exclusive events. These outcome of the event is not dependent on the outcome of the previous event (assumes that probabilities do not decrease or increase over time/situation). This type of problem keeps the math calculations very simple, as well as the necessary charts and equations for figuring out the answer.
• Is it effective? Although it was effective for me, I am not certain it was effective for all viewers. If you scrolled down underneath each video, you could see a long list of “questions” that were posted by viewers. Now, if all persons making “comments” or posting “questions” actually watched the video completely through (and stopped to re-watch parts he/she did not completely understand), then it would be fair to say that the videos are ineffective. However, if all persons only partly watched, or were more interested in using the site as a forum for getting their math homework done, then we cannot conclude that the videos were ineffective (rather, only that the viewers lacked the proper motivation to view the videos in their entirety). I felt that if you were to watch the first four videos in a row, you would have a fairly good idea of how probability works (at least for these simple equations with no external, unpredictable factors). You (a middle school student) could go from those videos to your math book and start doing those “picking a blue marble out of a bag of marbles” questions. One video alone, perhaps not entirely effective.
• Video instruction offers the ability to watch and re-watch a lesson. Also, a person who is watching a lesson online has the ability to stop a video and look for external (not in the lesson) information to supplement the material. That is, if Khan says “scenario” and you have no idea what he is talking about, you can quickly go Google the word, then come back to the lesson. It is the same information that you might receive in a classroom, only you have the option of watching it in the privacy of your own home. Whether or not there are fewer external distractions is another question (at school you have your friends to distract you, at home you have the television, the other websites online, music, etc). The video instruction is also good for students who are auditory learners or students with low proficiency in reading.
• Are there other ways to teach or reinforce this same content? I would more or less view these particular videos as supplementary. Khan suggested that he had teachers who said they would assign the videos as homework, or as a prelude to what goes on in the class, which is probably the best approach to using these videos (in my opinion). Anything done in the classroom can reinforce the videos. Students who understand the videos get to move forward, while students who did not understand them (or let’s be honest, did not watch them) get to have more of that traditional classroom instruction.
• If I were to teach the lesson, would I change anything? Did I mention the first video I watched was an Algebra II video involving probability? Sure enough, it was one of those tired old marble in the bag problems. Who on earth cares about their chance of getting a red marble? Do kids even know what marbles are anymore? I would try my best to find ways to make the problems relate to life outside of math problems written 30 years ago. Secondly, I notice that the videos do not involve any reading. This is not representative of what students will see in their books or on their tests; they need to know how to READ problems in order to figure them out. This is why the Khan videos are supplementary (sort of like a self-help book, shouldn’t be your only and primary source). So what might I do, in addition to using the class textbook and Khan website? I would write one or two probability problems of my own that are more exciting. Such as being stranded on a desolate island and having to draw straws to decide who is going to be sacrificed to the volcano gods to ensure that the whole island doesn’t blow up. This way, kids get in some reading, and even if the problem is not entirely realistic, at least it is interested enough to keep students from falling asleep (in theory, of course).
• Another quick note—this particular set of videos (the ones I mention above) might not be particularly practical for use with a new second language learner. Khan uses some terms that would need clarifying (scenarios, mutually exclusive events, etc.) in a classroom with a large number of ELs. As there are no visual written instructions/words, an EL who is watching the video might not even be able to pause it and look up the parts they do not understand because they might not know how to spell it. There are also notations that Khan uses that might be confusing to students who are learning probability for the first time. A teacher who wanted to use these videos in the classroom would need to make sure to gauge the language needs and levels of the students first.
• Also, the set I have chosen above does not really cover the standard that to me was the most important—the one involving the collection and analysis of data (7.SP.6: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency . . .). In a classroom, you would want to have the students perform some “lab” operations to observe and collect the data before making predictions.
