## More Problem Solving Rubrics: Teach to the Whole Class, Review in Guided Math Groups

Math Word Problem Solving Rubrics give students an opportunity to see where they are and where they need to go. Rubrics should be used as part of a conversation. They should provide some specific feedback about what’s great and what’s still in progress. Ideally, once students receive the feedback they get a chance to incorporate it as part of their learning journey. In other words, they should get a chance to fix what they got wrong:) You can discuss specific problems and errors in individual conferences or in small guided math groups. Gather students together who have made the same errors and discuss how to correct those errors. Here are some examples of word problem rubrics:

Example 3

Example 4: Click here (if it doesn’t download then Google this term *Word Problem* PTA (Scoring *Rubric*)

Happy Mathing,

Dr. Nicki

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## Beyond Answer Getting: Guided Math Group Work

Here is a must see video by Phil Daro on the need to teach our students more than “answer-getting” (click on the second tab at the top). Guided math groups is a space to help students really talk about the math they are learning. You want to guide conversations, guide conceptual understanding, guide procedural fluency and guide strategic competence building in a small, comfortable, academically rigorous learning situation. Three key elements of guided math group work:

1. Time to talk (each person gets to explain their mathematical thinking and their understanding of the thinking of others)

2. Time to listen (each person gets an opportunity to focus and try to comprehend the math that we are speaking about)

3. Time to practice (with the help of each other and the teacher, students will practice the math)

Whether you are working at the concrete, pictorial or abstract level, students need to know what the math is that they are working on. This should be explicit. We all have to seriously consider what it means to teach math and not answer-getting.

Happy Mathing,

Dr. Nicki

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## More about Fractions: Do the Work in Guided Math Groups

The National Math Report said a great deal about fractions in elementary school. Here are a few of the research highlights (p 17-18):

**Pictorial representations, without sufficient emphasis on the nature of wholes**…**may be an obstacle***Number line representation may be more effective.***Words**also seem to**influence the mental representations**that children form concerning fractions

*Recommendations*

**Focus on conceptual knowledge first****Procedural knowledge is equally important**

**Successful Interventions include:**

- the
**use of fraction names that demarcate parts and wholes**, **the use of pictorial representations that are mapped onto the number line**,**composite representations**of fractions that are**linked to representations of the number line**.**Conceptual and procedural knowledge about fractions less than one do not necessarily transfer to fractions greater than one, and must be taught separately**.

** ****Curriculum: **

**Spend time doing fractions and proportional reasoning…** with the *goal for students being one of learning rather than performance*. However, there should be **ample opportunity in the curriculum for accurate self-evaluation**.

What do you think of that? Number lines are big here! Pull out the number lines when you teach fractions…Also, self-evaluation keeps coming up. Do you give your students time to self-evaluate? How does that look across the grade levels? Notice the emphasis on a learning rather than just performing. We want students doing WITH understanding!

Happy Mathing,

Dr. Nicki

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## Graphic Organizers for Vocabulary Work: Guided math lessons

I am so excited. I found a great site with tons of graphic organizers. They are randomly listed so I have organized them by concept. I will post them during the next few days.

To start with, here are 2 great organizers for having students concretize their learning for the week. They are really well done- but I love the first one. I highly encourage everyone to use some version of this because it helps students to use the vocabulary and talk about the big ideas that they learned for the week. Take a look. And BIG BONUS—It comes in Spanish too!

Vocabulary and Goals/Standards

http://teacher.depaul.edu/Documents/ThisWeeksMath.pdf

http://teacher.depaul.edu/This%20Week%27s%20Math%20Feature.pdf

Vocabulary and Goals/Standards

http://teacher.depaul.edu/Documents/ThisWeeksMath-Spanish.pdf

Happy Mathing,

Dr. Nicki

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## The Importance of Students Setting Their Own Math Goals: Part 2

Happy New Year!

Hello Everyone. Happy New Year! I wish you all an abundance of rich mathematical experiences this year. What are your math goals? What do you want to do as an educator? What do you want your students to be able to do? I am currently doing some research on student goal setting and how it looks across the grade levels. Please write in and tell me what you do in terms of setting math goals with your students.

One thing I have been doing is having students reflect on their math tests! This can be done individually, in small guided math groups or the whole class could be filling out the form at the same time. This has been so amazing. I have developed a few forms but the gist goes like this:

- Take a look at your math test. What’s the first thing you think? How did you do overall?
- What was easy?
- What was difficult?
- What do you still need help with?
- What is your plan to learn the concepts you need to work on?

