CMP Middle School Interview

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

Teacher believes the CMP was created in response to the NCTM. He said the CMP aligns with the NCTM. Regarding the Common Core he said CMP may be in a transition process to align with those standards. 

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? 

Teacher said he uses mixed groups with high and low achieving students in the same group. He said he identifies these students early so he can scaffold their learning in the inquiry process.

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

Teacher said the role of homework and accountability in the CMP is for additional practice on the day's lesson. He said he counts homework as a grade and therefore the students are held accountable.

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? 

Teacher said he uses many of these techniques. He said he utilizes think pair share, jigsaw, peer teaching, with a strong student centered focus. He keeps track of group progress through group grades and roles are not established this year due to the challenges of being in a new school.

Inquiry and CMP Research

I have had experience teaching the CMP model in my Practicum for the past two weeks, so I have a little familiarity with how it is set up. The CMP model is inquiry based instruction. Essentially students are given basic tools to solve a problem, and then given class time to explore similar problems and solve them in a group setting. The problems are then summarized with a student centered focus (often with selected students teaching the class).

CMP uses the Launch, Explore and Summarize guidelines for instruction. Essentially, the Launch portion of the lesson is the "mini-lesson." The teacher guides students with a set, introduces them to the material and may even perform a guided practice of a similar problem to what the students will be exploring. In this portion, generally students are introduced to the material without much "entrenching" of knowledge. The Explore portion is the segment where student work on the assigned problems. The teacher circulates the classroom ensuring students are on task and asking questions related to the lesson. These questions should guide student thinking and answers to student questions should generally be in the form of another question. The summarize portion of the lesson essentially ties the lesson in a nice bow. This can be teacher or student lead. It also explores new ideas for solving problems and may introduce the next lesson to a certain extent. 

This is different to the direct instruction model because students are allowed to explore and then summarize their questions. Inquiry expects the students to make mistakes and learn "why" an algorithm works in math rather than just getting the algorithm and practicing.

 

In researching Inquiry based teaching and learning, essentially it is a teaching strategy centered around Constructivist philosophies. According to Wikipedia, "Inquiry learning is a form of active learning, where progress is assessed by how well students develop experimental and analytical skills rather than how much knowledge they possess." In sum, it is student centered and not teacher centered much like direct instruction. Inquiry based teaching presents a problem or question to students (usually in groups) and provides them the opportunity to solve the problem or question. Students use their life experiences and construct their knowledge with a teacher as a guide. 

Anticipatory Set and Closure

Anticipatory Set- From my research on the internet, I found that an Anticipatory Set introduces the lesson being presented and focuses students on the learning goal of the day. At times, it is the "hook" for the lesson. This can take on many forms. For example, in math, one can tell a personal story about the use of decimals in the real world. It can also be an engaging activity to help students focus their minds on the lesson. According to sothernct.edu, the anticipatory set is "A brief activity or event at the beginning of the lesson that effectively engages students' attention and focuses their thoughts on the learning objective" (http://home.southernct.edu/~gravess1/scsu_courses/edu493/as.htm). It can also serve to connect to previous lessons and previous experience.
In my personal experience with an anticipatory set in my middle school classroom, I brought in my framed police badge, patch, and card. I told them a life experience I had with math as a police officer and how that related to the learning objective. I had them hooked! It was awesome.

Closure- From my research on Closure, I found on multiple sites that it was not a lesson summary. It is student driven so they can internalize the learning target. According to the same website as above, "(Closure is) a natural stopping point in the lesson or especially at its end, which points back to the objective and captures its relevance to the unit. Closure keeps the big picture in view, either by relating the objective to other fields or topics, or by raising a related question to ponder in anticipation of the next lesson. Closure ensures that the objectives are met and applied, as students reapply or label the lesson for themselves." Like I said above, closure should be driven by examples of student work, or specific students teaching the class. It assists the students in applying the knowledge they learned so they can better internalize the lesson objective.

