kitchen table math, the sequel: algebra in 8th

Thursday, June 5, 2008

algebra in 8th

I first got going with all this math folderol when I discovered, in the pages of Wayne Wickelgren's Math Coach, that algebra-in-8th-grade is standard in Europe and Asia. That was a revelation. I had thought algebra-in-9th-grade was the natural order of things, if I thought about it at all. Which I didn't.

I had no idea algebra-in-8th meant no-calculus-in-9th, a fact my district did not call to my attention when they tracked C. into "Phase 3" math back in the 3rd grade.

Fortunately, I figured it out for myself in June 2004.

Here we are, 4 years later, and C. is completing algebra in 8th grade, many thanks to all you ktm regulars. (How do kids who don't have blog collectives helping them with homework do it?)

Meanwhile, the rest of the country is waking up to the fact that American kids are on the slow-track algebra-wise, thanks in part to the National Mathematics Advisory Panel report, which states bluntly that: More students should be prepared for and offered an authentic algebra course at Grade 8.

Apparently, there are school districts out there taking this injunction seriously:
The notion that students can master high school algebra before high school is relatively new, said Francis "Skip" Fennell, an education professor at McDaniel College in Westminster, Md., who is past president of the National Council of Teachers of Mathematics. The share of students completing the course in middle school nationwide has gone from next to nothing a generation ago to about 25 percent in the late 1990s to about 40 percent today.*
In my district (per pupil funding $25,000), the figure stands at approximately 30%, and it would be far lower if the district had its way. When C. was in 5th grade, the middle school succeeded in whittling enrollment down from the approximately 35% who were taking it at that time to today's 30%. The next fall, when C. entered 6th grade, the middle school principal told Ed and me he hoped to get rid of the accelerated course altogether; last year the new middle school principal tried to scuttle it but failed.

The district was successful in slowing the progress of kids in grades K-5. Math Trailblazers came in and acceleration went out. Gifted children were particularly hard hit. The accelerated track was gone and the regular track was far slower than it had been. Trailblazers teaches many topics a full year later than they had been taught prior to the Trailblazers era.

If this WAPO story
is accurate, affluent American kids are "thriving" in the international track, while poor and minority students are having a harder time of it. Somebody should talk to KIPP, where 80% of 8th graders pass Regents Math A.

I read a story like this and feel as if I'm living in a bubble. Elsewhere in the country, at least some school districts are working to move teachers and students onto the international track. Here, with per pupil spending rising to $25,000 and median household income somewhere in the neighborhood of $100K, putting students on par with their peers in Europe and Asia isn't even a topic for discussion.

Instead, it's the middle school model; it's character education; it's Project Lead the Way.


* How many of these courses are authentic algebra, it's hard to know.

29 comments:

PaulaV said...

I read the WAPO article and found the comments even more interesting than the story itself.

One commenter wrote, "So Prince William is slowing their kids to a crawl with Investigations while the neighboring counties are moving their kids ahead at a faster pace."

I'm in one of the neighboring counties, Loudoun. Right now our schools are using Investigations in elementary school. Yet, we tout our kids as being accelerated. How can that be when our county signed up to use this math program?

My assumption is that many of the white, affluent kids are being tutored on the side. Those are the ones being pushed onto the accelerated track.

Also, the fourth graders at my school are being taught pre-algebra by using Dr. Henry Borenson's hands-on math equations.

It looks complicated to me. When I asked my son about it, he said he understood it, but what he didn't understand was why his teacher was teaching algebra this way. He has been in Kumon for some time now so he sees the difference in the approach.

Unknown said...

My story is very similar to yours. Districts are sometimes reluctant to place students in pre-algebra in the 7th grade. I had to raise (you know :D) last year to have my son placed. We both even had to sign a waiver, taking full responsibility, if he failed.

Parents need to know that in order to be prepared for authentic Algebra in the 8th, a student needs Pre-Algebra in the 7th. Unfortunately this usually isn't open to everyone, as is recommended by the NMP. So they need to be prepared! And don't take "no" for an answer!

