Wild About Math! Making Math fun and accessible

Good storytelling ability related to good mathematical skills

Science News Online just published a fascinating article: Good Stories, Good Math. The article is subtitled: "Preschoolers who can tell good stories develop good mathematical skills by the first grade." Writer Julie Rehmeyer reports on a new study which reveals that there's apparently a very strong connection between mathematical ability and the ability to tell stories from different perspectives.

The researchers found that 3- and 4-year old preschoolers who were able to tell stories and switch perspectives while doing so performed better in mathematics 2 years later. An example of switching perspectives is this comment from a child:

"The waiter was mad when the frog jumped in the soup."

The child was managing multiple relationships, simultaneously keeping track of how the waiter was feeling and of what the frog was doing.

While I had never considered such a relationship, it makes sense to me. Mathematics is all about managing relationships between "things." It's about being able to think abstractly. Storytelling shares these characteristics, even though the storytelling abstractions are about people and what they might be thinking and feeling, and not mathematical abstractions.

An interesting refinement that the researchers made was one that allowed them to make a distinction between mathematical skill and skill in arithmetic. They are not the same skill and many people who are mathematically gifted perform arithmetic poorly.

The study is based on the work of Stanford University mathematician Keith Devlin. Rehmeyer explains that in Devlin's book The Math Gene, he argues:

"...that language arose when humans acquired the ability to visualize complex relationships among different objects when the objects themselves are not in view. The ability to do mathematics arises from that same ability to manipulate abstractions."

The implications of this study are huge. Can students be taught abstract thinking skills early in life through storytelling and improve their future mathematical ability?

How to get past “stupid” Math mistakes

I was recently asked how I deal with silly mistakes many of us make in algebra or arithmetic, especially in the context of a tutoring session. Common errors include forgetting to carry numbers when adding, getting confused about operating with plus and minus signs in one problem, and multiplying two digits incorrectly.

I consulted Michael Sheppard, director and lead educator for Big Sky Learning Center in Santa Fe. Michael shared a number of suggestions based on his 19 years of experience teaching kids in one-on-one and group settings. I've combined Michael's excellent suggestions with some of my own:

How kinesthetic folks learn Math

I'm not a Math teacher yet I feel I'm highly qualified to write on this topic. I am a lifelong Math learner and I am highly kinesthetic. Being kinesthetic means I am highly sensitive, I love to touch things, I enjoy moving my body, and I am aware of my feelings. In some ways I learn Math (and most everything else) differently than most teachers teach. This article shares six ways I engage my kinesthetic intelligence in learning Math and solving problems.

1. Being Hands On

This is perhaps the most obvious way us kinesthetic folks learn. If I'm solving a problem I have to make a picture. Part of drawing is about engaging the visual senses but a big part is about using my hands, touching the pen, and moving it along the paper. While I haven't gotten myself organized to gather together pens and pencils of different textures and colors and paper of different thicknesses and colors I'm sure these things would be helpful to myself and to others.

I also enjoy making paper models of mathematical things, cubes, Moebius strips, and other "manipulatives".

If someone describes a problem to me, or if I read it in a book or online I have to record it on paper, to make the problem mine and to fully engage with it.

As a side note, a huge part of my enjoyment of blogging is the kinesthetic pleasure I derive from typing on the keyboard. Really.

2. Moving and Pacing

I don't sit still. Learning involves movement. Often when I'm solving a challenging problem I'll be walking around the house, holding the picture I just drew, and pondering the solution. My body is just too restless to be still. Somehow my entire neurological systems seems to get engaged when I'm in motion and my creative thinking becomes enhanced. If I'm sitting down my legs will move, or sometimes I'll tap with my feet. And, I'll be tuned into the sounds and sensations around me.

3. Music and rhythm

Music doesn't only affect the aural senses. It also stimulates the kinesthetic senses. If you don't believe that, ask yourself if you've ever been moved by a piece of music, maybe even been moved to tears. I have.

I find it very helpful to have either music playing or white noise, like the hum of a computer monitor, when I'm thinking creatively. Think "The Mozart Effect", which is all about the positive effects of classical music on learning.

Some people learn by getting in sync with a rhythm. I have no doubt that some kids would learn to count much more quickly and easily if they counted while skipping rope, or while hopping, or maybe as they drummed or performed some other rhythmic activity.

I've even heard of kids who couldn't learn to read until they incorporated singing into the approach. Wow!

Review: What SUCCESSFUL Math Teachers Do, Grades 6-12

Alfred Posamentier, one of my great heroes, and Daniel Jaye have collaborated to produce a discussion of "79 Research-based Strategies for the Standards-based Classroom", which is the subtitle of the book, What SUCCESSFUL Math Teachers Do, Grades 6-12.

Posamentier is dean of the School of Education and Professor of Mathematics Education of the City College of the City University of New York. He has written a number of books that inspire teachers and students to approach Math with a sense of wonder. Jaye is the assistant Principal for Mathematics at Stuyvesant High School, a school for gifted students in New York City.

The book has 6 chapters:

1. Managing Your Classroom
2. Enhancing Teaching Techniques
3. Facilitating Student Learning
4. Assessing Student Progress
5. Teaching Problem Solving
6. Considering Social Aspects in Teaching Mathematics

Additionally, there's a resource section where the authors list over 100 topics for classroom exploration.

Each chapter consists of a number of teaching strategies. Each strategy is methodically broken down into:

1. Title of the Strategy
2. What the Research Says. This section refers to and describes specific studies that support the strategy being discussed.
3. Teaching to the NCTM (National Council of Teachers of Mathematics) Standards. This is an important section in that it explains how employing a particular strategy meets one or more specific principles or standards of the NCTM.
4. Classroom Applications. This section explains and lists ways to implement the strategy in the classroom.
5. Precautions and Pitfalls. This section alerts teachers about potential obstacles to realizing the goal of the strategy plus recommends ways to avoid these traps.
6. Sources. These are the references to the research behind the strategies.

The book is comprehensive, well organized, and thoroughly researched. Although I'm not a teacher or student these strategies all seem very valuable to me.

Some of my favorite strategies include:

1. Strategy 16: Find out about your students' motivation regarding mathematics, and use that knowledge to refine your instruction.
2. Strategy 19. Praise mistakes! This strategy addresses the shame and anxiety that many students feel in the classroom.
3. Strategy 33: To reduce math anxiety, focus on both the thoughts and the emotions of the students.
4. Strategy 63: Emphasize the general principles that underly solving specific types of problems.
5. Strategy 69: Find out about your students' families and how their values and practices might affect students' attitudes and performance in mathematics.

Posamentier and Jaye clearly know what they're talking about, both having spent considerable amounts of time in the trenches and both caring very deeply for the success of their students. Their competence shows in the tying together of strategy, research, and application in support of NCTM guidelines. Their caring shows in the overall tone of the book.

I highly recommend this book to all teachers, coaches, and tutors. As a Math tutor and mentor I found a number of important considerations to incorporate in my work with students.