Wild About Math! Making Math fun and accessible

2Nov/0710

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.

4. Understand the student's preferred learning style and teach to it, or use a multi-sensory approach.

There are many books and web articles about how humans learn. There's the multiple intelligences model developed by Howard Gardner. There's the left-brain/right-brain model. And, there's the Myers-Briggs Type Inventory (MBTI) that can provide insights into how students solve problems. There are lots of other analysis tools out there as well.

Use the models and assessment tools you're drawn to and find helpful or start with your intuition about how you or your child learns. In many cases, children inherit approaches and attitudes to learning either through environment or genetics. So, looking at how others in your family learn may give you insights about how you can best learn.

If figuring out your (or your child's) learning style is more than you're up to, or if you're teaching multiple students with likely different styles then try a multi-sensory approach. This could include simultaneous use of multiple approaches:

1. Using different colors to stimulate learning
2. Using pictures, graphs, diagrams, flowcharts, and other visual tools
3. Writing text on a white board
4. Having students copy the text into their notebooks
5. Verbally describing what you're teaching
6. Asking students to explain to you or to each other in pairs or small groups, what they're learning
7. Using manipulatives to engage the kinesthetic sense

5. Build a network of resources.

Don't go it alone. Network with friends, parents, Math teachers and others to help you out when you or your child gets stuck on a problem. Have someone to call when you're feeling discouraged. Find some good books and web-sites to help with approaches to teaching Math. Join some Internet forums.

6. Create structure.

As I increase my blogging activities I find myself needing more and more structure. If I decide I'm going to focus for one hour on producing useful content I find that the structure created by the time pressure helps me. Things that you might find helpful with Math are:

1. Setting a regular time for doing Math. Unplug the phone and get away from the computer during Math time to minimize distractions.
2. Having a regular place for doing Math. Maybe a favorite room or a particular table in the living room or dining room.
3. Collecting all your "Math stuff" in one place. That includes paper, pencils, sharpener, compass, protractor, the text book and your notebook and homework assignment.
4. Having your written list of goals in front of you so you know exactly what you're intending to achieve in your perfect learning place in the amount of time you've set aside.

7. Guide their exploration.

When helping someone to learn Math, develop the attitude that Math is a process of exploration, not a pile of boring techniques that lead to a right or wrong answer. Help your student by leading with this attitude. If your student is struggling to solve quadratic equations, for example, here are some exploration-oriented activities you could lead:

1. Look for patterns in solutions to equations that look similar but are slightly different.
2. Try completing the square rather than plugging numbers into an equation.
3. Graph the equation on paper, with a graphic calculator or computer program, and finding solutions that way.

The idea here is to get your student engaged and in relationship with what they're learning. Finding patterns and seeing other ways to getting to an answer are great approaches to getting past the sad fundamentalism that I so often see that says there's one right way to solve a problem. Once you know several ways to solve a problem you can always go back and learn it the way the teacher wants to see it done on the test.

In Professor Ross's homework assignments it was all exploration. Every single problem (over a dozen on most days as I recall) was an exploration problem. Finding patterns was the order of the day.

8. Assess gaps in knowledge.

This may seem obvious but it's worth stating explicitly: Don't do the harder stuff until you can do the easy stuff well. Finding the gaps in your knowledge (or child's or student's) is the first step in building Math skills. If you can't factor or solve quadratic equations make note of that then get good at quadratics before tackling cubics which, by the way, are much harder. Without a solid background in algebra, geometry will be very difficult as geometry uses algebra extensively.

Don't assume that because someone is in a particular grade that they have the requisite knowledge and skill to proceed to the next level. If you're having a tough time with a particular type of problem then try to figure out where you're stuck, what simpler and related problems you can solve, and what you're not understanding. Get a friend or teacher to help you with this assessment if you need it.

9. Strengthen the foundation.

Once you know where the holes are in your learning, it's time to fill them. Note: it's not shameful to have holes in your knowledge. We all do. I did well with many different branches of Math in school but geometry was a subject I shied away from and didn't really understand very well even though I did ok in geometry courses. Now, 30 years later, I'm teaching myself geometry from books and I'm enjoying actually developing a more solid foundation, starting from very basic axioms and theorems.