• Probability: Part 1, Part 2, Part 3 . . . Part 6 (I would not go as far as Parts 7 or 8 for middle school students as I believe Bayes Thrm. would simply drive myself and them to tears)
1. Part 1—simply introduces probability and explains how we can calculate the likelihood of predictable, equally likely events, such as flipping a “fair-sided” coin.
2. Part 2—explains the use of the probability tree for figuring out the “fair sided coin” problems (what is the likelihood of getting a heads out of 8 throws…)
3. Part 3—uses another event, free-throw percentages, to explain the concept
4. Part 4—more on free-throws
5. Part 5—using die (monopoly)
6. Part 6—an introduction to conditional probability (at which point I began to get lost; also, I ran out of time).
• What math does it teach or reinforce? Well, the obvious answer is “probability.” However, what it mainly covers is the probability of mutually exclusive events. These outcome of the event is not dependent on the outcome of the previous event (assumes that probabilities do not decrease or increase over time/situation). This type of problem keeps the math calculations very simple, as well as the necessary charts and equations for figuring out the answer.
• Is it effective? Although it was effective for me, I am not certain it was effective for all viewers. If you scrolled down underneath each video, you could see a long list of “questions” that were posted by viewers. Now, if all persons making “comments” or posting “questions” actually watched the video completely through (and stopped to re-watch parts he/she did not completely understand), then it would be fair to say that the videos are ineffective. However, if all persons only partly watched, or were more interested in using the site as a forum for getting their math homework done, then we cannot conclude that the videos were ineffective (rather, only that the viewers lacked the proper motivation to view the videos in their entirety). I felt that if you were to watch the first four videos in a row, you would have a fairly good idea of how probability works (at least for these simple equations with no external, unpredictable factors). You (a middle school student) could go from those videos to your math book and start doing those “picking a blue marble out of a bag of marbles” questions. One video alone, perhaps not entirely effective.
• Video instruction offers the ability to watch and re-watch a lesson. Also, a person who is watching a lesson online has the ability to stop a video and look for external (not in the lesson) information to supplement the material. That is, if Khan says “scenario” and you have no idea what he is talking about, you can quickly go Google the word, then come back to the lesson. It is the same information that you might receive in a classroom, only you have the option of watching it in the privacy of your own home. Whether or not there are fewer external distractions is another question (at school you have your friends to distract you, at home you have the television, the other websites online, music, etc). The video instruction is also good for students who are auditory learners or students with low proficiency in reading.
• Are there other ways to teach or reinforce this same content? I would more or less view these particular videos as supplementary. Khan suggested that he had teachers who said they would assign the videos as homework, or as a prelude to what goes on in the class, which is probably the best approach to using these videos (in my opinion). Anything done in the classroom can reinforce the videos. Students who understand the videos get to move forward, while students who did not understand them (or let’s be honest, did not watch them) get to have more of that traditional classroom instruction.
• If I were to teach the lesson, would I change anything? Did I mention the first video I watched was an Algebra II video involving probability? Sure enough, it was one of those tired old marble in the bag problems. Who on earth cares about their chance of getting a red marble? Do kids even know what marbles are anymore? I would try my best to find ways to make the problems relate to life outside of math problems written 30 years ago. Secondly, I notice that the videos do not involve any reading. This is not representative of what students will see in their books or on their tests; they need to know how to READ problems in order to figure them out. This is why the Khan videos are supplementary (sort of like a self-help book, shouldn’t be your only and primary source). So what might I do, in addition to using the class textbook and Khan website? I would write one or two probability problems of my own that are more exciting. Such as being stranded on a desolate island and having to draw straws to decide who is going to be sacrificed to the volcano gods to ensure that the whole island doesn’t blow up. This way, kids get in some reading, and even if the problem is not entirely realistic, at least it is interested enough to keep students from falling asleep (in theory, of course).
