CMP - Inquiry based teaching interview

Interview with LK, 10/24/11

Interview Questions to address the following:

How does the CMP curriculum align with the national Common Core and NCTM standards?

It was picked because it does align. You can move the concepts around. For instance, Data Distribution is 7^th grade booklet but it is an 8^th grade concept for Oregon, so it fits our needs really well.

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?

We do starter activities and review concepts, but for the most part we just give these students a calculator. If they do not know how to add or subtract by the time they are in 8^th grade, we do not have enough time in the day to help these students master these skills. They will get too far behind the rest of the curriculum. We want them to focus on problem solving skills, not calculating skills.

What is the role of homework (and accountability) in the CMP? ___CMP Investigations compose of small-groups (pair-share, teamwork, cooperative learning).

Practice skills learned in class. Accountability is up to the teacher, but it is not part of the CMP. We are not required to assign homework.

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?

We use our protocols of turn and talk, go around, private think time, a and b partners, etc.

When students are working on problems I walk around and do selecting and sequencing. I also ask students to revoice either what I said or what another student said.

Warm-Ups in Math Education

In my research and experience, warm-ups are a very valuable component to a lesson as they provide an informal assessment of information that you would expect students to already know. Furthermore, it is actually like warming up the student's brains as their brains begin firing and re-kindling stored information so it can be used. In essence, it acts like a "grabber" to engage the students. The warm-up is generally most effective when the problems target skills that are required in order to complete the task on that day. Sometimes, these warm-ups can be geared toward skills required for passing OAKS and by reviewing them daily in these warm-up activities, they are getting extra repetition.

Traditionally, math warm-ups consisted of the teacher placing 5 problems on the board or overhead projector and the students privately work on each problem when the tardy bell rings. The teacher then goes over the answers and asks if there are any questions. With the new and improved teaching methods such as CMP and inquiry based teaching, it is possible that the warm-up activities consist of the teacher posing a question, the students thinking about it, then turning and talking to their partner or table group in a discussion. The class then discusses some of the answers the groups came up with. The students warm up their brains through active discussion and listening to their peers instead of the traditional "chalk and talk" method, which can be boring for students. When the students come up with the answers themselves, it gives them a greater sense of ownership and can increase motivation.

CMP vs. Inquiry Based Model research

The Connected Math Project (CMP) emphasizes inquiry and investigation which forces students to be more engaged in the curriculum. This models shows that there is more to mathematics than calculating answers and memorizing definitions or processes. The goal is to be able to solve a variety of problems, and therefore students needs to spend time solving problems that require "thinking, planning, reasoning, computing, and evaluating". Students will be able to make sense of what they are learning and will be able to retrieve the information better at a later time than if they were simply memorizing a definition or process. Information is also connected to prior knowledge so that students can better retrieve information.

"Tell me and I forget, show me and I remember, involve me and I understand." The last part is what inquiry based learning is about. Students become involved in questioning to gather information as they seek understanding. It involves developing experimental and analytical skills more than accumulating and memorizing facts and knowledge.

The CMP model is far from the traditional "chalk and talk" methods of teaching. In the traditional methods, the teacher answers most of the questions and tells students what they should know as they stand in front of the class and preach. The CMP model is more closely tied to the inquiry based model in that the teacher asks more thought-provoking questions and the students come up with answers. In essence, the teacher becomes more of a facilitator of discussions rather than the one doing the discussing. The class as a whole may agree or disagree as part of the learning process, which engages the students. Teachers have to learn to be comfortable with long wait times as students are thinking about what to say. This is important because if the teachers intervene too early, then the learning opportunity for the students is lost. Students are much more engaged and involved in the learning process in this environment than in traditional teaching methods.

Closure and Anticipatory Set

http://k6educators.about.com/od/lessonplanheadquarters/g/closure.htm
http://www.edulink.org/lessonplans/closure.htm
http://www.proteacher.net/discussions/showthread.php?t=197015

Closure: wrapping up, or summarizing a lesson plan while providing the context and "big idea."

Activities:

1) 3-2-1 method: Have the students write down 3 things they learned, 2 questions they have, and 1 thing they liked.

2) Have a class discussion where the students compare and contrast newly learned concepts with old concpets. How do the new concepts build off of the old concepts?

3) Either write down or discuss 3 whats: 1) What did we learn? 2) So What? and 3) Now What?




Anticipatory Set: informing the students of the lesson objective while activating their prior knowledge to lead into the lesson. A unit opener.

Activities
1) Start with a question and have the students use their thumbs to indicate their level of understanding. The question should be based on previous knowledge and the next unit.

2) Ask students if any of them think they might want to use their creative skills to build something in the future. Could they see themselves doing it for a job? Provide examples of jobs that use mathematics such as engineers, builders, contractors, etc. Then introduce the next concept and how it directly relates to those jobs.

3) Review what an equation is and how to solve a one-step equation with one variable. Give them private think time: What do you think you would do to solve this two-step equation with 2 variables, x and y?

http://k6educators.about.com/od/lessonplanheadquarters/g/anticipatoryset.htm
http://www.hope.edu/academic/education/wessman/2block/unit4/hunter2.htm
http://creatinglifelonglearners.com/?tag=anticipatory-set
http://www.lessonopoly.org/node/2690

Practicum - Sharing a Lesson

The lesson objective was to have students discover that the length and width of rectangles are inversely related in regard to a constant area. Students were expected to come up with 5 dimensions of rectangles with a constant area of 350. (Examples, 1 X 350, 2 x 175) Students created a table and then plotted these points on a graph. The end result was a curve that is symmetric about the line y = x.

Prior to assigning this problem, students were asked for the general formula for area of a rectangle (L x W = A). They also tried solving dimensions of rectangles with area of 24. Overall, the class had a good idea how to do this and there were hardly any questions. They came up with all possible dimensions using whole numbers. The "AHA!" moment did not come until later.

I assigned the problem and required that students work with their elbow partners. The only students who struggled with the problem had their general equation mixed up ( Some of them solved for W or L and had the area on the bottom instead of the top). I stopped the class, asked for everyone's attention, and cleared up the problem since more than a couple groups had done the same thing. I had to stop later to talk to the class about their graphs because several groups did not have incremental changes on their axes. Each line must go up by the same amount in order to draw the graph properly. Some students also connected their lines to the axes, which could never be true for dimensions of a rectangle. Neither dimension can ever be zero. This was our final discussion right before the bell rang. The student's attempts and failures allowed them to learn more about the concept of inverse relationships.

If I were to re-do this assignment, I would not have changed a thing. It is OK for the students to struggle and somewhat necessary for them to learn. If I gave them ALL of the answers upfront, I do not think they would feel the same sense of pride and ownership over their work when they figured out the right answer.