CMP-Inquiry Middle School Interview

I interviewed my practicum supervising teacher, Tracy Thornton at Parrish Middle School.


1) How does the CMP curriculum align with the national Common Core and NCTM standards?
a. Does not completely align with common core.
b. District goes and makes scope and sequence (when and what to teach according to standards) but have had to make modifications because not 100% aligned.

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?
a. Providing tools to be successful and on grade level math (multiplication tables, divisibility books, sentence starters, small group instruction and some calculator usage).
b. Don’t focus on the basics…look at what you need to know and how those basics will support the lesson. Example: can do and master PEMDAS without knowing the basic multiplication.

3) What is the role of homework (and accountability) in CMP?
a. Accountability is high. Homework is a necessity for the practice part. They get the inquiry in CMP, but not the practice.

4) 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)? On going assessment(s) and checking for understanding?
a. Print out group norms. Why is it important to do math in teams? What does cooperative group work look like?
b. No assigned roles (moderator, scribe) etc.
c. Spiral journals and having everyone write makes them accountable for the information.
d. If teacher randomly goes up to group and asks random person, all group members should know answer.
e. Weekly or other week quizzes also holds them accountable. Their grade relies on the work being done.

Inquiry & CMP Research

The Inquiry Based Learning Model is an instructional method that focuses on active learning and much interaction where progress is assessed by how well students develop experimental and analytical skills rather than how much knowledge they possess. This is quite different from simply making students memorize information.

CMP to seems to be more inquiry based as opposed to the traditional direct instruction. The guiding principles for CMP are:

-coherence; it builds and connects from investigation to investigation, unit-to-unit, and grade-to-grade.
-focuses on inquiry and investigation of mathematical ideas embedded in rich problem situations.

The creators of CMP believe in helping students grow in their ability to reason effectively with information represented in graphic, numeric, symbolic, and verbal forms and to move flexibly among these representations.

The CMP model follows 3 phases: launch, explore and summarize. The launch phase entails the teacher launching the problem or new topic with the whole class. The teacher will ask questions, clarifies definitions and reviews old concepts which will all help connect together to blend into a cohesive lesson which blends old material and new concepts to build a new task. The explore phase can be done individually, in groups, and even a whole class. Students dousing the explore phase will gather data, share ideas, look for patterns, make conjectures, and develop problem-solving strategies. The teacher's role during this phase is to move about the classroom, observing individual performance and encouraging on-task behavior. The last phase (summarize) guides the students to reach the mathematical goals of the problem and to connect their new understanding to prior mathematical goals and problems in the unit. The summarize phase of instruction begins when most students have gathered sufficient data or made sufficient progress toward solving the problem. In this phase, students present and discuss their solutions as well as the strategies they used to approach the problem, organize the data, and find the solution. Additionally, with CMP homework is not to drill and kill, but is used to help grasp the concept.

Although the CMP model has many inquiry based qualities, it does hold some direct instruction --> guided practice --> independent work qualities as well. CMP is based off of concepts, skills, or procedures that support the development of an developed sequence. Through the CMP model in which the teacher is required to teach is introduces concept, model, and then individual work. Both the CMP and direct instruction model both review prior material to help build into new concepts. I think that is a great and important way to keep material fresh and unforgotten. I think both the creators of CMP and those who are direct instruction followers understand that reviewing material and looping is imperative.

The sixth grade math class where I am doing my practicum uses the CMP model and I think students are able to relate the concepts more to the real world which seems to help with retention. I really like what I've seen so far with CMP.


sources:
http://connectedmath.msu.edu/pnd/principles.shtml

http://www.thirteen.org/edonline/concept2class/inquiry/index_sub4.html

http://en.wikipedia.org/wiki/Inquiry-based_learning

Closure and Anticipatory Set

Closure:
The purpose of a lesson plan closure is to review the day's lesson and essentially wrap-up the day. During closure students are reminded what they have learned (or what they should have learned). In the Salem-Keizer district teachers are required to write and go over their learning target throughout the lesson. The learning target is essentially the big picture of what students should know and accomplish throughout the lesson. If closure is done correctly students will be able to see the importance and relevance of their learning target. Additionally, closure will help evaluate the effectiveness of the lesson, not the strength of the way it was presented.