• Another quick note—this particular set of videos (the ones I mention above) might not be particularly practical for use with a new second language learner. Khan uses some terms that would need clarifying (scenarios, mutually exclusive events, etc.) in a classroom with a large number of ELs. As there are no visual written instructions/words, an EL who is watching the video might not even be able to pause it and look up the parts they do not understand because they might not know how to spell it. There are also notations that Khan uses that might be confusing to students who are learning probability for the first time. A teacher who wanted to use these videos in the classroom would need to make sure to gauge the language needs and levels of the students first.
• Also, the set I have chosen above does not really cover the standard that to me was the most important—the one involving the collection and analysis of data (7.SP.6: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency . . .). In a classroom, you would want to have the students perform some “lab” operations to observe and collect the data before making predictions.
Thursday, September 29, 2011
Standards, Standards, Everywhere (apparently)
• compute probabilities for simple compound events, using such methods as organized lists, tree diagrams, and area models (NCTM)
• Compute and compare the chances of various outcomes, including two-stage outcomes (CMP)
• (7.SP.6. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.)
Initially, I made the mistake of matching the top two standards with the last standard. The following is my comparison:
The three standards converge on probability and its computation. However, they all vary on the breadth of strategies involved. The CMP standard is, by far, the most vague and seems to really only involve the computations themselves, with the added bonus of learning to “compare.” NCTM incorporates the task of reading/interpreting graphs and lists to the task of making those computations of probability. In contrast, 7.SP.8 is focused on data collection, observation, and predicting. Indeed, the computations/approximations for probability seem to be secondary to the other tasks and strategies in this particular standard (7.SP.8). the complexity of the tasks should be greater if they are able to meet that last standard—as it is intended to promote higher-order thinking skills (prediction) and practical skills (those that are applicable to life outside of the math classroom). Students whose teachers focus their curriculum around 7.SP.8 should be engaged in steps that are known as “scientific methods. The said standard, I argue, was written with specificity so that there was less of a chance of students spending all of their math class sitting at their desks, staring at books and copying numbers.
Surprisingly, just as I was about to post my thoughts for this week’s discussion, I noticed that I had failed to notice one standard—one that matches the first two more closely.
• 7.SP.8. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
Well, there you have it. The first standard (compute probability for simple compound events using lists, etc) and the above one (7.SP.8) really only differ on the event in question (be it the compound event or be it the oxymoron—a simple compound event?). The second standard (CMP) is a mix of the other two; it suggests computing probability for various outcomes, including two-stage outcomes—otherwise known as that compound event as seen in 7.SP.8—and simple compound events. Of course, this is not to say that they “blend harmoniously.” They just happen to all be the same thing, worded a bit differently every time. The good news? If you do some probability questions in your textbooks, you are bound to have met all three standards.
• Compute and compare the chances of various outcomes, including two-stage outcomes (CMP)
• (7.SP.6. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.)
Initially, I made the mistake of matching the top two standards with the last standard. The following is my comparison:
The three standards converge on probability and its computation. However, they all vary on the breadth of strategies involved. The CMP standard is, by far, the most vague and seems to really only involve the computations themselves, with the added bonus of learning to “compare.” NCTM incorporates the task of reading/interpreting graphs and lists to the task of making those computations of probability. In contrast, 7.SP.8 is focused on data collection, observation, and predicting. Indeed, the computations/approximations for probability seem to be secondary to the other tasks and strategies in this particular standard (7.SP.8). the complexity of the tasks should be greater if they are able to meet that last standard—as it is intended to promote higher-order thinking skills (prediction) and practical skills (those that are applicable to life outside of the math classroom). Students whose teachers focus their curriculum around 7.SP.8 should be engaged in steps that are known as “scientific methods. The said standard, I argue, was written with specificity so that there was less of a chance of students spending all of their math class sitting at their desks, staring at books and copying numbers.
Surprisingly, just as I was about to post my thoughts for this week’s discussion, I noticed that I had failed to notice one standard—one that matches the first two more closely.
