Tuesday, October 28, 2008

Press Release: Hands-On Equations in Africa & Asia

Hands-On Equations to be implemented in 1,000 classrooms in Africa and Asia

Contact: Henry Borenson, henry@borenson.com, 800-993-6284,
Or Patti Davis, patriciadavis@opportunityeducation.org, 402-660-2174

October 28, 2008--Borenson and Associates, Inc., an Allentown, PA firm known for its innovative algebra teaching system that enhances learning performance in U.S. schools, has been selected to provide its program to more than 1,000 classrooms in Asia and Africa.

Under the agreement, Hands-On Equations®, which is the name of the proprietary algebra program developed by Henry Borenson, will be implemented in 5th, 6th and 7th grade classrooms in Uganda, Tanzania, South Africa, Ghana, Sierra Leone, India, Sri Lanka and Nepal by Opportunity Education, a charitable foundation that provides educational tools for children in developing countries around the world.

“We are delighted to be chosen to provide our program to these students in developing nations,” said Borenson. “I’m confident the teachers in these classrooms will be very satisfied with the success they will see in their students.”

Borenson’s algebra teaching system uses manipulatives – similar to game pieces – to help students visualize an equation. Students use the manipulatives to make chess-like moves to balance an equation. “The program helps demystify the language of algebra and helps take an abstract concept and make it an intuitive process,” he said.

The Hands-On Equations® program has been introduced to over 25,000 teachers in the U.S. and is used in schools across the nation.

Opportunity Education chose to distribute Hands-On Equations® because the organization’s director of education, Patti Davis, had used the program as a classroom elementary school teacher, and had seen the improvement in her students’ abilities to learn algebraic principles and retain the skill set.

“I recommended Hands-On Equations® because I had had personal success using it in my classroom,” said Davis. “We chose the program because it is the easiest to understand, has the most applicability in classrooms in other parts of the world, and produces results.”

Providing the learning program to schools in developing nations supports the organization’s overall mission to supply curriculum and materials to classrooms in order to give children in developing countries the advantages of a U.S. education. “Providing the program and the materials the teacher needs to use to teach the program is imperative to help these countries meet their educational standards,” says Davis.

Opportunity Education was founded by Joe Ricketts, founder of TD Ameritrade. It is a charitable foundation that provides educational tools for children in developing countries around the world. For more information, go to www.opportunityeducation.org.

Borenson and Associates was founded by Henry Borenson in 1986. Borenson had taught honors mathematics classes at the Stuyvesant High School in New York City. For more information, go to www.borenson.com.

Thursday, October 16, 2008

Hands-On Equations Pre and Post-Tests for Level I

Complete instructions for administering pre- and post-tests for Level I are now available online. These instructions include a Summary Form for the teacher to record student scores and compare class results on each test, as well as class performance on each question.

On the pre-test, especially with students in grades 3 - 5, the scores are expected to be very low since these concepts and examples are not normally presented at these grades. The teacher should not be too surprised by low pre-test scores. If the teacher has gone through the training and implements the program as designed, he/she will see significant gains on the Lesson #6 post-test. This improvement is expected to be maintained as the students move away from using the game pieces to the pictorial notation in Lesson #7.



Pre-Test- 15 minutes



Post-Test After Lesson #6
(Students may use the game pieces on this post-test- time limit: 15 minutes)


Post-Test after Lesson #7
(Students do not use the game pieces-- just the pictorial notation)
Time Limit: 15 minutes








http://www.borenson.com/LevelIPrePostTestsOct08.pdf

Friday, August 15, 2008

HANDS-ON EQUATIONS STAFF DEVELOPMENT

ON-SITE STAFF TRAINING

Bring a nationally certified Hands-On Equations instructor to your district to provide first-class Staff Development on-site!

(See District Leaders Response to Our Workshops Below)


MAKING ALGEBRA CHILD’S PLAY® (Grades 3 – 8) HANDS-ON EQUATIONS® VERBAL PROBLEMS WORKSHOP (Grades 6 – 8; ½ day workshop grades 4 – 6)

FREE ONSITE STAFF DEVELOPMENT! Purchase thirty class sets of Hands-On Equations for Teacher and Thirty (30) Students and receive the training absolutely free!