Throughout my research I also picked up that closure of a lesson is not "a teacher activity, but an act of a learner" (http://www.okbu.net/ed/398/set.htm). Students should internalize the lesson during the closure. That is not something I really knew about closure, but I definitely see the importance. If students are able to internalize the lesson then students should be able to retain the information to a higher capacity.

Closure will also help the teacher decide if:
1. additional practice is needed
2. whether you need to reteach
3. whether you can move on to the next part of the lesson (http://www.edulink.org/lessonplans/closure.htm).

Anticipatory Set:
The purpose of an anticipatory set is to draw focus and get the attention of the students. It is also suppose to generate interest of the next lesson. Additionally, it is "provide a brief practice and/or develop a readiness for the instruction that will follow" (http://www.edulink.org/lessonplans/anticipa.htm).

An important point about an anticipatory set is that it should be done in student-friendly terms and should be engaging and not simply the teacher talking at the students.

I like to use warm-ups as an anticipatory set. Students are able to realize that there is a routine with warm-ups and help them settle down from earlier in the day, whether it be whatever happened at home prior to school or the prior classes they have attended. Also, I could also throw in questions that students may not be able to answer in the warm-ups. I can throw in a question from a unit that has not been covered to get students thinking about how to solve the problem which will increase their critical thinking skills as well wet the student's appetite on how to solve the problem.

Resources:
http://www.edulink.org/lessonplans/closure.htm
http://www.okbu.net/ed/398/set.htm
http://www.edulink.org/lessonplans/anticipa.htm
Madeline Hunter's Lesson Plan
http://k6educators.about.com/od/lessonplanheadquarters/g/anticipatoryset.htm

Practicum- sharing a Lesson

During my practicum experience I have had the chance to teach a lesson on adding/subtracting decimals at the sixth grade level. We used a checkbook register to replicate a real life experience and gave students practical knowledge.

The objectives outlined for the class were:
1) Students will be able to add and subtract decimals and justify their steps.
2) Students will be able to use a checkbook register to add deposits and subtract purchases from their previous balance.

The strategy I used was an "I do, you do." Because of time there was no real "we do." I modeled how to use the register to add deposits to previous balances and how to subtract purchases, but then students were to get together with their elbow partner to add and subtract additional deposits and purchases.

For students that understood the concept really well, they were able to add and subtract without much further guidance, but those who really did not understand what a checkbook registrar was and what it was used for it was difficult. The two ELL students in the class really struggled with the concepts of money as decimals. I do not think that they use decimals to represent their money, so it was difficult for them to understand that is what we did. If I were to change the lesson, I would go back and give more of a history and what a registrar was used for. I think giving background knowledge would help with the whole process and lesson. I would also talk about how our money is broken up and that it is represented by decimals. I did not even think of this being an issue when I started the lesson. Next time I will be more aware.

To check for understanding I collected the registrars and looked through each of them to make sure the addition and subtraction was done accurately (this was possible because the class only had 12 students). I was able to see some common mistakes like .40 + .70 = .11 instead of 1.10. The next day I addressed some of the math fallacies and hopefully as we continue with adding and subtracting fractions students will overcome the fallacies and understand the logic properly.

Warm-ups in Math Education

Warm-ups in math I think are imperative and should be done everyday which will promote a routine in the classroom as well as helps focus students when walking into class. We as teachers middle and high school teachers have less control of what goes on with our students before walking in our door; we typically get them one period of the day as opposed to being a self-contained classroom. Warm-ups can bring routine which can potentially calm the students down and get them focused on the math lesson ahead of them.

I think warm-ups should be short, not spending the whole class period doing them. They should also be something relatively simple, like a couple questions to review previous lessons. I think if we use warm-ups as a sort of pre-test or give them something beyond what they have learned it might deter them from trying or engaging in the lesson that follows.

Also, I think warm-ups should be an individual activity so that students can personally assess where they are in learning and understanding the material.

Additionally, I will make sure warm-ups are gone over and that we do not just give the answers to the question but will give the answer and demonstrate multiple ways if possible to see how one can get to that answer. It is valuable that students see that there is no one direct path to the right answer and that it is okay to get to the answer in multiple ways.

I think warm-ups are very important and can provide to be a great tool!

Standards, Standards Everywhere

I personally looked at the standards for numbers and operations.

