## Here are some great math power points! Use during guided math mini lessons

Power points are great tools to use as lesson launches. They can be quick, educational and quite engaging. They are a visual tool that you can accompany with a verbal explanation. I think we need to use them much more when teaching. Here are a few sites with some math powerpoints. I love the fact that many good math powerpoints are already made. And, because they are powerpoint, you can add to them, take stuff away and change them however you want. (Just remember to always give credit to the author of the original powerpoint).

Happy Mathing,

Dr. Nicki

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## Tiered Math Library Resource

Differentiation is the Key!

Here is a great website with a library of tiered math lessons!

http://www.doe.in.gov/exceptional/gt/tiered_curriculum/welcome.html

Happy Mathing,

Dr. Nicki

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## More RTI Math Resources

Here is the IES guide to RTI (federal gov) in Math. It outlines the interventions very clearly, with a discussion about the research findings of each recommendation. Well worth using as a study guide in PD sessions. Everybody that works with students in math should be aware of the information in the packet! Here are the research based recommendations:

Recommendation 1. Screen all

students to identify those at risk for

potential mathematics difficulties and

provide interventions to students

identified as at risk.

Recommendation 2. Instructional

materials for students receiving

interventions should focus intensely

on in-depth treatment of whole

numbers in kindergarten through

grade 5 and on rational numbers in

grades 4 through 8. These materials

should be selected by committee.

Recommendation 3. Instruction during

the intervention should be explicit and

systematic. This includes providing

models of proficient problem solving,

verbalization of thought processes,

guided practice, corrective feedback,

and frequent cumulative review.

Recommendation 4. Interventions

should include instruction on solving

word problems that is based on

common underlying structures.

Recommendation 5. Intervention

materials should include opportunities

for students to work with visual

representations of mathematical

ideas and interventionists should

be proficient in the use of visual

representations of mathematical ideas.

Recommendation 6. Interventions at

all grade levels should devote about

10 minutes in each session to building

fluent retrieval of basic arithmetic facts.

Recommendation 7. Monitor the

progress of students receiving

supplemental instruction and other

students who are at risk.

Recommendation 8. Include

motivational strategies in tier 2 and

tier 3 interventions.

Happy Mathing,

Dr. Nicki

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## Scaffolding is the Key! Small Guided Math Groups is the Place!

Josh Rappaport wrote an excellent piece on scaffolding. He notes that

“No one would attempt to climb Mount Everest in a day. But when we teach math, we often expect something similar from students. We expect them to learn a complex, multi-step process in one lesson, in one hour. We expect them to go from no awareness of the process, to awareness to competence to mastery. And we don’t take account of the fact that many math process[es] require a long ladder of thought steps. In edu-jargon, this process of taking all of the little steps into account — and teaching each step individually — is called “scaffolding.” ”

This is a brillant metaphor. See his whole post.

Guided math groups are an essential part of the “scaffolding” process. In a guided math group you can listen to students talk, you can watch them do the math and give immediate feedback and you can do some direct instruction as well.

I encourage us all to think about “How tall are those ladders we are using in math class?”

Happy Mathing,

Dr. Nicki

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## Great RTI Math Resource: Strategies for Guided Math Groups

RTI is a great structure for planning differentiated interventions! I do a great deal of workshops on it around the country. I find that people struggle with really knowing what research based math interventions look like. As a nation we are really good at knowing and talking about research based literacy interventions! We have to spruce up our knowledge on RESEARCH BASED MATH INTERVENTIONS! Math research is alive and well (as quiet) as it is kept.

Here is a great resource by the Federal Government about how to implement research based math interventions called Doing What Works!

Following the recommendations of the National Mathematics Advisory Panel they state that RTI interventions should:

• For K–5, focus on whole numbers, including place value and addition and subtraction operations with whole numbers

• For 4–8, focus on rational numbers and operations with fractions, decimals, ratios, and percents and complex operations with whole numbers

• Explicitly teaching how to solve word problems using problem types with examples and information about teaching students to identify irrelevant information

• Daily practice on fluency with math facts during interventions and cumulative review

• Strategy approaches to fact teaching, including counting on, deriving facts using properties

This website is filled with resources such as powerpoints and videos. It also has a great deal of information about screening and monitoring as well as actual implementation at all 3 levels.

