CMP Inquiry: Middle School Interview
I interviewed a 6th grade math teacher that teaches CMP. Here are her thoughts...
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?
Scaffolding happens on a daily basis. Allowing some or all students access to calculators helps. In theory, working in teams would address that also. Not on a daily basis, but more like once a unit I assess and tier the students based on ability. Some go ahead with the regular work and some get re-taught with me. This is a tough one though! I also have some students scheduled for after school study hall once a week and this helps keep them caught up with what we're learning. That way even at the end of the book they aren't totally lost.
3. What is the role of homework (and accountability) in the CMP?
Homework has a very small place in CMP. It is for practice of understood concepts. CMP discourages teachers from spending class time correcting homework with students since it promotes classtime for inquiry.
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)? Ongoing assessment(s) and checking for
understanding?
I assign group roles and attempt to build group interdependence through that. I've used self-reflections on how well a student contributed, how well he/she did his/her job, how well the team worked together. Often I won't answer a student's question until I know that the team has been asked. (Student A says "I have a question!" I ask Student B, "What's A's question?" If they don't know, I walk away until the team can prove they've heard the question and can't answer it themselves.) I have been guilty of doing too much work for the students, so recently I've attempted to use a spinner to randomly select a team to share. This (at least in my mind!) forces the team to work together and quickly to accomplish whatever I've asked them to do.
Inquiry & CMP Research
At my Practicum site they teach using CMP so this was the book I taught out of during my two weeks. It was very interesting to look at this book and the types of problems it sets up and questions it asks and compare that to my math experiences in middle school. CMP is definitely designed to part of the "inquiry model" and have students use math to solve problems that have some sort of meaning and connection to the world. The idea behind this model and book type is that students will understand the concepts and retain the information better than with the problem solving style of mathematics. In CMP you are using problem solving to understand a concept or idea greater than the problem solving itself. Now in theory I really appreciate this style of teaching and learning. Yet my experience in the classroom with it has made me a bit jaded.
As I was teaching I realized that the students weren't focused on the concepts or bigger ideas in the problems because they could not get the "basic" problem solving skills that would allow them to look at the application. I found myself doing a lot of inquiry style teaching with projects, activities, and manipulatives to supplement the book and it really did not work for the students. It was very difficult because I then had to adopt more of a direct instruction model and walk through the problems and processes with the students which is not what the book is meant for.
At heart I am a constructivist and an advocate of inquiry based learning, yet I can see how difficult it can be at times especially in math. Not only is it difficult for middle school students to think abstractly in general, but without fundamental math understanding the inquiry process is all the more daunting and seemingly unachievable for the students. I have been thinking about the ideas that we addressed at the beginning of this class regarding math having to build upon itself and the idea that maybe math did not have to be a linear process of understanding. This was an intriguing idea to me, but in my practice I saw how students with low levels of understanding of multiplication and division and their relationship to one another struggled through creating equations and applying that to graphs and then generating meaning from it. So I do think that learning math does build on itself especially in elementary and middle school and it is only once you get to upper level math that the process changes and it does not necessarily have to be linear.
Closure & Anticipatory Set
To me, an Anticipatory Set seems to include the following:
I used to give softball pitching lessons to girls aged about 9-14. I have been pitching since I was 11 years old and now pitch in college so I have quite a bit of experience. Giving pitching lessons is somewhat different than teaching in a "normal" classroom. It was mainly one on one instruction and obviously required much more physical action than many classes do. I taught girls with a wide age range and skill level. Some girls were just starting to learn to pitch and wanted to learn the basics, while others were more advanced and were working to learn new pitches to add to their repertoire.
While I was giving lessons I learned a ton about communication. Vocabulary was key. Many pitching coaches and their students develop their own type of vocabulary to describe movements that you need to be doing or that you should not be doing. Therefore, when starting with new coaches, or in my case new students, it takes some time to develop this vocabulary. Once this vocabulary is developed, learning can progress at a faster rate.
I think one of the things that worked really well for me is that I have been to quite a few different pitching coaches, so I am aware of a few different styles and ways of throwing different pitches. This allowed me to work with each of my students a little differently by trying out different ways of throwing pitches to find what worked best for them and their individual styles. I was able to do this very quickly and fairly easily. Assessment in pitching is immediate; you explain to the student what the pitch is supposed to do, show them how to hold the ball, walk through the steps with them, demonstrate, and then have them throw it. Within the first couple of times they throw the pitch you are able to tell if that style is going to work for that particular student. That does not mean that they are going to throw the pitch perfectly every time, but that their body understands the concept and will be able to do it with practice.
