Inquiry-based Math: Middle School Interview

Interview with a Middle School Math Teacher

L.B. is a 6^th grade math teacher who uses an inquiry-based method called CPM.

What is CPM?

Before CPM was adopted, the district was using a 14-year old book because they had didn't have any funding. She said she rarely used the book. During her 4^th year of teaching the school district adopted CPM. CPM stands for College Preparatory Math. There were 6 full days of training on how to use the book and do group strategies. She said it was “amazing.” The training even changed the way she structured some of her other classes. She refers to CPM as spiraling. Spiraling means that when a concept is introduced it is revisited again and again throughout the year. She says this is very important.

The same year it was adopted, it was overturned because the parents wanted traditional math. The parents said that there was “too much group work and they didn't want their child to have to sit with people who didn't speak English.” The parents also found it difficult to help their students with homework because there wasn't a book with examples. The parents went to the board and the board overturned CPM. The board spent another $500,000.00 and bought Holt instead (Holt is a very traditional approach to teaching math). Because the district had already paid for CPM they allowed CPM to be used as a supplement, but Holt was the main book.

This year, L.B. is using straight CPM this year because she believes it is best practices.

How does CPM align with Common Core and NCTM?

“It is totally aligned” she explained. There is a new version that has been revised so that EVERY lesson meets grade-level common core. CPM's philosophy cares more about teaching it well then they do about their own curriculum. She thinks they are non-profit.

Addressing the basics: How do you get students who aren't at grade level caught up?

CPM doesn't address this. L.B. often questions the importance of being able to do things like multiplication in your head. Calculators are in EVERYTHING! Still, she believes students should be able to do basic math in their head. When students are really impacted she calls the parents/talks to them during conferences and asks them to do flashcards with their students.

Homework

Homework is important because students need extra practice. CPM believes that if a student doesn't get it, why not give them another chance. Homework isn't graded. If you do it, you get full credit because you can always retry it and do it later. “Why take off points if they just don't get it yet?” L.B. explains that about 90% of students complete homework in CPM. It works. There's homework help online that gives them step-by-step clues.

Collaboration

Students work in groups of 4. CPM uses “heterogeneous groups.” To achieve this, L.B. designs the groups so that there are 2 students with high OAKS math scores, and 2 students with low OAKS math scores. Students are assigned roles. Students are either the resource manager, facilitator, recorder/reporter, or task manager.

Assessment

L.B. gives pretests when she knows the concept is brand new to the students. She gives quizzes every couple of weeks. At the end of the chapter she gives a test.

Inquiry & CMP Research

Inquiry
Inquiry-based learning is very student-centered.  The teacher does not give answer, the teacher guides and asks questions.  Inquiry-based learning draws on student's prior knowledge and it allows students to construct their own meaning.  It also involves sharing of knowledge and reflection.
CMP Research
Connected Mathematics Project (CMP) is about relating math to student's live.  It's about practical, logical application and practice.  In CMP the teacher instructs and models proper techniques in such a way to "launch" students. The teacher does not give answers, but instead guides students towards answers.  Next, students explore problems collaboratively, and finally the class shares and discusses. While the launching seems to be on the edge of traditional, CMP is primarily inquiry-based.

Closure and Anticipatory Set

Anticipatory Set
The anticipatory set is the introduction of the lesson.  The purpose of the anticipatory set is to get students focused on the upcoming lesson.  It can help activate prior knowledge, and it can get students excited. The anticipatory set should align with the previous lesson.  It should give students an idea of what they will be learning, and it should provide purpose for that learning.

Closure
The closure is the conclusion.  It involves reflection and evaluation.  It helps pull everything together.  IT reinforces the main ideas and purpose of the lesson.  Both the students and teachers should ask: What did we do today? Did we meet our objectives?  What will we do next?


Valuable Resources
http://k6educators.about.com/od/lessonplanheadquarters/g/anticipatoryset.htm
http://www.nancyanddave.com/Motivation.html
http://k6educators.about.com/od/lessonplanheadquarters/g/closure.htm
http://forums.atozteacherstuff.com/showthread.php?t=29266

Practicum: Sharing a Lesson

Fractions are Part of a Whole

Grade Level: 6

Unit: Fractions

Date: 3

Time: 45 minutes

Objectives

• SWBAT define the following: numerator, denominator, fraction
• SWBAT create a graphic organizer that contains strategies that will help them solve arithmetic problems that involve fractions

Prior Knowledge

• Students must already have had experience with number lines.
• Students should have made a Math Burrito Book (BB) the pervious day. A BB is a handmade journal that students take notes in. The BB will have labeled sections which the teacher and students may refer to:

-Cover: define fractions, name

-Vocabulary (1 page)

-Mixed numbers and Improper Fractions Recipe (1 page)

-GCF and LCD (2 pages)

-Adding and Subtracting (2 pages)

-Multiply (1 page)

-Divide (1 page)

-Questions I still have (1page)

-Aha Moments (1 page)

