Guided Reading for Math?

We often teach math differently than we do literacy, but the language used in math is often not only more complex, but also children come to math often with different levels of understanding. Families have vastly different comfort levels and knowledge of math- and this spread is often larger than traditional language. However children’s number ability is significantly and positively related to their ability to use complex language for number (Uscianowski et al., 2018).

              In my role as an Instructional Coach, I see the barriers that students face when they are unable to comprehend the literacy elements that are embedded within a complex math problem. If students cannot comprehend a math question or problem, then this will be a very large barrier for being able to solve the math.

One of the suggestions that I usually give is for teachers to use a complex math problem in a Guided Reading Group! This is different than guided math, where teachers might work with a small group of students to solve the math problem.

In a traditional Guided Reading group, you are helping students to read for meaning. Guided reading is meant to support independent reading and strategy use. It is not a prescribed protocol, but rather a flexible framework to help meet the needs of the students that teachers are working with. Guided reading, when done well, significantly can increase impact on reading ability.

Why not try guided reading to help students build cognitive, metacognitive and affective skills for reading complex math problems? I encourage you to give it a try.

If you are guided reading for math, here are some suggestions:

  1. Do NOT have students solve the problem. You are working to help them read for meaning. Help them to conceptualize and understand the complex problem. Help them to build common understandings and internalize this. Build strong metacognitive skills, and help them feel positive about their achievements.
  2. Allow students to interact with each other and ask questions. Learning is social, and students need opportunities to learn with others who are at similar levels. Which brings us to the next point:
  3. Help students who are in the same Zone of Proximal Development. The students you are working with should all be able to read the challenging text with the teacher- because they have similar developmental needs.
  4. Put scaffolds in place to help students to be successful while reading the math problem. Some students may need to read the problem aloud several times. Some students may need help understanding some of the vocabulary. Some still don’t understand the math concepts. Some have never experienced the ideas in the first place.
  5. Help students develop the mathematical concepts they need to process the text. They need to internalize the meaning of math problem. They may need help building understanding of some of the concepts. The Big Ideas can be interwoven with the weekly learning goals, or personal learning goals.
  6. Ask good questions. For instance, use questions to build background knowledge – something that many students may not have, but which is essential for developing the ability to read problems independently and internalize the meanings. Ask questions that allow the students to think and make conjectures and develop their own understandings of the math.
  7. Help students to model and represent their thinking. Studies show that when all learners can visually represent their thinking, they develop higher levels of comprehension.
  8. Help students to identify what they know, and what they don’t know orally, and in the form of a visual representation. Please do not have students rewrite the whole question. That can cause frustration and more anxiety about math.
  9. Connect the guided math problems to your weekly mathematical learning goals – make sure that they are real problems that you are teaching, and providing opportunities to solve within math class.
  10. Make sure your guided group meets your math goals.

This is not an exhaustive list, but I am deeply interested in pursuing this idea further.

Some other great comments shared earlier from @MarkChubb include the importance of teaching THROUGH problem solving, and the importance of teaching students how to read a problem. He also shared a word of caution that if our math goal is to improve literacy abilities, then we could miss key points about how to improve our students mathematical understandings.

I am looking to learn more and explore more. So far I have experienced difficulty finding research on this topic in academic libraries. If you are able to give this a try, please share your experiences here in the comments section, or contact me personally!

I would love to hear more!

Deborah McCallum

Reference

Uscianowski, C., Almeda, M. V., & Ginsburg, H. P. (2018). Differences in the complexity of math and literacy questions parents pose during storybook reading. Early Childhood Research Quarterly, doi:10.1016/j.ecresq.2018.07.003

Highlights • Parents ask more complex questions about characters’ actions than number or shape. • Parents with higher reading anxiety ask less abstract character’s actions questions. • Parents who enjoy literacy activities ask more abstract characters’ actions questions. • Child’s number ability was positively related to the complexity of parents’ number questions. • Parents pose more complex questions about number to their sons than daughters.

Feedback in Online Learning Environments – Canadian School Libraries Journal

Feedback in Online Learning Environments – Canadian School Libraries Journal
— Read on journal.canadianschoollibraries.ca/feedback-in-online-learning-environments/

Virtual Reality in the Math Class: Moving from Abstract to Concrete

I have been thinking about Virtual Reality (VR) and how it could support math class. I think that we can help our students develop deeper conceptual understandings of math if we can provide opportunities to help students experience the math in multiple immersive ways. We know that students learn best when they can experience the solutions, versus merely given an algorithm or a rule.

What I also know is that Kyle Pearce has discussed the importance of concreteness fading in his blog, where he describes how students move from concrete to representational to abstract: https://tapintoteenminds.com/concreteness-fading/ – But as Kyle suggests, using manipulatives is still more abstract than what is actually being measured. This is where Virtual Reality can help. What if students had the opportunity to not merely use manipulatives to represent what is being measured, but could actually access and measure the actual object?

When students only have opportunities to memorizing the tricks, tips, algorithms, and rules only, they lack the depth of understanding of the mathematical concepts.

But if we are moving students to abstract thinking as shared in Kyle’s blog, we also have to acknowledge that if the goal is to help students transfer their knowledge abstractly to new math, this won’t necessarily mean that students will continue to be able to engage in adaptive reasoning, conceptual understandings, and further justify mathematically what is actually going on in new problems. Merely moving to the abstract is not sufficient enough. Staying abstract can and will likely greatly affect their ability to transfer knowledge to new mathematical problems.

Ruth Beatty addresses this very issue in here video, where she discusses the importance of not just moving from concrete materials to abstract, but also important to move from abstract to concrete:

Here, Ruth basically describes the importance of allowing students to construct their understanding of the world by actively constructing their own understandings of the math with multiple representations, with more interactions, connections and meaningful experiences.

I think that this is great support for why VR could work in the mathematics classroom. Students can use VR to NOT just replace concrete representations to manipulate, NOT just to build patterns, but to ALSO interact with a wider repertoire of experiences and representations.

Therefore, the concreteness comes from not just working with manipulatives, but from our multiple relationships and personal interactions with objects, patterns & ideas – so any concept can become concrete through the use of VR – to provide multiple models and ways to interact with the mathematical concepts.

If we construct our understanding with multiple experiences, the concepts can become concrete in the minds of our students. VR as a way to provide more experiences and representations, and ways to interact with to create lifelong and personal relationships with the concepts – not just with the mathematical terms and algorithms themselves. Therefore, we can have students move from abstract to concrete with VR.

Have you done this in your math class? If so, what did you learn?

Deborah McCallum

Virtual Worlds Database

The Careful Consideration of eLearning – Deborah McCallum – Medium

https://medium.com/@DeborahMcCallum/the-careful-consideration-of-elearning-79feedd18082

Mrs Golding’s Musings: Article Study: A Measure of Concern

Mrs Golding’s Musings: Article Study: A Measure of Concern
— Read on mrsgolding.blogspot.com/2019/03/article-study-measure-of-concern.html

Executive Functioning in Math

https://medium.com/@DeborahMcCallum/executive-functioning-in-math-5aa383deb28a

Make your Feedback more Productive – Deborah McCallum – Medium

via Make your Feedback more Productive – Deborah McCallum – Medium

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