This was a learning experience for me and I think it was very helpful for me to be able to see different learning styles just within pitching, and also be able to see how important vocabulary and communication are. Now that I look back on it I am also able to see how I can apply what I learned as an instructor to teaching in a classroom. There will of course be differences, class size and content for instance, but vocabulary definition and common understanding, different methods of instruction, demonstration and practice are all applicable components of teaching.
Warm-Ups in Math Education
As a math teacher I would like to use warm ups as a way to gage how my students are doing and give them an idea of where we are headed. I think they can be multifunctional; you can use it as a time for students to transition from their last class to a math mindset, give them review to brush up on skills, and give them new problems to assess what they know. I like the idea of giving questions that apply to different levels of Bloom's Taxonomy, from simple recall to higher order application. I also want the students to feel like they have a say in what kinds of questions they are seeing and give me as the teacher feedback on the warm-up so having them label the questions either on a number scale or on easy/medium/hard scale would be useful for me to help track student progress and perception of the material. For example, if many of the students are labeling the recall questions as hard, I know there is problem and the students aren't understanding the material I need them to so that we can move to the higher order thinking questions.
However, I think I would need to try a couple of different kinds of questions/warm up activities to see what gets the best response from the students. Too often I see warm-up time turning into sit and talk with your friend time and wait for the teacher to give you the answer. This drives me crazy and seems like a waste of my time as well as the majority of the students. I also find it difficult when there are specific warm-ups that are required of the teacher to do. I have been in a situation like this and think it is hard to motivate students to do the warm-up activities when there is not necessarily a connection between the activities and what they are doing that day in class. There should be some review questions but I also think it is important for students to be able to directly correlate what they are doing in the warm-up to their objectives for the day/lesson/unit etc.
Appropriate Use of Technology
We selected an activity from the Illuminations website called "Too Big or Too Small?". This lesson includes 3 activities that explore number relationships, fractions and decimals.
The plan includes objectives, materials , and the instructional plan with the description of each activity. All three activities can be done individually or in pairs or groups. I would probably do a little bit of both styles, have them do one or two activities or parts of activities individually, and also work in pairs or groups.
For Activity 1, I think I would have to gage the level of my students interest in this activity because I am not necessarily interested in it but they might find it interesting and informational. I could see this activity being done in pairs and giving the students the basic information about the size and weights of dollar bills as the activity does for them to be able to complete it. I don't think that this activity is as relevant to the objectives as the other activities so I would probably spend less time on this activity than the other ones.
For Activity 2, I would have each student have their own cut out circles but be able to talk in groups and figure out questions about different fractions. This is a great visual and kinesthetic representation for fractions and you could even make it fun by making the circles pizzas or cookies!
For Activity 3, I would start with a group lesson/discussion of adding/subtracting/multiplying and dividing. I think the example they give is a great one because it shows the common mistakes that students make when beginning to multiply decimals and I really like the discussion of how that answer is not logical. The teacher then goes over how to multiply decimals and the students get to do the maze activity which looks fun!
Standards, Standards Everywhere
I interviewed a 6th grade math teacher that teaches CMP. Here are her thoughts...
1. How does the CMP curriculum align with national Common Core and NCTM
standards?
The CMP curriculum has a few gaps when it come to the Common Core and NCTM standards. Most of the problems can be adjusted by shifting the unit down a grade level. However, CMP did have to come out with some supplementary mini-units to fill those gaps. For example, 6th graders have a small unit on ratios and proportions, integers, and algebraic equations. The CMP curriculum does a good job of providing a foundation for teaching the NCTM "process standards" or the "Standards for Mathematical Practice." I understand those as developing math character in students. :) CMP does a great job for that.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?
3. What is the role of homework (and accountability) in the CMP?
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)? Ongoing assessment(s) and checking for
understanding?
