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Thursday, September 26, 2013

Math Review: Why, What, and How

Are you struggling to understand how to implement Math Review in your classroom? If so, you are not alone. Here are some helpful tips about why and how to incorporate math review.
Why Math Review
1.      Promotes mathematical reasoning and number sense
2.      Based on research and includes research-based practices that are effective with students, including repeated reasoning, effective feedback, and relational thinking
3.      Helps fill in the gaps
Components of Math Review
1.   K-1 Math Review should be focused on number sense, such as quantities and number order
a.   Shapes can be added later in the year when students have a strong number sense understanding
b.   K-1 should have manipulatives for every student to do all problems.
2.   Problems should be based on prior learning (can use TEKS Scaffolding document to help)
3.   10 - 15 minutes per day (for entire Math Review); There should be an additional 60 minutes (at least) for core instruction
a.   For 6-8 minutes, students work with a partner to discuss and complete math review
b.   Remaining 6-8 minutes should focus on processing the math review
3.   Includes specific feedback (through error analysis)
4.   Teacher models metacognition (NOT interactive)
a.   Teacher models 1 strategy the entire 1-2 weeks to solve similar problem types; Every student uses that strategy; For example, if one math review problem is addition with regrouping. If the teacher chooses base ten blocks to model how to solve the problem, students should also and the teacher uses this same strategy for the 1-2 weeks
b.   Multiple strategies can be taught during core instruction, but focus on 1 strategy in math review
5.   Includes error analysis
6.   Includes student reflection (for every problem)
a.   Younger students reflect orally
Reflections in Math Review
1.   Reflect on every problem
2.   Students reflect after processing
3.   Require vocabulary from key idea statement
4.   Younger students reflect orally
5.   K-1 does one problem at a time. Processes it, then reflects.
6.   Example reflection starters: I was successful at _____. I need to work on ______. I remembered ______. Tomorrow I want to ______. I need to remember ________.
Key Idea Statement
1.   Includes academic vocabulary and key understanding
Sequence of Processing Math Review
1.   Error Analysis
2.   Reflect
a.   Students write it. Share it with a partner. Have a few students share out.)
3.   Key Idea Statement
a.   Teacher says it. Students repeat it. Students say it to a partner. Students write it.
**Remember this: 24 Positive Exposures to a concept for 80% Mastery**


Tuesday, September 24, 2013

What does = really mean?




Do your students have a true understanding of what the equal sign truly means? If you showed students this equation: 2 + 4 = ___ + 5, would they give the answer 6? If you showed them this problem: _____ = 3 + 7, would they get stuck? How do we get children to understand that the equal sign is just a symbol that means that both sides have the same value. One way to help students understand the relational meaning of the symbol is to teach the concept of balance.

Donna Boucher from Math Coach's Corner has a great activity to get students thinking about the meaning of the equal sign. Check out her links below. They have great resources for this concept. 
http://mathcoachscorner.blogspot.com/2013/07/a-peek-inside-whats-cookin-meaning-of.html
http://mathcoachscorner.blogspot.com/2012/11/the-meaning-of-equal-sign.html

I love the Math Coach's Corner.




More with graphs

Now show the students this graph and have them compare the two. Do both graphs show the same data? How do you know? Have students defend their answers. Could be a good discussion. 



Interpreting Bar Graphs

Interpreting bar graphs seems like a simple concept. But if we go deeper it can be very complex.As I was reading my current issue of NCTM's Teaching Children Mathematics magazine last night I came across a graph that at first glance seems so simple. Then I took a second look.

Having students determine the number of pockets that day could be a challenging task and lead to a great discussion. You could also have students talk about what each column means. Can they compare the columns using math vocabulary correctly. What questions could your students write that would ask children to interpret the graph in other ways?


Processing Math Review

Math review is a time to clear up students' misconceptions and to focus on one strategy (per problem). The same strategy should be used by the teacher and students for 1-2 weeks. When processing the math review, it is not a time for the teacher to do an in-depth lesson. The teacher should process the math review at a perky pace, and any in-depth teaching that needs to be done should occur during the teacher's core lesson time.

For many teachers it is hard to understand what "processing the math review" might look like. The video below shows an example of how to process a math review problem.


The video shows how to use a place value chart to order numbers from greatest to least. Students would be expected to use the strategy of drawing a place value chart to order numbers for the entire 1-2 weeks of completing similar problem types during math review. 

Monday, September 23, 2013

Math Review: To Do or Not To Do

Math Review is an important component of Balanced Math. The purpose of math review is to promote mathematical reasoning and number sense. Here is a simple list of things to do or not do for math review. This list was created by a wonderful teacher at one of our local elementary schools.




Tuesday, September 3, 2013

Computational Fluency

Students can develop computational fluency using a variety of strategies.
What is Computational Fluency?
Students should be computing fluently with whole numbers. Computational fluency refers to having efficient and accurate methods for computing. Students exhibit computational fluency when they demonstrate flexibility in the computational methods they choose, understand and can explain these methods, and produce accurate answers efficiently. The computational methods that a student uses should be based on mathematical ideas that the student understands well.  Fluency with whole-number computation depends, in large part, on fluency with basic number combinations—the single-digit addition and multiplication pairs and their counterparts for subtraction and division.  Fluency with the basic number combinations develops from well-understood meanings for the four operations and from a focus on thinking strategies (Thornton 1990; Isaacs and Carroll 1999).
Principles and Standards for School Mathematics,
National Council of Teachers of Mathematics, 2000

Here is a sample of a few problem situations that can help students develop their computational fluency and demonstrate flexible strategies. Click on the title below for you copy. 


Primary Paradise: Make A Ten Math Strategy

This is a great "make ten" activity.
Primary Paradise: Make A Ten Math Strategy: OK today I felt a little old,  well really a lot old.  Many years ago I saved these little guys after taking pictures the old fashioned way...