Wednesday, February 27, 2008

The Guardian Review (UK)


Catch them young


Fear + loathing = algebra. Unless you're one of the thousands of 9-year-old Americans to have discovered that algebra = fun

Polly Ghazi
Tuesday October 24, 2000
The Guardian




The equation on the blackboard reads 2 (3x + 1) = x + 22. "Who wants to explain how they solved this?" asks the teacher, Vicki Fisk. A forest of young hands shoots up. Jack, aged 10, is chosen. He jumps up and runs to what looks like a colourful toy set up on a desk in front of the blackboard. He rearranges the blue pawns (representing x) and red numbered cubes set out on a plastic balance beam to produce the right answer, amid nods from his classmates at Somerset Elementary in Maryland, US.

"It's easy and it's fun. I really enjoy maths lessons now," confides Richard Kingdom, nine, whose family moved from Wiltshire to America two years ago. "Last year I was trying to do algebra in my head and I found it very difficult. Now I can take the pieces away with my hands and make the two sides balance and I understand what it's all about."

Had he stayed in England, Richard would not have been taught such a complicated equation until he was at least 12 years old. But in the US, a new philosophy of demystifying algebra - a subject that traditionally terrifies pupils - by starting children younger is producing highly encouraging results. And for thousands of American teachers it is a new breed of educational toy that is making all the difference.

The balance beam system used by Vicki Fisk, for example, has been made a mandatory part of maths lessons for eight- to 11-year-olds in Maryland's Montgomery County, one of the US's largest school districts. Nationwide, tens of thousands of teachers have had training in using the system, know as Hands On Equations, which was developed by Dr Henry Borenson, a Pennsylvania maths teacher.

"I wanted to literally make algebra child's play," explains Borenson, who developed his system with the help of children with learning difficulties. "We have had a lot of feedback that using the equipment greatly boosts children's self-esteem. Teachers who struggled themselves with algebra have called it a revelation."

America's National Council for Teachers of Mathematics is spearheading the drive to begin teaching some high school maths concepts, algebra in particular, to children as young as six. According to the council's president, Lee Stiff, results over the past five years have been impressive, aided by educational toys such as Borenson's. "We have evidence from a number of states showing that nine-year-olds are doing better at basic algebra than older kids who come to it cold," he said.

The American approach was welcomed last week by British maths experts, many of whom believe algebra is introduced too late into UK schools. Roger Fentem, a maths educator who trains primary and secondary teachers at the College of St Mark and St John in Plymouth, described as "astonishing" the prowess shown by Vicki Fisk's class. "In Britain we would expect a bright 12-year-old or an average 14-year-old to solve that equation," he said.

Barry Lewis, director of UK Maths Year 2000, launched in January to "challenge the national fear of figures", agreed. "The leap from physical numbers into abstract qualities such as using letters in equations is the critical place where maths leaves many students behind," he said. "We support making algebra accessible and exciting at as young an age as possible. This kind of educational toy, which emphasises the concept of balance as the central principle of algebra, is spot on."

Such educational toys, however, are not generally used in British schools although many secondary-school textbooks and maths computer games use balance beam illustrations to teach algebra. What's more the national numeracy strategy, launched in September 1999 to raise basic maths standards, explicitly excludes algebra teaching in primary schools. As a result, children do not start learning even the most basic algebraic equations or formulae, such as 5 plus x = 8, therefore x = 3, until they reach 11 or 12.

"Really children should be learning such formulae as soon as teachers start asking them "five plus what is eight?" which is usually around seven or eight years old," said Fentem. "Part of the way ahead is to raise primary school teachers' knowledge of basic algebra and their confidence in their ability to link numeracy lessons with algebra. Based on the success of the numeracy strategy so far, I believe we should see great strides in algebra standards among British children over the next few years."

Making such strides is not just about academic success. American research suggests that pupils who drop out of algebra are less likely to achieve successful careers in well-paid fields such as computing and engineering. And a recent British study found that students achieving maths A-level went on to earn incomes roughly 20% higher than fellow students with only arts A-levels.

Meanwhile, a pioneering maths-teaching programme developed by Exeter University's School of Education will give some insight over the next few years into whether teaching algebra early could be as successful here as in the US. Forty primary schools around the country are using specialised lesson plans to introduce simple algebraic concepts to children as young as five. "I believe teaching algebra at 11 or 12 is far too late. Pupils find it very scary because they have no foundations in place to understand what the x and the brackets mean," says Professor David Burghes, who heads Exeter's School of Education and sat on the government's national numeracy task force.

"We find that five-year-olds have no problems understanding that 5 plus a square box equals 7 and then working out that the box equals 2. In fact they love it. But my views are not mainstream in Britain. I am out on a limb."

Back in Montgomery County, Vicki Fisk has no doubts about the pluses of teaching algebra at an age when some children are still learning to read. "The kids just love it - and they learn very fast," she says. "I have a friend who teaches seven- and eight-year-olds using Hands On Equations and they actually start crying when they have to miss a maths lesson!"

A class of nine- and 10-year-old American children individually solved these eight equations in just under half an hour. Can you do better? (Answers at bottom of page)

1 3x + 2x = 10

2 4x + 2x = x + x + 20

3 3x + 5 = x + 19

4 2(3x + 1) = x + 22

5 5x + 2 = 3x + 12

6 2x + 1 + x + 4 = x + 16 + x

7 5x - 3x + x + 8 = 2x + 1 + x + x

8 2(x + 4) = x + 10

Join in our online debate on school maths at 12.30pm. Should it really be compulsory up to GCSE level, or are there better and more useful ways of developing logic and reasoning skills? The authors of two recent books from the Institute of Education, Why Learn Maths? and The Maths We Need Now, will be live online to answer questions and fight their corners.