Inquiry & CMP Research
At my Practicum site they teach using CMP so this was the book I taught out of during my two weeks. It was very interesting to look at this book and the types of problems it sets up and questions it asks and compare that to my math experiences in middle school. CMP is definitely designed to part of the "inquiry model" and have students use math to solve problems that have some sort of meaning and connection to the world. The idea behind this model and book type is that students will understand the concepts and retain the information better than with the problem solving style of mathematics. In CMP you are using problem solving to understand a concept or idea greater than the problem solving itself. Now in theory I really appreciate this style of teaching and learning. Yet my experience in the classroom with it has made me a bit jaded.
As I was teaching I realized that the students weren't focused on the concepts or bigger ideas in the problems because they could not get the "basic" problem solving skills that would allow them to look at the application. I found myself doing a lot of inquiry style teaching with projects, activities, and manipulatives to supplement the book and it really did not work for the students. It was very difficult because I then had to adopt more of a direct instruction model and walk through the problems and processes with the students which is not what the book is meant for.
At heart I am a constructivist and an advocate of inquiry based learning, yet I can see how difficult it can be at times especially in math. Not only is it difficult for middle school students to think abstractly in general, but without fundamental math understanding the inquiry process is all the more daunting and seemingly unachievable for the students. I have been thinking about the ideas that we addressed at the beginning of this class regarding math having to build upon itself and the idea that maybe math did not have to be a linear process of understanding. This was an intriguing idea to me, but in my practice I saw how students with low levels of understanding of multiplication and division and their relationship to one another struggled through creating equations and applying that to graphs and then generating meaning from it. So I do think that learning math does build on itself especially in elementary and middle school and it is only once you get to upper level math that the process changes and it does not necessarily have to be linear.
Closure & Anticipatory Set
To me, an Anticipatory Set seems to include the following:
- A brief layout of the days goals, objectives, and tasks
- A connection between today's activities and previous learning
- A connection between learning and student lives and interests
I think often a warm ups take the place of an Anticipatory Set, especially if the class has limited time and warm ups are mandated. To me an Anticipatory Set is much more than a warm up. It is a discussion, an activity, a way to generate student interest and investment, and a vehicle in which you can layout the days plans and expectations. I can be as quick or as lengthy as the teacher and the students make it and provides the students with information and relevance, it gives them a reason why they are there.
For example, as a class students could create a list of information they already know about the topic and then we can think about where we see this topic in our lives outside of the classroom.
I found this link useful when thinking about Anticipatory Sets.
The way I think about it, Closure is the Anticipatory Set that comes at the end of the class. It is not just a summation, but provides a refocus for the students on what it was that day they were expected to come away with. It also should provide the teacher with information on how the students are doing with the topic. I really like doing exit cards as a closure. Based on the questions, it lets the students know what I expected them to know and gives me an idea of their subject matter understanding. I have found that based on their responses, I have a better understanding of where they are at in the learning process. It answers the questions; do I need to reteach, do they have a firm understanding, can we move on or is more time needed? Which are all important when it comes to creating my following lesson plans.
A succinct and informative definition of Closure can be found here.
Sharing a Lesson
I used to give softball pitching lessons to girls aged about 9-14. I have been pitching since I was 11 years old and now pitch in college so I have quite a bit of experience. Giving pitching lessons is somewhat different than teaching in a "normal" classroom. It was mainly one on one instruction and obviously required much more physical action than many classes do. I taught girls with a wide age range and skill level. Some girls were just starting to learn to pitch and wanted to learn the basics, while others were more advanced and were working to learn new pitches to add to their repertoire.
While I was giving lessons I learned a ton about communication. Vocabulary was key. Many pitching coaches and their students develop their own type of vocabulary to describe movements that you need to be doing or that you should not be doing. Therefore, when starting with new coaches, or in my case new students, it takes some time to develop this vocabulary. Once this vocabulary is developed, learning can progress at a faster rate.
I think one of the things that worked really well for me is that I have been to quite a few different pitching coaches, so I am aware of a few different styles and ways of throwing different pitches. This allowed me to work with each of my students a little differently by trying out different ways of throwing pitches to find what worked best for them and their individual styles. I was able to do this very quickly and fairly easily. Assessment in pitching is immediate; you explain to the student what the pitch is supposed to do, show them how to hold the ball, walk through the steps with them, demonstrate, and then have them throw it. Within the first couple of times they throw the pitch you are able to tell if that style is going to work for that particular student. That does not mean that they are going to throw the pitch perfectly every time, but that their body understands the concept and will be able to do it with practice.