Find a good book in the subject you're filling holes in and go through exercises in the book, chapter by chapter. If the book is thick but your holes are few then perhaps do just a handful of exercises in each chapter until you've discovered the places where you're stuck then study that material carefully. Start with the easy problems. This will help to build confidence.

10. Aim for understanding and finding patterns over memorization or technique.

I'm not a fan of memorization, partly because it's not a great skill of mine, but mostly because it reinforces the idea too many people have that Math is this dry thing devoid of any life or meaning. So many students are taught in school to memorize some technique and plug numbers into it to get the "right" answer. Ugh!

I have found that memorization and technique comes with understanding. Professor Ross taught us "Think deeply of simple things." That teaching has served me well. I always strive to understand things by looking at them closely and deeply and finding simple aspects of problems I'm exploring. Once I've understood something and practiced solving related problems a number of times the technique and memorization come with no effort and the satisfaction is much deeper.

11. Celebrate and build on small successes.

If you've followed the advice in this article you will achieve some nice successes over time. Celebrate each one. Celebrate that you are less anxious when you open your Math book. Celebrate that you now understand how something works that you had only memorized before. Celebrate that you identified and filled a gap in your education.

How do you celebrate? It can be as simple as giving yourself a pat on the back, bragging to your friends, or buying yourself a little treat. The idea is to acknowledge then reinforce the success and use that success to get to the next level.

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  2. Nice article

    Definitely agree with “aim for understanding or finding patterns rather than memorization or technique.”

    Although memorization of formulas and equations are useful, it is really important to understand how or why they work, so that they can be applied to a number of different instances.

    Mark

  3. I liked this article, it had many good suggestions for me as I prepare to teach math in elementary school. I think that the teacher’s enthusiasm makes a big difference in a classroom. When I was growing up in the late 70’s and early 80’s, I don’t remember a single one of my math teachers excited about math. When it came time to learn math, I watched a few problems demonstrated on the board of how to solve, and then we were left on our own to do the 20-30 problems in a book. I mostly remember having a few minutes to start the problems in class, but by the time I was home, and finishing the other problems, they became more complicated. When I would ask my parents to help, my mom would go and read the lesson, or unit, and reteach the best she could my concepts. My dad, a math minor in college, would show me a completely different wat to get to the answer and this only confused me more, probably even damaged my relationship with him. Math became this frustrating jumbled up maze of steps and procedures that were always hard to keep straight and know when to apply one set of rules to the right set of problems.

  4. I think these 11 steps really would make a difference for ALL students, including those who are kinesthetic learners, English Language Learners, and so many others. My environment was sit down, be quiet, watch the teacher solve everything on the board (because they were smarter than the rest of us) and then try to apply the same steps to my own set of problems. There was no discussion, no thinking through problems, no journaling, no talking among peers to arrive at solutions. What a shame!

  5. Number and operations. This article emphasizes finding patterns and relationships rather than memorizing facts. I enjoyed learning number and operations of all NCTM content standards, but it did take me a long time because the only learning strategy was memorizing. It was later, as an adult, that I learned relationships and fun patterns. This is so important to a child, because number and operations are the foundation of higher math skills.

  6. Assessment. This article suggests that assessment finds the holes in learning, and then making attainable goals with ways to attain them. Depending on how the goals are met, this becomes the assessment. My assessment growing up, came in the form of formal, summative assessment, with a test at the end of each unit in the textbook. It was the same for every student and never personal to my own needs.

  7. The NCTM process standards are problem solving, reasoning and proof, communication, connections, and representations. Along with this article, I can see why the process is more important than just getting the answer. The process, is what develops the brain to look for clues, come up with a way to solve and then arrives at the answer. It is better to struggle, discovering these points on one’s own, rather than the text or teacher giving you the way to set up the problem with half of the answers in the back of the book.


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