Here are some sites I have found interesting in terms of students setting goals:

Student Goal Setting Templates:

2 of my favorites from the link above:

http://worksheetplace.com/mf/goali.pdf

http://worksheetplace.com/mf/goala.pdf

Another good template:

http://specialed.about.com/od/worksheets/ss/goalsetting_2.htm

Have your students set math goals online:

http://www.googolpower.com/content/math-facts-challenge

Scroll Down to Goal Setting: I especially like the mini-goal template and the secrets of goal setting poster…

http://www.educationworld.com/tools_templates/

Cedar Rapids Schools students at work setting goals:

http://quality.cr.k12.ia.us/Photo_Album/Goal_setting/goal_setting.htm

Great Article

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2846585/

Happy Mathing,

Dr. Nicki

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## The Importance of Students Setting Math Goals

It’s a New Year! It’s time to think, reflect and plan…that leads me right into a discussion of setting math goals with students. The research shows that verbal and visual feedback on performance has an impact on student achievement! Students need to know how they are doing and how to get better at it. They need time to process that information. The research shows that when feedback is displayed in a graph format students “get it” even more (Fuchs & Fuchs; Gunter, Miller, & Venn, 2003; Sutherland & Snyder, 2007 cited in Figarola, Gunter, Reffel, Worth, Hummel, Gerber 2008). Moreover, researchers found that when students received feedback and set goals, they got better in math (Codding, Lewandowski, and Eckert 2005 cited in Figarola et. al 2008 ).

Figarola et. al, found that students both with and without dis/Abilities could benefit from using computers to graph their math progress. These researchers argue that once teachers figure out how to automate the process of graphing the data, that it is easy and that “graphs serve as a powerful visual means to document student progress on an ongoing basis and can be shared with parents and administrators.” Also, teachers can make quick instructional decisions based on the graphs.

Try graphing the data and having your students set goals based on that data! When students know where they are going, they are much more likely to get there!

References:

(See this article about first and second graders graphing the data and action planning and not only meeting but exceeding their goals!)

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2846585/

Happy Mathing,

Dr. Nicki

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## What are you doing everyday? Things to think about for Guided Math and Whole Group Conversations

In 1933, Dewey suggested that:

When the teacher fixes his attention exclusively on such matters as these [the acquisition of skills and knowledge], the process of forming underlying and permanent habits, attitudes, and interests is overlooked. Yet the formation of the latter is more important for the future. (1933, pp. 57-58) (cited in Merz, 2009).

Do you agree? Isn’t it at least just as important to shape habits, attitudes and interests as it is to teach them their multiplication tables or how to divide fractions? How we teach is just as important as what we teach? At the end of our lessons, do our students feel like, “Whew, I’m glad that’s over with.” Or do they walk away wanting more, desperate for the next lesson?

I love this quote because I think *Dewey reminds us that we do teach and touch the future*. What we do daily, will affect them for the rest of their lives. And they will either walk away from your class, thinking they are capable, that smart is learned, that they can do it if they try, or that they can’t and they hate math.

If as Dewey states, “the latter is more important for the future”- habit, attitudes and interests, how do you then begin to think about teaching more than 3 x 4 =- 12?

How do we teach this too? We set up spaces to cultivate great habits, attitudes and interests. All of our moves, many of them implicit shape our students attitudes. We have to be attentive to how each step we take shapes this for them.

Guided math groups provide us a special space to cultivate these aspects of learning math because we can give more individualized attention. We can attend to these in our groups and coach our students more one to one.

Any thoughts? Please share:)

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## Teaching staying power, sticktoitness and the right attitude: Mathematical Disposition and Guided Math Lessons (Part 5)

Polya (1969) [the grandfather of problem solving] states: *This is the general aim of mathematics teaching – to develop in each student as much as possible the good mental habits of tackling any kind of problem. You should develop the whole personality of the student and mathematics teaching should especially develop thinking. Mathematics teaching could also develop clarity and staying power. It could also develop character to some extent but most important is the development of thinking. My point of view is that the most important part of thinking that is developed in mathematics is the right attitude in tackling problems, in treating problems. (Part II, pp. 5-7) (cited in Merz, 2009).*

Polya provokes us to think about what we do everyday. He says that we are charged with developing in students ” the good mental habits of tackling any kind of problem.” We have to come up with rich math tasks so students can engage in this type of thinking. And, dare I say most of those types of problems are not on page 47 in problems 3-10:) **Real problems, with real contexts helps students to see that math is a real subject. **

What do you think of his statement that we should “develop the whole personality of the child and math should develop thinking?” This idea makes math class look very different from many teach, test and move on scenarios. If we are teaching to develop personality and thinking, then what on earth does that look like?