This was a learning experience for me and I think it was very helpful for me to be able to see different learning styles just within pitching, and also be able to see how important vocabulary and communication are. Now that I look back on it I am also able to see how I can apply what I learned as an instructor to teaching in a classroom. There will of course be differences, class size and content for instance, but vocabulary definition and common understanding, different methods of instruction, demonstration and practice are all applicable components of teaching.
Warm-Ups in Math Education
As a math teacher I would like to use warm ups as a way to gage how my students are doing and give them an idea of where we are headed. I think they can be multifunctional; you can use it as a time for students to transition from their last class to a math mindset, give them review to brush up on skills, and give them new problems to assess what they know. I like the idea of giving questions that apply to different levels of Bloom's Taxonomy, from simple recall to higher order application. I also want the students to feel like they have a say in what kinds of questions they are seeing and give me as the teacher feedback on the warm-up so having them label the questions either on a number scale or on easy/medium/hard scale would be useful for me to help track student progress and perception of the material. For example, if many of the students are labeling the recall questions as hard, I know there is problem and the students aren't understanding the material I need them to so that we can move to the higher order thinking questions.
However, I think I would need to try a couple of different kinds of questions/warm up activities to see what gets the best response from the students. Too often I see warm-up time turning into sit and talk with your friend time and wait for the teacher to give you the answer. This drives me crazy and seems like a waste of my time as well as the majority of the students. I also find it difficult when there are specific warm-ups that are required of the teacher to do. I have been in a situation like this and think it is hard to motivate students to do the warm-up activities when there is not necessarily a connection between the activities and what they are doing that day in class. There should be some review questions but I also think it is important for students to be able to directly correlate what they are doing in the warm-up to their objectives for the day/lesson/unit etc.
Appropriate Use of Technology
We selected an activity from the Illuminations website called "Too Big or Too Small?". This lesson includes 3 activities that explore number relationships, fractions and decimals.
The plan includes objectives, materials , and the instructional plan with the description of each activity. All three activities can be done individually or in pairs or groups. I would probably do a little bit of both styles, have them do one or two activities or parts of activities individually, and also work in pairs or groups.
For Activity 1, I think I would have to gage the level of my students interest in this activity because I am not necessarily interested in it but they might find it interesting and informational. I could see this activity being done in pairs and giving the students the basic information about the size and weights of dollar bills as the activity does for them to be able to complete it. I don't think that this activity is as relevant to the objectives as the other activities so I would probably spend less time on this activity than the other ones.
For Activity 2, I would have each student have their own cut out circles but be able to talk in groups and figure out questions about different fractions. This is a great visual and kinesthetic representation for fractions and you could even make it fun by making the circles pizzas or cookies!
For Activity 3, I would start with a group lesson/discussion of adding/subtracting/multiplying and dividing. I think the example they give is a great one because it shows the common mistakes that students make when beginning to multiply decimals and I really like the discussion of how that answer is not logical. The teacher then goes over how to multiply decimals and the students get to do the maze activity which looks fun!
Standards, Standards Everywhere
Oregon has done a pretty good job of creating standards that directly relate to the Common Core and NCTM Standards. Therefore, our standards are pretty closely related. The NCTM standards are more broad where as the Common Core standards narrow down the focus to one of the specific expectations identified within the NCTM standards. The standards we chose to focus on were:
NCTM STANDARD: Understand meanings of operations and how they relate to one another
Grades 6–8 Expectations:
Grades 6–8 Expectations:
In grades 6–8 all students should–
- understand the meaning and effects of arithmetic operations with fractions, decimals, and integers;
- use the associative and commutative properties of addition and multiplication and the distributive property of multiplication over addition to simplify computations with integers, fractions, and decimals;
- understand and use the inverse relationships of addition and subtraction, multiplication and division, and squaring and finding square roots to simplify computations and solve problems.
Core Standards: 8.NS.1. Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.
Here you can see how we focus on the first, and a maybe a little bit of the second, bullet points of the NCTM standards through our core standard. Understanding decimals and fractions is crucial for not only this objective but as a basis for their other math skills that they will need to develop.
