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).

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.