In my experience with closure and CMP, I have tried to do a number of things to bring closure. In general, I have them complete a summary statement, specific to the lesson objective. I have also included, student summaries and had them direct the questioning.

Practicum-Sharing a Lesson

Grade level: 6th				Unit: Decimal Operations	Lesson Title: Strategies for adding/subtracting decimals
Date		Time	60 min

Objectives: I can solve problems that require decimal addition and subtraction and develop an understanding for place values. Assessment questions, #1, #2, #4 and #5 Prior Knowledge: Knowledge of a decimal number, basic algorithm understanding for addition and subtraction.

Time	Lesson Plan	Monitoring/ Assessment
	Warm-up activity (written on the board)- Students work independently and solve the warm-up problems. Once completed, randomly select students to solve the problems in front of the class explaining their process. If a student gets stuck, scaffold learning. If a problem is wrong, ask for agreement and solve the problem. Anticipatory Set: Place value/addition activity Mini Lesson: Use the getting ready handout p.8-9. Examine the problem with the students. Think, pair, share.  Do you agree with the clerk? Why? Use non example…10+10 and misalign the place values Identify with the students what the clerk did wrong in the problem (place value, decimal alignment). Write on the board what the clerk did wrong. Ask why one cannot add eight dimes to one dollar. Guided Practice: Go over #1 in problem 1.2 with the students (student read aloud) and write the example of a table on the board with the answer. Group Work: Release students to solve the remainder of the problems in 1.2. Teacher circulates around the room to answer questions and gauge understanding. Ask why place value is important and what each place value is valued at. Identify groups with correct answers. Assist and focus groups on work. Summarize: Ask students to come up and explain how they solved problems 2-4. Assign independent practice Independent Practice: ACE questions Materials: Math journal, Transparency 1.2, Construction Paper, Markers
5 minutes 3 minutes 5 minutes 10 minutes 10 minutes 15 minutes 12 minutes		Teacher monitors work Random students solve problems Asking questions to volunteers Teacher talking with each group/picking students with answers (charting groups/students with correct answers) Teacher evaluates homework and checks for understanding

 

Adaptations/Modifications:

ESOL	I have several ESOL students in my classroom. I will adapt by asking them specifically if they understand the content.
TAG	TAG students will be given more practice in group work (if necessary)
Special Needs	Any special needs would be addressed based on specific students
Literacy	Reading aloud, reading independently documenting math work

The lesson objectives to this lesson are listed in the "Objectives Heading" in the lesson plan. Essentially, I want students to understand the importance of place values in a decimal addition and subtraction problem. I will implement this strategy by using examples of proper place value alignment and "non-examples" and the effects of misalignment has on the result of the problem. I am using Connected Mathematics which follows the Launch, Explore, Summarize (Direct Instruction) style of teaching. 

So, what worked? I have only taught this lesson in my micro-teaching cohort activity. I think the portions of the lessons that really worked was the guided practice portion. In expressing the proper way of solving a decimal problem, and modeling this way with the students, they can see how to solve the problem effectively.

It is important to see if students are "getting the material." Checking for understanding is an important tool for knowing if students are meeting the learning target/objective. In my lesson above, I do this in a couple of different ways. The first way is through the warm-up activity. Since the warm-up activity will focus on the material covered, I can gauge how much of the material students know, and how much I need to teach them. In the warm-up, I call on random students, which holds them accountable to doing the work. In the group work portion, I walk around to each group and chart how each student and group is doing. I am asking specific questions related to the material to gauge this understanding. In the summary portion of the lesson, I am asking students who performed unique ways of solving a problem to teach the other students what they did. Independent practice will also be assigned and I will check for understanding in their homework assignments. 

As my lessons continue, I will evaluate the data I collect on the group work and in the homework. I will also evaluate through summative assessments as the unit evolves. I will use this data to format my lessons to come. If the majority of the class is not understanding a concept, it is my job to clarify that concept to the entire class.

