Inquiry and CMP Research

Guiding principles:

•     Both the big idea of the curriculum or unit are identified for the student as well as the underlying skills and concepts, so the student will know what they are learning and how it connects to what they have learned. 
•      It is made clear how the concepts the student is currently learning are connected to what the student has learned in the particular lesson, unit, grade, and how the concepts are connected to what the students have learned in previous grades.
•       The most effective way of learning math includes a process of investigation for the student, where they are actively exploring and solving an idea or problem
•       The explorations are purposefully in depth to support deeper understanding and memory by the students.
•       Part of making problems in depth is having students read and write problems in multiple representations—graphic, numeric, symbolic, and verbal, and to fluently move between these representations.
•       Calculators and computers have changed the way people think about and solve mathematical problems, and the curriculum reflects this transition.

   Comparison of CMP and direct instruction:

In direct instruction, the initial phase is a set, or hook, where the teacher’s goal is to introduce and interest the student in the material. In contrast, the initial phase of CMP is Launch, where the teacher helps the students understand the problem setting, the mathematical challenge, and the concept. In both methods, the teacher is introducing the lesson.

The main difference between the two methods is evident in the next sections. Typically in the direct instruction method, the teacher moves on to the instruction step of the lesson while the CMP method moves to the Explore step. In instruction, the teacher is instructing the class how to accomplish the goals of the lesson, and providing examples of the concept that is being covered while the students are listening to the instruction, answering questions that the teacher asks, and taking notes or following along either in groups or individually. In the Explore step of CMP, the students are presented with a problem and they gather data, share ideas, and look for patterns, while the teacher roams the class and helps individuals and groups.

The final stage of the CMP method more closely resembles the instruction phase of its counterpart. This is where the teacher helps guide the students to the goals of the lesson, clearing up areas of frustration along the way. In case some groups did not make it to the final product of the lesson, the teacher must also find a way to get everybody caught up. In direct instruction, the final activity also wraps up the lesson, and makes sure everybody is on the same page about what should have been learned.  

Anticipatory Set and Closure

Anticipatory Set

http://www.edulink.org/lessonplans/anticipa.htm

http://nataliemckinney.com/downloads/Madelyn_Hunter_Lesson_Cycle_-_Anticipatory_Set.pdf

The anticipatory set is in the opening of the lesson and provides the hook to motivate students to be interested in the lesson. It can also focus students attention on a specific topic, provide a connection to a past topic, and provide a preview for what the lesson is going to be about.  

The anticipatory set can also provide priming for the lesson. Priming is important because it “accelerates the understanding of concepts and gives the brain information to build into a more complex semantic structure or hierarchy later on.” (Jensen, 2005). Examples of an anticipatory set include provocative questions, review of the previous lesson, a story, or an intriguing statement or fact.

Jensen, Eric (2005) Teaching with the Brain and Mind ASCD: Danvers, MA

Closure

http://www.edulink.org/lessonplans/closure.htm

http://template.aea267.iowapages.org/lessonplan/

Closure is the last activity done in the class. As such, it helps organize student learning by letting them know that they have arrived at the end of the lesson. One of the main ideas behind closure is that it will bring the lesson into a coherent picture for students in order to eliminate confusion or frustration with the lesson. A good closure activity will often summarize the main ideas of the lesson to let students know what they have learned or should have learned from the lesson. Another goal of a closure activity is to help tie the current lesson with the next lesson if possible. In order to do this, let students know what key information from the current lesson they will be able to use in the next lesson.

Not only is closure helpful for students but it is also vital for the teacher. A good closure activity will tell the teacher if additional practice is needed, if parts of the lesson need to be re-taught, or if the teacher is able to move on to the next topic. The ability to use closure as a means for adjusting the lesson is critical in education, and has become increasingly more important as the transition is being made to standards based grading and graduation because ideally every students needs to understand every topic. Examples of closure activities include a survey or exit card, asking the students what they learned, or having the students write a reflection or application.

Practicum- Sharing a lesson

This is a lesson that I taught in an algebra 1 class today at McNary High School. The objective for the lesson was for the students to be able to write an equation, a chart, and a graph from a word problem. The students had already been doing this for the past two days, so I was pretty confident that they could complete the task quickly. After the warm-up, I broke up the lesson into 3 sections. In the first section I went over a group/class problem and checked for understanding by a combination of randomly calling on students to contribute and doing a thumb check. As usual, it was hard to get a good picture of understanding with the thumb count because there was limited student participation. However, I think I was able to keep most of the students tracking by calling random names.  

The second section was individual work on a problem like the one that I did with the class. During this section I tried to go around and answer questions for student who were struggling. During this section of the class I was bombarded by quite a few students who wanted to go to the restroom/get a drink of water/ etc. Also, the students who finished with the problem quickly were left wondering what to do next. On the positive side, I think the students who got the one-on-one attention understood the concept much better than they had the previous days. I was also checking to see how students were doing by glancing down at their papers. I think enough students are having difficulty with it that I may do another review problem with the same concepts for a warm-up tomorrow.

The third section was supposed to be a short amount of time for the students to do homework in class, but I didn’t set that expectation strong enough in the beginning of the class so once students were done with the in-class problem they decided it was time to talk and goof-off. In reflecting back this was the section that needed the most work. If I were to reteach this lesson, I would add more structure to the lesson and pulled the students’ attention back to me more. I think if I would have had a little bit more for the students to do in –class, and if I would done a better job of setting up the layout of the class in the beginning, this last section would have gone much smoother. Yesterday’s lesson went much smoother, but the students had quite a bit more to do, giving it more structure.