Call 800-993-6284 to schedule your onsite workshop!



What District Leaders Say About Our Workshops

"Our teachers loved the workshop, Making Algebra Child’s Play! Students and teachers caught on to the math concepts very quickly and the use of the manipulatives to clarify operations was great!"

Dr. Robin Gillespie, Supervisor of Gifted Education
Jefferson County Schools (Grades 3-5)
Birmingham, AL
August 25, 2008
24 Participants
9.96 rating


"I thoroughly enjoyed the workshop! I believe it is a great enhancer for all students, but especially for visual and tactile learners. It really helped me to see how algebraic problems help to visually teach students."
Shaundala Summers, Campus Magnet Coordinator

TASD7 (Grades 4&5)

Texarkana, AR
August 11, 2008
11 Participants
10 rating


"We enjoyed the seminar and found it to be beneficial to our math program. The manipulatives and basic principles help to visually teach students."

Anita Corum, Elementary Curriculum Director
Princeton Christian School (Grades 3 - 8)
Homestead, FL
August 6, 2008
16 Participants
9.14 Rating


"I coordinated 32 workshops this summer and Tina Weiner’s workshop was among the best. All the participants were very happy with the results."

Paul Farrer, Academic Outreach Coordinator

Institute for Advanced Learning Research (Gr. 3-12)
Danville, VA
July 29, 2008
15 Participants
9.53 rating







Borenson and Associates, Inc., P.O. Box 3328, Allentown, PA 18106

(800) 993-6284 * Fax (610) 398-7863. www.borenson.com

Friday, August 08, 2008

Hands-On Equations Distance Problem - Honors

Errata Sheet

Hands-On Equations Verbal Problems Book

Level III Distance Problem, Page 107/44 and Solution Page 133/44

This problem has been modified as shown below.

This may be considered an honors problem

for students in grades 6 - 9.

The solution remains the same as that shown in the book.

44. A motorboat, after traveling for one hour in tranquil waters, begins to go downstream with the current, thereby increasing its speed by 2 miles less than one-third of its original speed. After going downstream for one hour to reach its destination, and after unloading one of the passengers, it reversed direction and went upstream against the same current for one hour to arrive at a refueling station. At that point the motorboat still needed to travel an additional 36 miles to reach its starting point. Find the speed of the motorboat in tranquil waters, and the distance it traveled to arrive at its destination. [III, 25]

Sunday, May 04, 2008

Using Hands-On Equations to Solve Verbal Problems

Word problems, also known as verbal problems, provide the students with the opportunity to think through a situation in depth. Short cuts such as "clue words" will not serve the students well, as every so called "clue word" is often not a clue at all. For example, teaching that the word "is" means "equal," presents a difficulty with a problem such as, "Four times a number is increased by 2...." Certainly no equal sign is involved here.

Hence the use of clue words, although designed to be helpful to the students and to serve as a crutch, is actually a disservice to the student since it does not convey to the student that there are no short-cut to doing verbal problems, rather the student must think!

There are methods, however, that the student can use to help break down the problem and represent the various elements. The following example shows how this can be done with one such problem using Hands-On Equations. This problem is taken from the Hands-On Equations Verbal Problems Book. Using Hands-On Equations, this problem is accessible to students as early as the 4th grade.

Theresa could purchase four small gifts and a $3 doll for the same price as three of the same small gifts and one $5 doll. What was the price of each of the small gifts?

Solution:

We let the blue pawn represent the price of each of the small gifts. The price of four of the small gifts would therefore be represented by 4 blue pawns. The $3 doll would be represented by a red 3 cube. And likewise for the other side.


The setup for the problem therefore looks as follows:


From here, we can use legal moves (remove three blue pawns from each side) to simplify the setup.


From this simplified setup we can see that the blue pawn is worth 2. Hence, The cost of each small gift is $2.