Answers, x=...

1 2
2 5
3 7
4 4
5 5
6 11
7 7
8 2


Monday, February 18, 2008

The Old Schoolhouse Product Review

Algebra! That one word can strike fear into any child's heart, but it doesn't have to be that way. Algebra can be taught to a child as young as third grade, or an older student or parent that needs a hands-on, easy-to-understand method. Let me introduce you to Algebra: Hands-On Equations developed by Henry Borenson.

Each student kit includes a visual that is laminated to be durable. It illustrates the two sides of an algebra equation and its equality by using an image of a balance scale. The student manipulates the equation by using colored pawns and colored number cubes. He/she is able to physically show the problem with the manipulatives and find the answer by making both sides of the balance scale equal. Problems begin with simple concepts and end with such problems as 3x-2(-x+4)=x+(-32). The instruction manual is clear and easy to use. Videotapes are available that teach each lesson and would be great for independent work for the student. After the student uses the manipulatives to solve the problem, he/she then completes a worksheet for extra practice.

With this method anyone, including myself, can be taught algebra without the frustration. For the first time in my life, I actually understood how to do algebra and why it works. You and your child do not have to fear algebra. With Algebra: Hands-On Equations, the solution to algebra is in your hands! I give it an A+!

-- Product Review by: Debra Cogburn, Lead Product Reviewer, The Old Schoolhouse Magazine

Here's another Algebra: Hands-On Equations review!

The Algebra: Hands-On Equations Learning System is a visual and kinesthetic teaching system for introducing algebraic concepts to students in third through eighth grades. Supposedly, the patented teaching system developed by Dr. Henry Borenson, enables children, as early as third grade, to access algebraic concepts normally presented in the seventh through ninth grades. My first thought was let's round up the kids, put on the course Instructional VideoManual and see what happens.

That’s just what I did. I sat three children, ages five, nine and 11, in front of the television and fired it up. After an initial groan or two when it was discovered that they were about to watch something educational, the room became quiet. These children were glued to this video watching the demonstrator present problems and solutions.

My 11-year-old was in control of the remote so he stopped the video each time a new problem was given. He and his nine-year-old brother worked the problem independently, then compared answers, and then started the video rolling to see if their answer jived with the one presented. I was amazed. They loved the video, the manner of instruction, and solving these problems. We completed the first five of 26 lessons before taking a break. What fun. What an education in just a few short minutes.

When we turned the video off, my 81-year old mother said, “Is that all we get to see?” I had no idea she was also watching and working the problems. She held up her paper and announced that she hadn’t missed one yet. The only one who was totally unenthused about this product was my five-year-old, but then Dr. Borenson wasn’t gearing his system to five-year-olds. I considered our home test of this product a total success.

If you’re interested in teaching your children fundamental algebraic concepts, I wouldn’t hesitate to recommend Algebra: Hands-On Equations. Also, if you’re one of those people who is terrified of the thought of teaching algebra to your children, this is the product for you. Please consider Hands-On Equations when preparing to teach basic algebraic concepts.


-- Product Review by: Dr. Heather W. Allen, Senior Analyst, The Old Schoolhouse Magazine

Wednesday, February 13, 2008

MONTESSORI REVIEW

HANDS-ON EQUATIONS REVIEW
Heidi Anne Spietz
American Montessori Consulting

Dr. Henry Borenson has masterfully created Hands-On Equations®, a system for helping children understand algebraic linear equations. This visual and kinesthetic teaching system for introducing algebraic concepts to students in grades 3 to 9 is very consistent with Montessori principles.

By manipulating pawns and cubehs children learn how to set up equations on a replica of a balance scale. They achieve "balance" by performing "legal moves". The visual aspect of this exercise is splendid, for the child can actually see how the equation is solved. Children learn to solve simple equations and progress to learning advanced equations which involve positive and negative integers.

I first became aware of the Hands-On Equations program in 1995 at a NCME Montessori conference in Newport Beach, CA. I was impressed then, and continue to be impressed now with the recently released Hands-On Equations Instructional DVD Manual, which allows the learner to pause any lesson on the DVD at any point in time and practice the concepts presented. I spent ample time reviewing the DVD and the newly released Hands-On Equations Verbal Problems Book.

In concert with the Montessori approach, the Hands-On Equations program encourages students to solve new problems but also provides them with the opportunity to review and practice previous concepts as well. Detailed instructions for each lesson are available for the presenter.

The Hands-On Equations Learning System, along with the DVD manual and the Hands-On Equations Verbal Problems Book is a package which is perfect for use in many learning settings. This combination of items is called the Hands-On Equations Home Packet, and is available for $125. Teachers wishing to actually view the Hands-On Equations lessons before presenting them can spend time reviewing and applying the concepts presented. By so doing, the teacher will feel more confident when she provides assistance during the actual presentations and practice sessions.

Montessori knew that students would need to review concepts from time to time. Because the program is very suitable for individual viewing, the student can progress at a rate comfortable for him. The hands-on aspect of the exercises is sure to appeal to children who have participated in advanced Montessori math exercises. If a student progresses with the lessons but finds along the way that he needs to review a concept, he can simply program the DVD to replay the lessons.

Dr. Borenson's presentations are extremely clear. He has an engaging manner which will be a real relief to the student who has felt intimated by algebra in particular, as well as math in general. Gifted students will benefit by being able to set their own pace. All students will enjoy seeing their peers actually working with the Hands-On Equations materials.

For additional information about this fine, innovative learning program please visit www.borenson.com.


Heidi Anne Spietz
American Montessori Consulting
http://www.amonco.org