11 tips for building a strong Math foundation for kids
During my high school years I spent two summers at the Ross Math Program studying Number Theory and other more esoteric branches of mathematics. The head of the program, Professor Arnold Ross, was not only a brilliant mathematician but he knew how to teach Math to bright students in a way that we all learned some rather difficult Math and really enjoyed it. He taught using a "discovery" method that encouraged exploration and that guided students to bigger discoveries and proofs from simpler ones.
This article incorporates what I learned from Professor Ross with what I've learned from other life experiences.
1. Create a fun environment.
A favorite quote of mine is "Environment is stronger than willpower." For two summers I got to live and breathe the truth of that statement. Imagine twenty or so bright and motivated high school students going to class together, eating meals together, living in the same dorm, working on problem sets (homework) together and you have the makings of too much fun and an awesome learning environment. None of us had to exert too much willpower to thrive in that environment.
Granted, most of you don't have the luxury of this natural learning environment but there are things you can do to lead with fun. If you're in a teaching or helping role, is there a Math club your students or children can join? Can you create one? Can you get a few of the neighborhood kids together one evening or Saturday every week to learn Math together?
If you're working one-on-one with a student or doing Math on your own see my article 10 Ways to get wild about Math for ideas on creating a Math-friendly learning environment.
2. Define success.
From years of personal growth work I've realized the value of having a vision of what I want to achieve. Success for you or your student might be to learn the multiplication table or to be good at solving a variety of algebra word problems, or perhaps to attain a particular score on the Math part of the SAT. Or, success might be an increased self-esteem or greater confidence on Math tests.
Get clear on what you want to achieve, write down the outcomes as specifically as possible, review and adjust as needed, and you'll be well on your way to Math success.
3. Develop a plan for achieving success with measurable goals.
Step 2 was the vision piece. This is the action step.
How can you help your child to better learn his multiplication tables? Maybe the action steps are:
1. You draw the multiplication table, your child copies it.
2. You show him patterns in the table that can simplify learning.
3. You use flash cards to teach the basic Math facts.
4. You have your child create his own flash cards.
As in visioning, the more specific and clear you can be with your action plan the more likely you are to succeed.
Measurable goals are critically important and you can have multiple goals on the way to achieving the big goal. For learning the multiplication table intermediate goals might be:
1. Lower anxiety when working on learning the table
2. Can fill in a quarter of the table by himself using patterns you've shown him
3. Consistently gets half of the flash card problems right
4. Gets 100% of the problems right
A timetable for achieving goals can be very helpful but it can also backfire, especially if you don't have a good sense of how long it should take to learn something. I recommend setting time goals but being very willing to adjust them as needed. Remember, any progress is better than no progress even if it's not as much as you would like to see. Finally, if your child has self-esteem challenges I would de-emphasize the performance aspect altogether and focus on building his confidence.
Math for humans
Since writing my last post I got a copy of Mark Wahl's Math for Humans: Teaching Math Through 7 Intelligences.
Wahl is brilliant. He provides inspiration, explanation, and techniques (with plenty of examples) for using Gardner's Multiple Intelligences to teach Math to students who may excel in one kind of intelligence over another. The 1997 edition of the book I have was written when Gardner's theory included 7 intelligences. The theory now includes 8 intelligences and Wahl's book has been updated to reflect that.
Wahl leads in his introduction with a great story of a second grader he met who was a budding artist, possessing very high spatial intelligence. She couldn't, however, learn (i.e. memorize) her addition tables. Judgment aside about the value of her teacher and parents forcing that she learn the tables in the timetable and not hers, Wahl undertook the challenge to teach her the arithmetic table. He had her make pictures of the symbols in "8 + 7 = 15" on a large index card and then had her make cards for other Math facts. This student was able to learn Math facts by making her own artistic flash cards. She got to learn by using her high spatial intelligence.
The book provides examples of how to "season", as Wahl likes to say, Math lessons with the multiple intelligences (MI). He gives examples for:
- Linguistic Intelligence (writing about what you learned or experienced)
- Spatial Intelligence (diagrams with symbols, flow charts for procedures, visual mnemonics, charts, mind maps, graphs, Venn diagrams, branching trees)
- Musical-Rhythmic Intelligence (clapping, singing, humming, rhythmic movement, rhythmic words, jingles)
- Bodily-Kinesthetic Intelligence (cubes, blocks, Cuisenaire Rods, calculators, and other manipulatives)
- Intrapersonal Intelligence (sharing of thoughts, feelings, and ideas with others)
- Interpersonal Intelligence (discussing of cross-cultural and historical aspects of Math topics)
- Logical-Mathematical Intelligence (deepening the analysis of concepts, posing questions, making connections, furthering exploration)
Wahl discusses brain hemisphericity, how to use left and right brain skills together to do Math. He discusses learning styles, how to use an understanding of a student's temperament to create an environment for succeeding in Math. He explains the value of students working cooperatively toward solving problems. And, Wahl presents a chapter on dealing with Math anxiety.
While the first half of the book presents and illustrates quite a bit of theory, the second half grounds us with concrete examples, quite a number of activities, that apply what we've learned earlier to real-world classroom and tutoring experiences.
All in all, Math for Humans is a fabulous book, chock full of very inspiring information and ideas with tremendous power to help teachers, tutors, coaches, and parents to teach Math in ways that students can really get and enjoy.
10 ways to get wild about Math
Some of you reading this blog might wonder how anyone could like Math. Or, maybe you really enjoy Math but a friend, child, or student of yours hates Math. What can you do to increase your appreciation and enjoyment of Math or to help someone else increase their appreciation?
Here are some suggestions:
1. When you are in a helping role - as teacher or tutor or friend - the relationship is EVERYTHING.
People who don't like Math are often afraid of Math and likely have shame about not being good at Math. Do whatever it takes to not judge the person's struggles with Math. Be supportive. Applaud their successes no matter how insignificant those little triumphs may appear to you.
2. Be aware of your preferred learning style.
Different people learn differently. Sounds obvious, doesn't it? Well, schools don't seem to get it. The traditional lecture benefits mainly the auditory learner which comprises only 20-30% of the school-aged population. I could never learn Math via lecture. I'm very kinesthetic and visual. I need to do Math in a very hands on way and I need to draw lots of pictures to cement my understanding. If you're in a class that's taught in a mostly auditory way and you're not a mostly auditory kind of person then takes lots of notes, draw lots of pictures, use different color pens to stimulate your brain and do lots of sample problems. Here's a good read on learning styles.
3. Beyond learning styles, understand multiple intelligences.
In 1983 Harvard Professor of education Howard Gardner developed the theory that the traditional emphasis on IQ was a very limiting way of measuring intelligence. He proposed that there are 8 different kinds of intelligences that promote a broader sense of human potential. You can read more about Gardner's multiple intelligences in this great article. Understanding Gardner's work gives you 8 different ways to teach or learn Math. The work of Mark Wahl is all about Gardner's multiple intelligences.