Check: $11=$11

ATTENTION TEACHER OR HOME SCHOOLER:

If you would like to provide these types of problems to your upper elementary and middle school students, you may wish to obtain the HANDS-ON EQUATIONS VERBAL PROBLEMS BOOK, which has more than 250 number, coin, age and distance problems, as well as general story problems, for all three levels of Hands-On Equations, along with solutions!

Additionally, if you are a teacher in grades 3 to 8 you may wish to attend a Making Algebra Child's Play workshop this season, In this workshop, you will learn how to use the Hands-On Equations program to solve equations, and also how to apply the concepts to verbal problems.

If you have already attended a Making Algebra Child's Play workshop, or are already using Hands-On Equations in your classroom or in your math program, and you are teaching in grades 6 and up, we encourage you to consider attending the Day2 Hands-On Equations Verbal Problems Workshop. In this workshop, you will review the key ideas of Hands-On Equations and you will also see how to apply these ideas to solve a wide variety of consecutive integer, age, coin and distance problems, including rowing up and downstream! This workshop will also be of interested to teachers of the gifted grades 2 and up, and teachers of low-achieving high school students.

............................................................................................................

Kira Brennan, age 8 presented the solution below to the above problem:

Kira's solution in her words:
"I solved the problem by drawing a picture of four presents and a person with a doll that has a $3 tag on it in her hands, and put an equal sign next to, and then I drew three presents and a girl holding a $5 doll in her hands.











"When I saw the picture, I saw that each present could be a blue pawn, and the doll could be a block (cube). So I put four blue pawns and a red 3 cube on the left hand side, and three pawns and the 5 cube on the right side. I guessed then that each present costs $2, but I took three pawns off each side anyway, and I could see you have to add $2 to 3 to equal $5 on the other side. Also, I counted 2-4-6-8-11 on the left, and 2-4-6-11 on the right, 11 equals 11, so each present must cost $2. It's harder if you just set up the equation, I think, but it was easy after I drew the picture."

Kira Brennan,
Age 8
(Note from Kira's mom: Kira has not tried verbal problems yet, so it was her idea to draw the picture first. I scanned her first sketch she did quickly to solve the problem, but then she insisted on drawing another one with the entire solution)

--------------------------------------------------------------------------------------------

This problem is appropriate for students in grades 5 and up who have had Level I of Hands-On Equations

Pedro’s dad is three times Pedro’s age. In 10 years, Pedro’s dad will be twice as old as Pedro will be then. How old is each now?


Sunday, March 30, 2008

A COMMENT ON THE NATIONAL MATH PANEL REPORT

The Final Report of the National Advisory Math Panel noted that many students "have difficulty grasping the syntax or structure of algebraic equations and do not understand the procedures for transforming equations or why transformations are done the way they are." It is indeed true that for many students algebra is a foreign language. Many students simply do not understand the meaning of the symbols used in algebra. Some students succeed by memorizing rules or procedures for solving equations.

All students, however, would benefit from instruction in algebra that made the concepts visual and hands-on. This is where Hands-On Equations comes in. A study recently completed, "The Effect of Hands-On Equations on the Learning of Algebra by 4th and 5th Graders of the Broward County Public Schools, shows that such instruction can be provided as early as the 4th and 5th grade. Of the 195 students from the regular classrooms which participated in this study, more than 80% of the students experienced success in solving equation such as 3x = x+12 and 4x+3=3x+9 after seven lessons of instruction. On a retention test administered three weeks later with no Hands-On Equations instruction in the interim, the students did equally well.

The students learning via Hands-On Equations develop an intuitive and indeed a kinesthetic sense of important algebraic principles, such as the subtraction property of equality, by physically removing three blue pawns, representing the x's, from both sides of the balance scale.

If students beginning an Algebra 1 course have not been fortunate enough to have had this hands-on experience earlier in their educational career, it is still important for the regular high school algebra teacher to provide this experience to the students. Even a few short lessons can demystify basic algebraic equations and how to solve them.

Ideally, though, it is best to provide this hands-on experience earlier on, say in grades 4 to 6. Indeed, the ability to solve such equations should be a prerequisite, in the view of this educator and publisher, for a student to enter an Algebra 1 or even a pre-algebra class. If the students have had Hands-On Equations they will have no trouble at all solving these types of equations with the game pieces, and then pictorially using only paper and pencil. (The retention test noted above was administered without the game pieces.)