Here are NCTM's:
Grades 6–8 Expectations: In grades 6–8 all students should–

work flexibly with fractions, decimals, and percents to solve problems;
compare and order fractions, decimals, and percents efficiently and find their approximate locations on a number line;
develop meaning for percents greater than 100 and less than 1;
understand and use ratios and proportions to represent quantitative relationships;
develop an understanding of large numbers and recognize and appropriately use exponential, scientific, and calculator notation;
use factors, multiples, prime factorization, and relatively prime numbers to solve problems;
develop meaning for integers and represent and compare quantities with them.

Common Core:
6th Grade: Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

Compute fluently with multi-digit numbers and find common factors and multiples.


Apply and extend previous understandings of numbers to the system of rational numbers.

7th Grade: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

8th Grade: Know that there are numbers that are not rational, and approximate them by rational numbers.

Salem-Keizer's:
umber and Operation Goals

Number Sense

Use numbers in various forms to solve problems (6, 7, 8)

Understand and use large numbers, including in exponential and scientific notation (6, 7, 8)

Reason proportionally in a variety of contexts using geometric and numerical reasoning, including scaling and solving proportions (6, 7, 8)

Compare numbers in a variety of ways, including differences, rates, ratios, and percents and choose when each comparison is appropriate (6, 7, 8)

Order positive and/or negative rational numbers (6, 7, 8)

Express rational numbers in equivalent forms (6)

Make estimates and use benchmarks (6, 7, 8)

Operations and Algorithms

Develop understanding and skill with all four arithmetic operations on fractions and decimals (6)

Develop understanding and skill in solving a variety of percent problems (6)

Use the order of operations to write, evaluate, and simplify numerical expressions (7, 8)

Develop fluency with paper and pencil computation, calculator use, mental calculation, estimation; and choose among these when solving problems (6, 7)

Properties

Understand the multiplicative structure of numbers, including the concepts of prime and composite numbers, evens, odds, and prime factorizations (6)

Use the commutative and distributive properties to write equivalent numerical expressions (7, 8)

____________

When looking at the standards it looked like NCTM's were the shortest and most vague of the standards. Both the Salem-Keizer district and the CC were pretty specific and went into specifically which grade level different standards were expected in. NCTM simply breaks down the standards for middle school grades (6-8) as whole. I thinking having to refer back to the NCTM, CC and school district standards will have a tendency to cause some confusion. Although there are definitely veins of similarity between the standards, I think I would have a tendency to look at the school district and CC as opposed to NCTM when designing lesson plans. I think that when you look at NCTM and because it only gives an overarching standard for middle school it will be a little more difficult to break down according to grade. CC and at least the Salem-Keizer district have standards for the each grade level which I personally think will make lesson planning a tad bit easier.

Appropriate Use of Technology

Category 2: Lessons 6-8 NCTM

Here is the link for the numbers and operations lesson I chose: http://illuminations.nctm.org/LessonDetail.aspx?id=L252. The lesson title is "Too Big or Too Small?"

Learning Objectives

Students will:
develop intuition about number relationships
estimate computational results
develop skills in using appropriate technology

Materials

One thousand or more fake dollar bills (play money or rectangular sheets of paper the approximate size of a dollar bill) --> Will have to make if one does not have fake bills.
Scissors
One copy of Circle Template (on colored cardstock) for each student --> Can be downloaded from the above link.
Calculators
Decimal Maze Activity Sheet --> Can be downloaded from the above link.

The teacher definitely used NCTM standards in the objective.

There are 3 activities within the lesson: Activity 1: Exploring The Size of a Million Dollars

This activity explores whether one million dollars will fit into a standard suitcase. If so, how large would the suitcase need to be? How heavy would it be? You may have students work in small groups (2 or 3 students per group) to explore these questions.


Begin the investigation by telling the following story:

Just as you decide to go to bed one night, the phone rings and a friend offers you a chance to be a millionaire. He tells you he won $2 million in a contest. The money was sent to him in two suitcases, each containing $1 million in one-dollar bills. He will give you one suitcase of money if your mom or dad will drive him to the airport to pick it up. Could your friend be telling you the truth? Can he make you a millionaire?
Involve students in formulating and exploring questions to investigate the truth of this claim. For example:

Can $1,000,000 in one-dollar bills fit in a standard-sized suitcase? If not, what is the smallest denomination of bills you could use to fit the money in a suitcase?
Could you lift the suitcase if it contained $1,000,000 in one-dollar bills? Estimate its weight.
Calculators should be available to facilitate and expedite the computation for analysis.