Polya goes on to state that teaching math is about teaching character, staying power and the right attitude.

Let’s all think about how we write that into our lesson plans!

References:

Merz, A. (2009). Teaching for Mathematical Dispositions

as Well as for Understanding: The Difference Between Reacting to and

Advocating for Dispositional Learning. *Journal of Educational Thought*

Vol. 43, No. 1, 65-78.

Polya, G. (1969). The goals of mathematics education. Retrieved March 3, 2005, from http://www.mathematicallysane.com/analysis/polya.asp.

Unpublished videotaped lecture presented to T.C. O’Brien’s

mathematics education students

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## Mathematical Disposition: More than an attitude (using guided math groups to foster the many aspects) Part 4

Much has been written about mathematical dispositions or ways of thinking and being NCTM (National Council of Teachers of Mathematics, 1989, 2000) and others (e.g., Maher, 2005; De Corte, Verschaffel, & Op’T Eynde, 2000: Polya, 1969). The research tells us that mathematical disposition is much more than an attitude. It is about ways of thinking, doing, being and seeing math. It includes confidence, flexibility, perseverance, interest, inventiveness, appreciation, reflection and monitoring (Merz, 2009).

Given that, how do you cultivate each one of these in your class?

- What do you do to
**boost students’ confidence**? Name 2 things. What could you do? Name 1 more. How might you do this in a guided math group? Since you only have a few students in a group, you can attend more individually to each one. One way to do this is to give problems that they can do. Success breeds success and confidence.

2. What do you do to help **foster flexibility**? This idea of thinking in many different ways? Do you engage in ongoing strategy talk? Do you have a culture of sharing in your class that goes beyond the answer but talks about how people got the answer or didn’t get it?

3. What do you do to **build perseverance**? How do you teach that? How do you do that? So that students’ perseverance levels increase over time?

4. What do you do to **spark interest**? How do you connect math to their lives? Where is the math in Pokeman or Dragonball Z?

5. What do you do to **encourage inventiveness**? Do we publicly celebrate inventive thinking? How do we get our students to think hard about the math their doing and take risks?

6. What do you do to **cultivate appreciation of math**? Do you make connections to real life situations that are important to them so students see that math really does matter?

7. How often do we get them to **reflect about the math** they are learning? Do we consistently use entrance and/or exit slips so they can think about their learning? Do we use individual pupil responses like thumbs up, thumbs down or sideways to check in with them? Do we use red, green, and yellow slips so they can give us immediate feedback about speeding up the lesson, slowing down the lesson or stopping to explain further? Do we ask them to do oral and or written reflections on their quizzes and tests and make plans to learn what they are still struggling with? You can do this in small guided math groups! This is an excellent space for these types of discussions.

8. How do we get student’s to **monitor their learning**? Do they have action plans that they reflect on? Who is responsible for knowing where they are? Just us? Think about how powerful it would be if they knew too! And if their parents knew, more than just a few times a year. The more people who know, the more likely the student is to get there! Think of the power of everybody being on board. What does a consistent inclusive monitoring system look like?

References:

Alice Merz

Journal of Educational Thought

Vol. 43, No. 1, 2009, 65-78.

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## What they think

It ‘s really important what students think about themselves, about us and about each other. Students should think they can. Really. Just like the choo choo train did. The research shows that if they they can, they’ll keep trying until they do. Resnick (1999)wrote a great article about the conceptualization of “smartness” in America (see reference below). If our students really believed they could, with the correct instruction and encouragement, they would.

Furthermore, the recent National Math Report (2008) states that what children believe about what they can do matters. It matters in a big way. It discusses how when children believe in themselves, they try harder, they put more effort into learning math and that effort increases their engagement, which in turn raises performance.

They would be able to do so much more than we can even imagine. Moreover, if they thought that we were really on their side, batting for them, cheering them on, searching every kind of way to help them learn it (whatever “it” might be); if they were truly convinced that we were there to teach them until we reach them, they’d try harder too. Finally, if they became cheerleaders for each other as well, really concerned about the learning of each other– helping each other and encouraging each other…they’d do better. I really believe they’d do much, much much better:)

Referenceshttp://www.fwisd.org/math/Documents/MakingAmericaSmarter.pdf

http://www2.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf

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