The Task Group on Conceptual Knowledge and Skills noted, "Without any doubt, the foundational skill of algebra is fluency in the use of symbols." Students working with Hands-On Equations develop a high level of comfort in working with algebraic linear equations of increasing complexity with unknowns on both sides of the equation. If, in addition, the students develop strong computations skills, as advocated by the Panel, the success level of such students in Algebra 1 should be significantly higher than has been the case in the past. Borenson and Associates, Inc. hopes to conduct research in this area in the 2008-2009 academic year with algebra 1 students.

If your district has a large number of students failing algebra 1, and you would like to participate in a research study to determine if Hands-On Equations instruction can make a difference in student success when they repeat the course, please send a note of inquiry to info@borenson.com.

Friday, March 21, 2008

BROWARD COUNTY HANDS-ON EQUATIONS RESEARCH STUDY

The Effect of

Hands-On Equations®

on the Learning of Algebra by 4th and 5th Graders of the

Broward County Public Schools

by Henry Borenson and Larry W. Barber


Hands-On Equations Interim Report: March 17, 2008

A Study of the Strength of Acquisition of Algebraic Concepts by 4th and 5th Graders via Hands-On Equations and a Measure of the Retention of the Pictorial Notation

(The full 30 page research report may be found here. If you wish a hard copy please send $10 to cover postage and handling to Borenson and Associates, Inc., PO Box 3328, Allentown, PA 18106).

ABSTRACT

The Broward County Public Schools agreed to participate in a research study to determine the effectiveness of the Hands-On Equations® program in providing its students with a successful experience with algebra. The study sought to determine whether the 4th and 5th grade students of the district could learn to solve equations such as 3x = x + 12 and 4x + 3 = 3x + 6, equations normally presented in the 8th or 9th grade. If the students were successful with these concepts, they would have overcome at an early age one of the obstacles to the learning of algebra.

The teachers who participated in this study received a full day of training in the use of the program. The workshop they attended, the Making Algebra Child's Play® workshop, was conducted by a certified Borenson and Associates, Inc. instructor in the fall of 2007. Immediately after instruction, the teachers administered a pre-test to their students, and then proceeded to teach the first seven lessons (Level I) of Hands-On Equations. They also administered two post-tests and a three-week retention test.

This report presents the meta-analysis conducted on six 4th grade regular classes, three regular 5th grade classes and five gifted and talented 5th grade classes, a total of 14 classes involving 326 students. The Appendix includes the test results for other classes participating in the study. For various technical reasons explained in the report these additional classes could not be included in the meta-analyses.

Since the teachers and students participating in this study were representative of those in the district as a whole, the results shown herein are indicative of the results that would be expected if the Broward County Public Schools were to implement the program district-wide in the 4th and 5th grades.

The authors wish to thank Miriam Sandbrand, Mathematics Curriculum Specialist, K-5, for her efforts in coordinating this study and to the teachers who participated in this study.


GENERAL SUMMARY

BROWARD COUNTY RESEARCH STUDY

A total of 326 students from 14 different classes were included in this study. The raw scores and percentage scores are shown below. We note that the average 4th graders saw their scores triple from the pre-test to each of the post-tests and to the retention test; the average 5th graders saw their scores more than double from the pre-test to these post-tests and to the retention test.


Pre-test

Post-test after

Lesson #6

Post-test after

Lesson #7

3-Week Retention

Test after Lesson#7

Grade 4, n=111

Study #131MA

Regular students

26.8%

(m=1.61)

84.2%

(m=5.05)

t(P, P6)=20.50

84.2%

(m=5.05)

t(P, P7)=20.45

81%

(m= 4.86)

t(P, P7-R3)=19.49

Grade 5, n=84

Study #138MA

Regular students

37.7%

(m=2.26)

88.3%

(m=5.30)

t(P, P6)= 19.62

88.5%

(m=5.31)

t(P, P7)=17.09

84.7%

(m= 5.08)

t(P, P7-R3)=14.71

Grade 5, n=111

Study #139MA

Gifted/Talented

78%

(m=4.68)