Happy Mathing,

Dr. Nicki

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## The Magic of Base Ten Blocks: Develop Conceptual Understanding in Guided Math Groups

This is a great site that shows you how to use base ten blocks to develop conceptual understanding of the operations. I would do all of these activities with the students in small guided math groups with real base ten blocks. I would then hold small guided math sessions at the computer so I could use this site to teach at the pictorial level. Finally, I would have the students work with this site during center time.

Happy Mathing,

Dr. Nicki

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## Fractions: Work it out in Guided Math Groups

**Fractions**

The National Math Report has a great deal to say about Fractions. First it notes that although fractions, decimals and proportions are introduced early on, many folks (adults included) still have problems problem solving with them! There should be an emphasis on “**understanding and manipulating** fractions.” This type of work is done in small guided math groups so you can build understanding at the concrete, pictorial and abstract level and you can work with a variety of manipulatives.

* “A fraction is defined as a point on the number line, based on the concept of a part whole relation, with the unit segment [0,1] (the segment from 0 to 1) serving as a whole.”*

The Report notes that to fully assess students understanding we have to **distinguish between the difference of students “formal fractional notation” and “their intuitive ability to understand fractional relations and perform calculations using fractional quantities.”**

Many of the **mistakes **regarding fractions are **due to “faulty procedure. ** Children’s accuracy at **recognizing formal procedural rules for fractions and automatic retrieval of basic arithmetic facts predicts computational skills**, above and beyond the influence of intelligence, reading skills, and conceptual knowledge.”

The research shows that the more they work with fractions the more their conceptual knowledge grows. Most interestingly “**motivation also has positive effects **on fraction learning. **Learning goals rather than performance goals may produce higher self-efficacy, skill, and other achievement outcomes** in students. **Performance goals with self-evaluation** components may **be more effective** than without.”

How do you teach fractions now? How much time do you spend on building conceptual understanding? In the New Common Core, starting at 3rd grade, fractions has its own domain. I encourage everyone to talk on the grade level about the differences between learning goals and performance goals. Note what the report states. Do you have a self-evaluation piece for students as part of your performance goals?

See this great resource from the Center for Comprehensive Reform and Improvement : Beyond Slices of Pizza: Teaching Fractions Effectively

Happy Mathing,

Dr. Nicki

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## Bar Diagramming to Solve Word Problems: Great Strategy to Teach in Guided Math Groups

Randy Charles wrote a must read monograph on word problems. In this article he talks about the two main ways that teachers teach words problems: 1) key word approach 2) Polya’s problem solving phases. He reiterates that research says don’t use the keyword approach! He also makes a good point about Polya’s phases as being a framework, not a step by step guide to solving problems. He goes on to talk about how bar diagramming is a visual approach that provides many possibilities for students to approach word problems. He then gives several examples. READ THE ARTICLE IT COULD CHANGE THE WAY YOU THINK ABOUT WORD PROBLEMS! Let me know what you think!

Happy Mathing,

Dr. Nicki

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## Solving Word Problems Part 1: Work it out In Guided Math Groups

Word Problems are one of the biggest challenges for students in math. In 1977, Australian educator Anne Newman discussed five steps that students need to work through in order to solve a word problem successfully–

(1) reading the problem / READING

(2) comprehending what was read /COMPREHENSION

(3) transforming the words into a mathematical strategy/TRANSFORMATION

(4) applying a mathematical procedure/PROCESS SKILLS

(5) writing the answer/ ENCODING

Her research showed that over 50% of errors that children make occur in the first three steps– before they even begin to solve the problem!

WOW!

She suggested a 5 step protocol for word problem solving error analysis. She would ask the following questions:

1. *Please read the question to me. If you don’t know a word, leave it out.*

2. *Tell me what the question is asking you to do.*

3. *Tell me how you are going to find the answer.*

4. *Show me what to do to get the answer. “Talk aloud” as you do it, so that I can understand how you are thinking.*

5. *Now, write down your answer to the question*.

The five questions link to the 5 processes (noted alongside them). Whereever the student has a break down, this is where the teaching point begins. Now, if asked to rework the problem and the student gets it right and can self correct, Newman labels this as a careless error. All other errors are teaching points. Try this out on your students and let me know what happens.

Reference:

Reference 1 (Be sure to watch the video)

Happy Mathing,

Dr. Nicki

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