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.