[If your child needs extra tutoring in order to succeed at that point, I think that it would be much better to start then than to wait until high school when they would already be behind internationally.]

It's very strange to me that I ended up resorting to the "parental involvement" piece of the No Child Left Behind Act in order to get the district to listen. I had all the other academic ducks in a row, presenting pages of research, but NCLB was what they finally heard.

[I'm not really a fan of the ways in which NCLB has be implemented, but I was a desparate mom, pulling out all the stops!]

SteveH said...

"* How many of these courses are authentic algebra, it's hard to know"

This is "Skip" talking. I've heard this before and I thought it was rubbish then. In our affluent community, the number of kids taking a real algebra course is about 25 percent. That's only becuase we are finally using the same algebra text as the high school. Before this year, the school used CMP, so the percentage was ZERO.

Can you imagine a school not providing classes (prerequisites) that allow kids to enter a high school course? I've talked before about this philosophy and curriculum wall between K-8 and high school. They are in two different worlds.

My son just took an exam that will decide whether he will be allowed (not able) to move into algebra from pre-algebra. The assumption is that the onus is all on the student. Some kids do well and they assume that only a few kids are supposed to be able to do algebra before high school. Besides, they have only scheduled one class of algebra, so that's the determining factor.


"The notion that students can master high school algebra before high school is relatively new..."

No it isn't. When I was growing up, many took "authentic algebra" in 8th grade. It was perhaps a sink-or-swim approach, but at least kids like myself had the curriculum to get there without any outside support.

SteveH said...

"Parents need to know that in order to be prepared for authentic Algebra in the 8th, a student needs Pre-Algebra in the 7th."

I would like to know what parents think. I know that algebra in 8th grade is key, and I knew that when I was growing up. I guess many parents don't really understand that. The problem is not that the kids are delayed one year. It's that they are headed to the math track to nowhere. It shouldn't be this way, but few seem to recover to get to pre-calculus or algebra II. The damage has been done and most kids will think that they are just not good in math.

Our high school guidance section talks about how parents can prepare their kids for college and they recommend that they start in seventh grade. They tell parents to focus on math, reading comprehension, writing, and foreign language. There is not a whisper about this by our K-8 schools.

Schools know that parental involvement is important, but they don't admit how important it really is. It would be interesting to see exactly how much parents do for their "good" students. I know how much I do. Put another way, how many good students would be left if parents just checked (not fixed or discussed) to see that homework was done.

Anonymous said...

"... a student needs Pre-Algebra in the 7th..."

What is covered in Pre-Algebra? Is there a standard definition of what this means?

wordsmith said...

What is covered in Pre-Algebra? Is there a standard definition of what this means?

This is what Wiki has to say. Speaking as a math instructor at a community college, I would say it's an alright definition, but I would emphasize that for a student to do well in algebra, he absolutely needs to know the basics cold, especially manipulating fractions. A student should also understand the concept of the inverse of an operation; he doesn't need to know a formal definition of the concept, but he should definitely know that + "undoes" or "gets rid of" - and vice versa, and ditto for the relationship between * and /.

I've seen too many students at the post-secondary level who have been crippled because they've been taught to use the calculator as a crutch rather than a tool. They wrongly suppose that a calculator can do all the work for them, and then when they get to rational expressions or something equally nefarious (in their view), they panic, and it all goes downhill from there.

It all boils down to the basics. Kids should be able to add, subtract, multiply, and do long division without a calculator, and without breaking a sweat. Everything else in math truly builds on this foundation. If the foundation is messed up, the rest of the building will be a nightmare. It doesn't matter if they don't see the importance of these basic operations - that will come with time. The Karate Kid didn't see the relevance of "wax on, wax off" until later, after the foundation was laid and he was thoroughly prepared to advance to the next level. It's the same with math, and I daresay the majority of our kids are being cheated with these dumbed-down curricula and the active discouragement from administrators with regards to placement in more challenging math courses.

