CMP-Inquiry Middle School Interview

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

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.

2.   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? 

• 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.
• About CMP and the inquiry approach and kids with low ability.  It is hard.  If you follow the grouping strategy of CMP then being very strategic in building the groups is important.  Most of the time, I try to put mixed groups together so kids can learn from each other.

1.   What is the role of homework (and accountability) in the CMP? ____

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.

2.   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? 

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.

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. 

Warm-ups in Math Education

Warm-ups are an important aspect in a math classroom. Warm-ups serve many functions, including getting students in a “math” frame of mind, reviewing material from previous lessons, reviewing basic skills such as fractions, percents, etc, review skills that may not be a normal part of everyday lessons such as OAKS testing preparation or use of calculators, or even pre-viewing or priming what you will be doing that day.  Warm-ups can also provide the teacher an opportunity to check for students pre-existing knowledge and/or misconceptions on the lesson that is being taught that day, so the teacher can gauge how fast or slow he/she needs to go and which topics and students need special attention.

I believe that warm ups should take under 10 minutes, especially in a 40 minute or 50 minute period system. I also believe that warm-ups should not be graded, but instead should be checked by a group discussion or calling on individual students.    

Appropriate Use of Technology

Since I could not find an activity that matched my standards area of measurement, I chose to review the Area Tool at www.illuminations.nctm.org. The area tool is an exploratory tool that can be used to track how the area changes given different side lengths in triangles, parallelograms, and trapezoids. It could also be used in a lesson on proportions and similar triangles and shapes. Unfortunately, because the angles and lengths are on a slider scale and there is no way of getting exact measurements, it would be very difficult to use this tool in a lesson on the Pythagorean Theorem or trigonometry.

While it does have limitations, the area tool does accomplish its main objective of determining how the base length and height of a figure affects its area very efficiently. Using this tool is much more efficient than drawing the figures out on graph paper. Students can instantly make connections between the areas instead of painstakingly graphing the figures out and running the risk of losing the information through the tediousness of the activity.

This same lesson could be taught using graph paper, plastic shapes, or other manipulatives. While these other methods would work, they do not provide the same efficiency that the area tool can. If I were designing this tool, I would include the option to input exact measurements and angles, and output angle measurements.

Standards, standards, everywhere

I chose to evaluate how the NCTM standard of “understanding relationships among units and convert from one unit to another within the same system” compares with a similar standard in the Common Core and CMP standards. For the most part all three standards cover essentially the same thing. However, there are several differences between the three standards.  One is that the Connected Math Project standards include conversion between customary and metric systems whereas the Common Core and NCTM standards keep the conversions within the same system. Another difference is the NCTM and CMP consider converting measurements a sixth through eighth grade skill where the Common Core standards place it in the fifth grade classroom. Lastly, the common core standards are the only ones that explicitly state that the skill must be implemented in multi-step, real world problems, which is surprising to me since that seems to be one of the main objectives of the Connected Math Projects standards. While the standards do not match up identically one to one, creating multi-step, real world measurement problems that include converting between customary and metric systems would easily cover all three sets of standards.