95.3%

(m=5.72)

t(P, P6)=8.06

95.3%

(m=5.72)

t(P, P7)=8.14

94.2%

(m= 5.65)

t(P, P7-R3)=6.05

These three meta-analyses demonstrate that 1) Each of the combined group of 111 regular 4th graders, 84 regular 5th graders, and 111 gifted and talented 5th graders achieved a large and significant gain from the pre-test to the post-test following Lesson #6, and 2) This significant gain was maintained on the post-test following Lesson #7, where the students did not use the game pieces (rather, they used the pictorial notation learned in Lesson #7). These results confirm the results of previous studies conducted with 4th, 6th and 8th graders that students who learn the Hands-On Equations (HOE) methods of solving equations can be equally successful with or without the game pieces. In other words, the students are able to transfer their hands-on learning to the pictorial method presented in Lesson #7, which uses only paper and pencil, and be equally successful in solving the equations.

Additionally, the current study showed that after a three-week period of no HOE instruction, the students performed essentially the same as they did three weeks earlier on the Lesson #6 and Lesson #7 post-tests. Since the three-week retention test was conducted without the use of the game pieces, the current study demonstrates that 4th and 5th grade students are able to retain the methods they have learned in the program and are able to solve algebraic equations using the pictorial notation even after a period of three weeks without HOE instruction.

In summary, the results obtained in this study are consistent with previous studies which show that when teachers who have been trained in the Hands-On Equations program instruct their students in the use of the program, and go through the first seven lessons of the program as prescribed, the students learn the algebraic concepts presented, they do well on the posts-tests, and they remember what they learn, with or without the use of the game pieces.


Appendix 9

Item Analysis

Below, we show the percentage of students who obtained the item correct on the pre-test vs. the percentage of students who obtained the comparable item correct on the three-week retention test for each of the three meta-analyses.

Grade 4, n =111. Study #131MA Regular Students

Percentage of Students with Correct Item Response


Equation

Pre-test

Retention-test

Question #1

2x = 8

48%

92%

Question #2

x + 3 = 8

70%

89%

Question #3

2x + 1 = 13

22%

82%

Question #4

3x = x + 12

9%

86%

Question #5

4x + 3 = 3x + 6

8%

79%

Question #6

2(2x+1) = 2x +6

8%

59%

Grade 5, n =84. Study #138MA Regular Students

Percentage of Students with Correct Item Response


Equation

Pre-test

Retention-test

Question #1

2x = 8

68%

94%

Question #2

x + 3 = 8

87%

93%

Question #3

2x + 1 = 13

42%

83%

Question #4

3x = x + 12

15%

89%

Question #5

4x + 3 = 3x + 6

10%

87%

Question #6

2(2x+1) = 2x +6

5%

74%

Grade 5, n =111. Study #139MA Gifted/Talented Students

Percentage of Students with Correct Item Response


Equation

Pre-test

Retention-test

Question #1

2x = 8

97%

99%

Question #2

x + 3 = 8

95%

96%

Question #3

2x + 1 = 13

87%

99%

Question #4

3x = x + 12

71%

91%

Question #5

4x + 3 = 3x + 6

71%

95%

Question #6

2(2x+1) = 2x +6

46%

85%



Appendix 4

TEST QUESTIONS FOR STUDY #131MA

Pre-Test Questions

1. 2x = 8

2. x + 3 = 8

3. 2x + 1 = 13

4. 3x = x + 12

5. 4x + 3 = 3x + 6

6. 2(2x + 1) = 2x + 6

Post -Test after Lesson #6

1. 2x = 10

2. x + 3 = 8

3. 2x + 2 = 10

4. 3x = x + 4

5. 4x + 3 = 3x + 9

6. 2(2x + 1) = 2x + 8

Post-Test After Lesson #7

1. 2x = 6

2. x + 3 = 10

3. 2x + 1 = 7

4. 3x = x + 2

5. 4x + 3 = 3x + 7

6. 2(2x + 1) = 2x + 10

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