Best Practices Research
Best practices in Education and Instruction seem a bit ambiguous to me. When attempting to research what are best practices in education and instruction especially in mathematics, there was just so many takes on what best practices are and how to implement them. But while wading through all this material I found a gem. The Beaverton School District here in Oregon has developed a document that lays out 14 Best Practices in Mathematics (education & instruction). A few of these Best Practices that stood out to me are (paraphrased and quoted):
Encourage Multiple Problem Solving Strategies- Provide students with a wide framework and knowledge of problem solving strategies and encourage them to look at the information provided to choose and apply the appropriate strategies. Encourage students to evaluate the strategy they chose and discuss its appropriateness and reasonableness.
Provide broad mathematical experiences in all curricular areas- Provide purposeful opportunities for constructing knowledge through a broad range of authentic mathematical experiences across all curricular areas.
Set challenging goals and give e!ective feedback-Set clear and challenging mathematical goals. Maintain high expectations for all students at all stages of their mathematical development.
Encourage self-assessment and reflection- Give students opportunities to examine their own as well as other students’ work to view evidence of learning and to give and receive constructive feedback.
Establish school/family/community partnerships- Establish home/school/community partnerships to collaborate in support of the mathematical development of all students both at home and at school. Know students as individuals (interests, attitudes, home/school/community experiences).
In addition to these educational practices, there are many instructional practices that can give insight into effective ways to teach mathematics.
Assess to inform instruction and summarize learning-The key for us is having pre-tests that are specific enough that the information they cover can be taught and measured within a specific. Beyond that, we also create shared assessments on a weekly basis to determine what has been retained or needs to be revisited.
Provide differentiated classroom instruction using a variety of instructional methods and interventions- Based on the needs of your classroom, the instructional methods you use will alter. Whether you will use whole class instruction, small groups, peer instruction, direct instruction or constructivist methods, we as teachers will need to be flexible and change our styles to incorporate the needs of our students.
Reinforcing Effort and Providing Recognition-These strategies address students' attitudes and beliefs. Most students are not aware of the importance of believing that their level of effort is related to their achievement. When students are rewarded or praised for achieving specific goals, their level of achievement is higher.
Cooperative Learning- When students are provided with opportunities to interact with each other in a
of criteria to group students; that there should be formal, informal and base groups and that the size of learning groups should be continually monitored. These activities support the ideas that there should be a variety of ways their learning is enhanced.
So while this concept is a bit more broad than I know what to do with at this point, some of these best practices shed light on how I can work to make my future math classroom successful and effective for students.
References:
Integrating Technology into the Classroom using Instructional Strategies based on the research from:Classroom Instruction that Works
My name is Alexandria Charlotte Watilo, but most people just call me Alex. I have two younger sisters that mean the world to me and two parents that are my role models, friends, and inspiration. I would be lost without my boyfriend and good friends who provide me with an endless amount of good times and love. I play softball at Willamette University and don't know what I would do without sports in my life. Some random tidbits; I love to read, go camping, be by the water whether it be a pond or an ocean, ride quads, dirtbikes, and snowmobiles, scrapbook when I can find the time, travel, I am allergic to shrimp and can't stand peanut butter, I like the idea of eating healthy but love junkfood, I have a tortoise named Daphne... If there's more you want to know, ask. I'm an open book.
A Blurb About Me
My name is Alexandria Charlotte Watilo, but most people just call me Alex. I have two younger sisters that mean the world to me and two parents that are my role models, friends, and inspiration. I would be lost without my boyfriend and good friends who provide me with an endless amount of good times and love. I play softball at Willamette University and don't know what I would do without sports in my life. Some random tidbits; I love to read, go camping, be by the water whether it be a pond or an ocean, ride quads, dirtbikes, and snowmobiles, scrapbook when I can find the time, travel, I am allergic to shrimp and can't stand peanut butter, I like the idea of eating healthy but love junkfood, I have a tortoise named Daphne... If there's more you want to know, ask. I'm an open book.
But let's get down to what this blog is really all about. It's supposed to be about education, schools, technology, what my role as an educator is going to be, teaching, learning, growing. So at this point in my journey I hope to become a High School History/Social Studies teacher. I may also teach Middle School and if so I hope its math because my knowledge of ancient Mesopotamia and other Middle School Social Studies topics leave much to be desired. This blog will follow me through my journey of "becoming an educator" and hopefully be something I can continue, and look back, on as my experiences take me beyond the realm of a Master's program.
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