-Back Cover: fractions in real life

Materials/Resources

Teacher: whiteboard, dry erase markers, document camera, pencils, paper, Pizza Worksheet, optional pizza order script

Students: assembled Burrito Book, Pizza Worksheet, pencil, paper

Lesson

Time	Procedures	Monitor/Assess
Set: Make sure students have Math Burrito Books (BB) on desks. Before class begins ask a student to make a phone ring sound when you give them the signal (a nod, wink, point, etc.) Pass 1 Pizza Worksheet to each student. Wear an apron if you have one available. Give student the Signal. Student makes a phone ringing sound.
5 min	Introduction: Teacher pick up fake phone and pretend you're taking a pizza order. See last page for example script. Write the order on a copy of the Pizza Worksheet on the document camera. Have the order be in fractions (for example ½ pepperoni, ¼ cheese, ¼ pepperoni and olives). Somewhere in the beginning of the order cover the phone and say to class “Are you getting this? You better write it down.” At end of order say, “Okay the pizza will be ready in 3 minutes.” Then tell the students they have 3 minutes to draw the pizza.	Teacher: “Are you getting this? Better write it down.” Walk around and observe students pizza sketches. (similar to 4, & 9)
5 min	Ask for volunteers to come to doc cam and draw one fraction of the pizza on the board. Continue until the order is complete. Ask questions such as: What fraction of the pizza has just pepperoni? What fraction of the pizza has pepperoni anywhere on it? What fraction has mushrooms? Collect Worksheets	Student Volunteers complete pizza order on the document camera. Class answers questions. Collect Worksheets
15 min	I do/We do: What are fractions? (take 3-5 responses). Draw a number line on the whiteboard. Above the fractions write: A FRACTION IS PART OF A WHOLE. Have students write this on front cover of BB. Have class say the definition together. How does this relate to pizza? Where would a fraction go on the number line? Ask for examples of a whole number. Where would fractions go on number line?Draw popsicle sticks and have students come to whiteboard and place fractions on a number line.	“What is a fraction?” Class repeats definition. How does it relate to pizza? (Volunteers) Place fraction on a number line (Popsicle sticks) Write in BB
	How do we say fractions? Draw popsicle sticks and have students give various ways of saying fractions. What are other ways to say this? (ex. One half, one over two, one divided by two).	Can somebody please say this fraction? (Draw Popsicle sticks)
	Does anyone know what a numerator is? Denominator? (call on 2-4 students) “Please write this, with an example, in the vocabulary section of your Burrito Book.” Define numerator and denominator.	Does anyone know what a numerator is? Denominator? (Volunteers) Write in BB
10 min	You do: I am going to assign each table group a vocabulary word. I want each table group to then come up with a nonverbal way of defining that word. It cannot include words or numbers. What are examples of nonverbal ways to define vocabulary? Can someone please summarize the directions? Assign each table group one of the following: Fraction, numerator, denominator.	Please give examples of nonverbal ways of defining vocabulary. Can someone please summarize the directions? Walk around and observe progress.
10 min	Share nonverbal definitions. Each table group presents their nonverbal definitions.	Sharing/Presenting
Homework: Students will complete a worksheet titled Fractions in my Home. This worksheet asks students to interview their family members and make observations around their home to find out how they use fractions. Students will share their findings next class during warm up.

Reflection

What's next? Adding and Subtracting. Use M&Ms as a warm-up.

What worked?
       The most well-received part of my lesson was my set. As a warm-up, I pretended to take a pizza order over the phone. I had students write down the order, and then I gave students 3 minutes to make (draw) the pizza. It was effective because I was excited about it and sold the concept. It was upbeat and relatable, which made it engaging.

      I also made sure to get the students up and moving. Whenever appropriate I had students come to the board/projector. I had students draw the different parts of the pizza, and write fractions on a number line. Utilizing active participation helped my students stay on-task and focused.   

What would I change?

      I need to spend more time on the number line concept.  I underestimated student's prior knowledge about number lines.  I will need to cover this more in depth during another lesson.

      I also learned that I need to study-up on my vocabulary. I want to make sure I give my students the most accurate and clear definitions possible. I will conduct necessary research before each lesson and keep that information with my lesson plan materials for reference.   

Adaptations/Modifications

ESOL When walking around and observing students, check on this student at least twice. Student is seated by his classmate/friend who is fluent in both Spanish and English.

TAG The nonverbal group project is open-ended so they may take it to any level

Special Needs ADHD: Assign this student the “ringing” task to help him focus. When walking around and observing students, make sure this student is paying attention and is on task.

Literacy Not applicable to this lesson

Other Not applicable to this lesson

Warm-up Worksheet

Twality Pizza 

I want:

_______Pepperoni

_______Pepperoni & Olives but...

I want ________of that with Mushrooms                                               students draw pizza here

______Pepperoni & Sausage

Phone Script (for teacher):

*RING RING RING*

Hi, Thank you for calling Twality Pizza. Would you like you hear our specials?

We have our Tasty Titan Taco Pizza on special for $9.99. What would you like?