• 7.SP.8. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
Well, there you have it. The first standard (compute probability for simple compound events using lists, etc) and the above one (7.SP.8) really only differ on the event in question (be it the compound event or be it the oxymoron—a simple compound event?). The second standard (CMP) is a mix of the other two; it suggests computing probability for various outcomes, including two-stage outcomes—otherwise known as that compound event as seen in 7.SP.8—and simple compound events. Of course, this is not to say that they “blend harmoniously.” They just happen to all be the same thing, worded a bit differently every time. The good news? If you do some probability questions in your textbooks, you are bound to have met all three standards.
Thursday, September 15, 2011
Best Practices Research
So, we were to discuss “best practices” in education this last week. Here is the list I compiled in class, to start.
Differentiated assessment
Differentiated instruction
Teaching higher-order thinking skills
Using technology
Inclusion
Diversity
Smaller class sizes, etc.
Workshop methods (which is the “in” thing for language arts instruction, currently)
Student-centered learning (as opposed to teacher-focused instruction)
Cooperation
Real life problems and practical applications
Informal assessments
Technology
Technology
Technology
Basically, “best practices” are those that are (pardon my saying it) those that are in vogue. They will vary over time and population and region. Currently, Willamette is highly interested in educating the their “teachers” to be sensitive to the needs of a diverse population who are willing and eager to implement technological activities in the traditional classroom. We (the students of this program) are encouraged to think that it is not only ideal but necessary to use technology whenever possible. This line of thinking has evolved for a number of reasons, I am sure. One is that students seem to like technology. Twenty years ago, I was delighted to play Oregon Trail and Number Munchers. A mere two decades later, we want to use “smart boards” instead of chalkboards or whiteboards and have finally stopped telling kids that they need to learn cursive because they will use it in college.
But what does that mean in terms of “best practices?” Is it because we think that students learn better when they are able to use technology to access the material? Or is it primarily because we recognize that what we have been teaching has become antiquated and that we are doing a disservice to students to teach them things that they will ONLY use as adults if they continue to be students. The five paragraph essay, for example—only necessary in the academic world. Knowing “point-of-view,” probably only necessary for literary positions. And probability (hah!) is apparently only applicable in gambling and in business and economics (in terms of how a company might use it to allocate their merchandise, or so one of my classmates claims), which means that you could simply learn those calculations when you were trained for that job. If “technology” is to be a “best practice,” then it must be something that is not only useful to students in the long scheme of things, but it has to improve their understanding of some of the things that we deem “necessary” to a public education. If our goal in public education is to make sure that students are knowledgeable in a number of areas (math, science, reading and writing, etc), then technology, as a practice, has to service those goals. Otherwise, it is time to change the practice or the goal.
“Best Practices” in any field (or in terms of academics, the content areas) are widely contentious, too. I remember in kindergarten that I was taken out of the classroom to do activities in another room by myself while the rest of the class had to learn phonics, using that “hooked on phonics” program. Obviously, that program, and others like it, are the sorts of practices that someone decided were the best for teaching students how to speak and read and write. Thus the reason “basal readers” came into existence. Someone thought it was the best way to teach literature and reading. There are still some who stand by it. Yet there are others (and more of them than the previous) who think that basal readers are boring and that they stunt the growth of most of the students. They think that learning phonics and spelling and grammar in isolation (as opposed to within some sort of meaningful context) results in nothing but disassociation and stagnation. What are their perceived “best” practices? Self-selected texts, workshop settings for writing and discussion, journal writing, and focus on strategies for self-correction and understanding rather than rote memorization. I put myself in that second category, if you so desire to know.
I am not supremely knowledgeable on changes in trends in mathematics (in terms of how it is taught). I admit that I think it looks about the same in junior high school as it does in college, at least in the classes that I have taken. That means that even over time, there are a few ideas that continue to remain predominant in the strategies employed to teach math. One is that calculations are important. Students must not only be able to do them by hand, but they must show all their work. Second is that there is some sort of “logical” order to learning it. You have to learn one thing before the other. Given all the other changes in the world (my dad used a slide rule to do calculus, I used an electronic calculator) within a 40 year period, why is it that we assume that our methodology and the “order” of learning should stay the same? People know, for instance, that if you speak to babies as if they are idiots (otherwise known as “baby talk”) then when they start speaking, they will often mimic those patterns—as if they are incapable of speaking like any adult human being. Yet, if you speak to them as if they are equals, they will often mimic the same speech pattern. Perhaps they will not be as linguistically aware (their vocabulary is still developing, as well as their competence in various contexts) as an adult, but at least you can understand what they are saying.