Note: The dimensions of a one-dollar bill are approximately 6 inches by 2.5 inches. Twenty one‑dollar bills weigh approximately 0.7 ounces.

You may wish for students to locate these facts about dollar bills on their own, using internet or other appropriate resources. The students will also need to determine the dimensions of a "standard" suitcase.



Activity 2: Estimating Fractions Between 0 and 1

The model suggested here is easy to make and will help you evaluate your students' understanding of fractions between 0 and 1. Encourage students to make estimates using familiar benchmarks (e.g., ½, ¼, ¾).

Copy the Circle Template (download it) onto light-colored cardstock.


Give each student a copy and ask them to cut out the circles and make a cut in the radius of each.

Have students put the circles together so that they can see the fractions printed on one side of one circle. Ask questions such as these:

Show a small part of the shaded circle (less than ¼). Can you name the part represented?
Show a large part of the shaded circle (greater than ¾). Can you name the part represented?
Ask students to reverse the circle with the printed fractions so that they cannot see the fractions. Ask students if they can:

Show a fraction that is a little bigger than ½. What name can you give it?
Show a fraction that is between ½ and ¾. What name can you give it?
Continue asking questions that allow students to show their understanding of the fractions represented.

Other fraction models should also be used to evaluate students' understanding of fractions.


Activity 3: Exploring The Effect of Operations on Decimals

This activity provides an opportunity for students to explore the effect of addition, subtraction, multiplication, and division on decimal numbers.

Write the problem (as described next) on the chalkboard or overhead. Ask students to discuss what they notice. Lead a discussion that focuses on these key points:

In computing the product of 4.5 and 1.2, a student carefully lined up the decimals and then multiplied, bringing the decimal point straight down and reporting a product of 54.0.


Reflection on the answer should have caused the student to realize the product was too big. Multiplying 4.5 by a number slightly greater than 1 produces an answer a little more than 4.5. Instead, this student applied an incorrect procedure (line up the decimals in the factors and bring the decimal point straight down) and did not reflect on whether the resulting answer was reasonable.

Tell students that they will be playing a game to practice decimal operations and their effects. Encourage students to trace several paths through the maze while always looking for the path that will yield the greatest increase in the calculator's display.

Give each student a calculator and a copy of the Maze Playing Board activity sheet.
Maze Playing Board Activity Sheet --> download!
Students are to choose a path through the maze. To begin, have the students enter 100 on their calculator. For each segment chosen on the maze, the students should key in the assigned operation and number. The goal is to choose a path that results in the largest value at the finish of the maze. Students may not retrace a path or move upward in the maze.

In pairs or in groups of three, students should discuss their strategies (after playing the game) and what worked best for them.

Students should be able to achieve a score in the thousands. The path highlighted below gives a result of roughly 6332.


Possible follow-up activities include finding the path that leads to the smallest finish number or finding a path that leads to a finish number as near the start number (100) as possible.


I think the first activity where students explore the size of a million dollars is the best in regards to critical thinking. People are always drawn by the topic of money and I think because of that students are more willing to invest time in figuring out the problem. This activity helps with the 8.NS.1 standard. It addresses the need to understand that informally that every number has a decimal expansion. The dimension of the bills is a great example of this (The dimensions of a one-dollar bill are approximately 6 inches by 2.5 inches. Twenty one‑dollar bills weigh approximately 0.7 ounce). The other activities in the lesson does address the standards but seem to be more "math activities" and does not use more of a real life scenario like the first.

Questions to consider when the activity is in progress are: Are the students were engaged in the activity? Was the activity more of a fun activity without meaning or was it properly helping develop the understanding of mathematical concepts. Did the students meet the objectives of the lesson? If not, how can I change the lesson for the better?


If you were were to teach this lesson, I probably would not do all three activities. I would use probably the first activity/scenario where a friend calls about the million dollars. I would use that as a sort of group warm-up to get the math juices flowing and then get into another lesson. I think warm-ups can serve as review in math and also allows students to practice what they have learned. I think this could be a great warm-up.

I think the activity uses a very constructivist approach. The students are not being lectured to directly. They are suppose to critically think on their own to figure out the answers. I think this sometimes is very helpful in math where people usually associate teaching math with direct instruction. Students in these activities are constructing their own understanding of money and how it relates to math. I think the activity has some great aspects to it!