...uh huh, uh huh, uh huh... (cover phone and look at class) Are you getting this down??

(back to phone. slowly) so let me see if I got this... you would like ½ pepperoni, and then ¼ pepperoni and olives.... BUT you want ½ of that with mushrooms. And then the last quarter should be pepperoni and sausage.

Perfect! We'll have that ready to pick up in 3 minutes! Bye!

Did you get that? 3 minutes to get that pizza made!

Warm-ups in Math Education

Based on your research and personal philosophy, what is the purpose of warm-ups in your classroom?

          Warm-ups are a great way to assess students' learning and retention of knowledge.  A teacher may use warm-ups to assess what the class learned from previous lessons.  Warm-ups can help answer the question: Is it time to move one, or do I need to spend more time on the concept?  To do this the teacher may present a problem similar to problems students worked on in the previous class or as homework. 

          Warm-ups are also a great way to find out about student's interests and prior knowledge.  When given prior to a unit, the teacher can use warm-ups as a sort of pre-test measuring what students already know about a topic.  Warm ups are versatile! If a teacher wants to know what students want to learn about a concept, all s/he has to do is ask the students: Where do you use fractions in real life? What do you already know about fractions? What do you hope to learn about fractions? 

          Warmups also become routine.  Routine is an important part of learning.  Routine reduces stress because students know what to expect.  Warmups get the brain focused, and the juices focused.  They help student recall what they recently learned.  The short-nature of warm-ups (5-10 minutes) means students have to think fast.  It helps focus students, and transition them from the subject of their last class (such as U.S. history) to their current class (such as math)--It helps their brain switch gears.  

Appropriate Use of Technology

Walk the Plank

http://www.google.com/url?q=http%3A%2F%2Filluminations.nctm.org%2FLessonDetail.aspx%3Fid%3DL682&sa=D&sntz=1&usg=AFQjCNEXHIXrF9GLee-sZWmiNs55HJme3w

"When one end of a wooden board is placed on a bathroom scale and the other end is suspended on a textbook, students can "walk the plank" and record the weight measurement as their distance from the scale changes. The results are unexpected— the relationship between the weight and distance is linear, and all lines have the same x‑intercept. This investigation leads to a real world occurrence of negative slope, examples of which are often hard to find."  

1. Categories: Learning Objectives, Materials, Instructional Plan, Questions for Students, Assessment Options, Extensions, Teacher Reflection, NCTM Standards and Expectations.

2. Methods and Strategies: This is a hands-on activity using everyday materials.  The teacher holds student interest by using a pirate accent.  

3. Critical Thinking/Problem Solving Observed:  

Why is the slope of the graph negative?

[As the person moved away from the scale, the weight displayed on the scale decreased.]

Why does the weight shown on the scale not accurately reflect your weight?

[The weight shown will be significantly more than your actual weight, because it includes the weight of the plank.]

When a student whose weight was about half of the teacher's walked across the plank, what did you notice about the slope of that student's line on the graph?

[The slope of the line was about half of the teacher's line.]

4. What would I change? The method of assessment is observation and a worksheet.  I would prefer to have students create something more original.  I would have students create something similar to what they would create if they were doing a science experiment. I would relate this to science inquiry (yay for across curriculum teaching). I would have students write about this math "experiment" as they would a science experiment.  What background knowledge do you have?  What is your hypothesis? List the materials procedures, collect and record data, analyze data.

Standards, Standards, Everywhere

Begin by reviewing a simplified overview of the Common Core (CC), NCTM, & District (CMP) standards

• Use the following resources to gain a greater depth of understanding with the middle school mathematics standards. 
• NCTM   |    Common Core    |    CMP 
• Describe how or if these standards harmoniously blend together. Eg, was it a struggle?
• Be specific. Share your assigned standard and experience.

Category: Grade 7-8 Algebra

CMP focuses on "recognizing", "distinguishing" and "identify" relationships and patterns.  It focuses on construction, familiarity and description.  CMP standards suggest that students should have a deep understanding of mathematical concepts.  Students should be able to do more than just compute, they should be able to jusify and explain their answers.  Students should be able to connect one mathematical idea to another through observations of relationships and patterns.  It focuses more on relating math to real, everyday life than NCTM or Common Core.

NCTM was similar to CMP.  It also focuses on identifying relationships as an indicator of understanding.  It also focuses on the connection of mathematical concepts.  Students should be able to "understand patterns" and "analyze."

Common Core is more specific and focused than the other standards.  Students are expected to identify patterns and make connections within the concept of algebra (rather than find connections across the math curriculum).  It does not ask students to justify or explain their answer.  It simply asks students to understand how to find and compute an answer.  It focuses on strategy, accuracy and efficiency. 

Summary: Common Core focuses on accurate, efficient, compuation--whatever gets the math done correctly.  NCTM focuses on building upon prior knowledge about math, and focuses on making connections within the field of mathematics.  CMP focuses on making connections between math and life. CMP conveys the idea that Math should be relevant because it is important and it is everywhere.