I don’t mean to suggest, of course, that it would be a terrific idea to stop teaching arithmetic, or that we can simply just teach whatever we feel like because there is no logical order to teaching math. Instead, it means that I think that we need to work with the system to figure out what really “has” to come first. Elementary students can understand some basic ideas of physics, so why not assume that there are other “advanced” ideas that we can throw at them and see if they stick? I would like to think, too, that we could stop teaching math as though it were an isolated task. If there are practical, realistic, real-life applications for the things that we are teaching students, why not let them know what they are? Why do we first assume that it is “too much” for them to handle at a specific point in time? I can tell you with certainty that I know very few practical applications for the math that I spent my years learning. Adding and subtracting and multiplying, of course, are easily applicable to life. Being able to calculate percentages is important (for financial applications, saving money). But I’ll bring up “probability” yet again (sorry, readers). I spent about seven months scratching my head while attempting to think of a useful (and realistic) application for probability. No, I’m sorry, I have never needed to figure out the probability of me choosing a red shirt out of my drawer at random. I have never needed to figure out my odds in a casino. When someone told me that car dealerships/manufacturers use probability to figure out how many cars to send to various markets, I was flabbergasted. Why not teach that? Sure, kids don’t necessarily yet care about cars when they are in middle school, but at least they will know that there is a useful purpose for having to calculate exact numbers for probability. Because otherwise, especially for those of us who do not have numbers dancing in our heads, probability is more or less just a “vague idea of the odds”—not a precise calculation.
I apologize to the classmate who I paraphrase above, as I do not believe I ever asked your name while we were in class having this discussion about probability. I hope I understood you correctly, and I still secretly want to ask you to show me some examples of how it works, because I am pretty impressed that probability could apply to something real.
Blogging—the new “best practice.”
Differentiated assessment
Differentiated instruction
Teaching higher-order thinking skills
Using technology
Inclusion
Diversity
Smaller class sizes, etc.
Workshop methods (which is the “in” thing for language arts instruction, currently)
Student-centered learning (as opposed to teacher-focused instruction)
Cooperation
Real life problems and practical applications
Informal assessments
Technology
Technology
Technology
Basically, “best practices” are those that are (pardon my saying it) those that are in vogue. They will vary over time and population and region. Currently, Willamette is highly interested in educating the their “teachers” to be sensitive to the needs of a diverse population who are willing and eager to implement technological activities in the traditional classroom. We (the students of this program) are encouraged to think that it is not only ideal but necessary to use technology whenever possible. This line of thinking has evolved for a number of reasons, I am sure. One is that students seem to like technology. Twenty years ago, I was delighted to play Oregon Trail and Number Munchers. A mere two decades later, we want to use “smart boards” instead of chalkboards or whiteboards and have finally stopped telling kids that they need to learn cursive because they will use it in college.
But what does that mean in terms of “best practices?” Is it because we think that students learn better when they are able to use technology to access the material? Or is it primarily because we recognize that what we have been teaching has become antiquated and that we are doing a disservice to students to teach them things that they will ONLY use as adults if they continue to be students. The five paragraph essay, for example—only necessary in the academic world. Knowing “point-of-view,” probably only necessary for literary positions. And probability (hah!) is apparently only applicable in gambling and in business and economics (in terms of how a company might use it to allocate their merchandise, or so one of my classmates claims), which means that you could simply learn those calculations when you were trained for that job. If “technology” is to be a “best practice,” then it must be something that is not only useful to students in the long scheme of things, but it has to improve their understanding of some of the things that we deem “necessary” to a public education. If our goal in public education is to make sure that students are knowledgeable in a number of areas (math, science, reading and writing, etc), then technology, as a practice, has to service those goals. Otherwise, it is time to change the practice or the goal.