If I were to reteach this lesson, I would probably use more non examples and invite more students to show me their work. Can I make time slow down? It seems that this lesson is fairly jam packed, so finding ways to reduce some of the "fluff" in the lesson without removing important ideas would probably help.

Warm-ups in Math Education

According to About.com, Daily warm ups or do nows are tools that every teacher should have in their educational arsenal. Warm ups can be given to students at the beginning of the period to review a previous topic or to introduce new material. They give students something to accomplish of an educational nature while allowing the teacher time to take roll and perform other housekeeping duties.They can also reinforce the key points that you want students to remember. Therefore, every teacher can benefit from including warm ups each day.

Warm-ups in math education serve many purposes for both teachers and students. The purposes it can serve for the teacher are: Student assessment, focused students in the class, introduces or reviews materials, promotes individual and group work, and allows the teacher to complete clerical tasks. Warm-ups can become something the students expect when they walk into the classroom. They serve as a "jump start" for students.

The purposes it can serve for the student are: Allows practice or review of the material, test preparation, provides a stress-free environment for students to make mistakes, and allows them to work on individual or group work.

In my experience with warm-ups in the classroom so far, I have seen a few strategies implemented that I thought to be effective use of the time. The first was a warm-up activity focused on individual students. Students were to complete the task alone and then be ready to explain to the class their reasoning. The second was a group-based activity. Essentially the same idea as before, but promoting group work and roles as a focus. Material in the warm-ups was a variety of review and an introduction into new knowledge.

In all, math warm-up are good for both student and teacher. It provides that first 10 or so minutes of class to focus and initiate the "math brain." I know I will use warm-ups in my classroom.

Appropriate Use of Technology

Fraction Models

Explore different representations for fractions including improper fractions, mixed numbers, decimals, and percentages. Additionally, there are length, area, region, and set models. Adjust numerators and denominators to see how they alter the representations and models. Use the table to keep track of interesting fractions. http://illuminations.nctm.org/ActivityDetail.aspx?ID=11

 

For my project, I had numbers and operations related to fractions and decimals. I copied and pasted the above description of the activity I found and used to relate to this topic. The mathematics that it reinforces is fractions, decimals, mixed numbers, and percents. As the numerator and denominators are adjusted, the student can see the related decimal, mixed number, and percent. The activity also displays a visual representation of the fraction. 

 

I thought the activity could be very effective as is addresses the kinestetic and visual learner. The technology offers a quick reference to fractions that may be difficult to picture in a students mind. It teaches the student what a mixed number or a percent looks like. This technology should be coupled with a supporting teacher lesson, using many types of materials to explain fractions as they relate to other numbers (ratios, percents, and decimals). If I were to teach the lesson, I would either do this activity as a warm up to the lesson, or after I taught an introductory lesson.

Standards, Standards, Everywhere

My group had numbers and operations and the associated standards. I found the NCTM standards/expectations for numbers and operations were pretty general as they covered 6 - 8 in general terms. There were a total of seven general standards for three grade levels. These were:

• 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. 

In deciphering the above standards, I found action verbs being utilized such as, work, use, and develop. As one can see they are very general, but point to the overall concepts that students should know and demonstrate before going on to high school.

As I viewed the Common Core and CMP standards, I found they were more difficult to decipher. For example, for the number system in the common core standards, there were broad headings like "Apply and extend previous understandings of numbers to the system of rational numbers." After the heading there are more specific objectives or benchmarks for the student to achieve.

In the CMP standards, there were focused objectives for Number and Operation goals. It also had guided objectives in relation to standards and the texts being used for the material. In my middle school classroom, we are using Connected Math and I have found it user friendly and comprehensive. It breaks down the standards into daily student objectives.

Overall, I found the National Standards to be broad concepts and Common Core and CMP standards more focused. It was like a "funnel effect" for the standards, as I got to CMP, they were more focused and deliberate to daily or lesson objectives.