Sorry for the rant.

SteveH said...

"What is covered in Pre-Algebra? Is there a standard definition of what this means?"

I don't like the term "pre-algebra" just like I don't like the term "pre-calculus". I had trigonometry in high school.

I took a quick look int the National Math Panel report and couldn't find a reference to pre-algebra. They seem to be most concerned about defining "school algebra" and assume that you have a curriculum that will get you there in 8th grade.


However, you find pre-algebra in most math curricula. I'll wager that most of them are the same. I will caution that you can get different series from the same publisher. If the texts are labeled simply as Pre-Algebra and Algebra, they are probably the most rigorous. When they add sub-titles, like "Tools for a Changing World", then they are probably less rigorous.

My son's Glencoe Pre-Algebra book contains these main topics.

1. Coordinate points
2. Variables and Expressions
3. Plots
4. Adding and subtracting positive and negative numbers and variables
5. Multiplying and dividing positive and negative numbers and variables.
6. Solving simple one-step and two-step equations.
7. Introduction to powers and exponents.
8. Prime factorization
9. Greatest common factor
10. Simplifying algebraic fractions
11. Multiplying and dividing monomials
12. Rational numbers
13. Add, subtract, multiply, and divide fractions and rational expressions
14. Ratio, proportion, and percent
15. Functions and graphing
16. Linear functions; slope-intercept and two point forms
17. solving equations and inequalities.
18. Real numbers and right triangles.
19. Two-dimensional figures
20. Three-dimensional figures

Some of these topics my son has seen before, but they are now focusing more on their use with variables.

Unfortunately, many mistake these topics for ones that are in a "real" algebra course.

Instructivist said...

My McDougal Littell Pre-Algebra book has pretty much the same topics SteveH lists.

http://www.mcdougallittell.com/ml/math.htm?lvl=4&ID=1005500000030861#

Table of Contents:

Variables, Expressions, and Integers
Solving Equations
Multi-step Equations and Inequalities
Factors, Fractions, and Exponents
Rational Numbers and Equations
Ratio, Proportion, and Probability
Percents
Linear Functions
Real Numbers and Right Triangles
Measurement, Area, and Volume
Data Analysis and Probability
Polynomials and Nonlinear Functions
Angle Relationships and Transformations

There is a more detailed breakdown at the site. There is also a workbook for each lesson that gives immediate feedback.

[Unfortunately, many mistake these topics for ones that are in a "real" algebra course.]

Hmmm?

Aren't these part of beginning real algebra?

SteveH said...

"Aren't these part of beginning real algebra?"

I guess I didn't say that right. Many think that there is not much more than this in a regular algebra course. That's why the NMP had to stress "school algebra". When our school used CMP, there was not much more about linear equations than what my son is now getting in his pre-algebra course.

Ben Calvin said...

wordsmith – concisely put. I think that is the most compact definition I’ve heard of what’s required.

Unknown said...

These lists above would be what I consider as "authentic PRE-algebra" although the NMP didn't use this term.

I've been told that CMP is equivalent to Algebra I, but when I reviewed those materials, I quickly decided that they were NOT even equivalent to AUTHENTIC PRE-ALGEBRA. By that I mean that those materials could not (imo) prepare a student for success in an authentic algebra I course as recommended by the NMP.

Of course, some would disagree.

It would be nice if districts would provide parents with data on which courses prepare the most students for success in subsequent years.

Anonymous said...