“Best Practices” in any field (or in terms of academics, the content areas) are widely contentious, too. I remember in kindergarten that I was taken out of the classroom to do activities in another room by myself while the rest of the class had to learn phonics, using that “hooked on phonics” program. Obviously, that program, and others like it, are the sorts of practices that someone decided were the best for teaching students how to speak and read and write. Thus the reason “basal readers” came into existence. Someone thought it was the best way to teach literature and reading. There are still some who stand by it. Yet there are others (and more of them than the previous) who think that basal readers are boring and that they stunt the growth of most of the students. They think that learning phonics and spelling and grammar in isolation (as opposed to within some sort of meaningful context) results in nothing but disassociation and stagnation. What are their perceived “best” practices? Self-selected texts, workshop settings for writing and discussion, journal writing, and focus on strategies for self-correction and understanding rather than rote memorization. I put myself in that second category, if you so desire to know.
I am not supremely knowledgeable on changes in trends in mathematics (in terms of how it is taught). I admit that I think it looks about the same in junior high school as it does in college, at least in the classes that I have taken. That means that even over time, there are a few ideas that continue to remain predominant in the strategies employed to teach math. One is that calculations are important. Students must not only be able to do them by hand, but they must show all their work. Second is that there is some sort of “logical” order to learning it. You have to learn one thing before the other. Given all the other changes in the world (my dad used a slide rule to do calculus, I used an electronic calculator) within a 40 year period, why is it that we assume that our methodology and the “order” of learning should stay the same? People know, for instance, that if you speak to babies as if they are idiots (otherwise known as “baby talk”) then when they start speaking, they will often mimic those patterns—as if they are incapable of speaking like any adult human being. Yet, if you speak to them as if they are equals, they will often mimic the same speech pattern. Perhaps they will not be as linguistically aware (their vocabulary is still developing, as well as their competence in various contexts) as an adult, but at least you can understand what they are saying.
I don’t mean to suggest, of course, that it would be a terrific idea to stop teaching arithmetic, or that we can simply just teach whatever we feel like because there is no logical order to teaching math. Instead, it means that I think that we need to work with the system to figure out what really “has” to come first. Elementary students can understand some basic ideas of physics, so why not assume that there are other “advanced” ideas that we can throw at them and see if they stick? I would like to think, too, that we could stop teaching math as though it were an isolated task. If there are practical, realistic, real-life applications for the things that we are teaching students, why not let them know what they are? Why do we first assume that it is “too much” for them to handle at a specific point in time? I can tell you with certainty that I know very few practical applications for the math that I spent my years learning. Adding and subtracting and multiplying, of course, are easily applicable to life. Being able to calculate percentages is important (for financial applications, saving money). But I’ll bring up “probability” yet again (sorry, readers). I spent about seven months scratching my head while attempting to think of a useful (and realistic) application for probability. No, I’m sorry, I have never needed to figure out the probability of me choosing a red shirt out of my drawer at random. I have never needed to figure out my odds in a casino. When someone told me that car dealerships/manufacturers use probability to figure out how many cars to send to various markets, I was flabbergasted. Why not teach that? Sure, kids don’t necessarily yet care about cars when they are in middle school, but at least they will know that there is a useful purpose for having to calculate exact numbers for probability. Because otherwise, especially for those of us who do not have numbers dancing in our heads, probability is more or less just a “vague idea of the odds”—not a precise calculation.
I apologize to the classmate who I paraphrase above, as I do not believe I ever asked your name while we were in class having this discussion about probability. I hope I understood you correctly, and I still secretly want to ask you to show me some examples of how it works, because I am pretty impressed that probability could apply to something real.
Blogging—the new “best practice.”
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