Here's the TOC from Chalkdust Prealgebra, a curriculum popular among homeschoolers. We used this this past year and I feel confident that my girls are ready for a rigorous algebra course:

Disc 1 - 2 hours 9 min.
Chapter 1- Whole Numbers
# 1.1 Introduction to Whole Numbers
# 1.2 Addition and Subtraction of Whole Numbers
# 1.3 Multiplication and Division of Whole Numbers

Disc 2 - 2 hours
# 1.4 Solving Equations with Whole Numbers
# 1.5 The Order of Operations Agreement

Chapter 2- Integers
# 2.1 Introduction to Integers
# 2.2 Addition and Subtraction of Integers
# 2.3 Multiplication and Division of Integers
# 2.4 Solving Equations with Integers
# 2.5 The Order of Operations Agreement
# 2.4 Solving Equations with Integers
# 2.5 The Order of Operations Agreement

Disc 3 - 1 hour 57 min.
Chapter 3- Fractions
# 3.1 Least Common Multiple and Greatest Common Factor
# 3.2 Introduction to Fractions
# 3.3 Addition and Subtraction of Fractions
# 3.4 Multiplication and Division of Fractions

Disc 4 - 2 hours 17 min.
# 3.5 Solving Equations with Fractions
# 3.6 Exponents, Complex Fractions, and The Order of Operations Agreement

Chapter 4- Decimals and Real Numbers
# 4.1 Introduction to Decimals
# 4.2 Operations on Decimals

Disc 5 - 2 hours 4 min.
# 4.3 Solving Equations with Decimals
# 4.4 Radical Expressions
# 4.5 Real Numbers

Chapter 5- Variable Expressions
# 5.1 Properties of Real Numbers
# 5.2 Variable Expressions in Simplest Form
# 5.3 Addition and Subtraction of Polynomials
# 5.4 Multiplication of Monomials
# 5.5 Multiplication of Polynomials

Disc 6 - 2 hours 12 min.
# 5.6 Division of Monomials
# 5.7 The Order of Operations Agreement

Chapter 6- First Degree Equations
# 6.1 Equations of the form x + a = b and ax = b
# 6.2 Equations of the form ax + b = c
# 6.3 General First-Degree Equations
# 6.4 Translating Sentences into Equations

Disc 7 - 2 hours 12 min.
# 6.5 The Rectangular Coordinate System
# 6.6 Graphs of Straight Lines

Chapter 7- Measurements and Proportion
# 7.1 The Metric System of Measurement
# 7.2 Ratios and Rates
# 7.3 The U.S. Customary System of Measurement
# 7.4 Proportion

Disc 8 - 2 hours 20 min.
# 7.5 Direct and Inverse Variation

Chapter 8- Percent
# 8.1 Percent
# 8.2 The Basic Percent Equation
# 8.3 Percent Increase and Percent Decrease
# 8.4 Markup and Discount
# 8.5 Simple Interest

Disc 9 - 2 hours 20 min.
Chapter 9- Geometry Part One
# 9.1 Introduction to Geometry

Chapter 9- Geometry Part One
# 9.2 Plane Geometric Figures
# 9.3 Triangles

Disc 10 - 2 hours 12 min.
# 9.4 Solids
# 9.5 Composite Figures

Chapter 10- Statistics and Probability
# 10.1 Organizing Data
# 10.2 Statistical Measures
# 10.3 Introduction to Probability


In comparison, this is the TOC from UCSMP Transition Math, which is what they would be using if they were at public school:

Table of Contents

CHAPTER 1: Decimal Notation

CHAPTER 2: Large and Small Numbers

CHAPTER 3: Measurement

CHAPTER 4: Uses of Variables

CHAPTER 5: Patterns Leading to Addition

CHAPTER 6: Problem-Solving Strategies

CHAPTER 7: Patterns Leading to Subtraction

CHAPTER 8: Displays

CHAPTER 9: Patterns Leading to Multiplication

CHAPTER 10: Multiplication and Other Operations

CHAPTER 11: Patterns Leading to Division

CHAPTER 12: Real Numbers, Area, and Volume

CHAPTER 13: Coordinate Graphs and Equations


The neighborhood kids are not happy with the curriculum. Their main complaint is that they are supposed to read the chapter themselves, do the assigned problems, and the next day the teacher answers questions. There isn't really any systematic instruction.

I went to a math meeting at the middle school the other night, and the teachers verified that this is the model they use, beginning with Transition math and going through all high school math courses. They called it the "piggybacking" method.

At the end of 5th grade, the top 10% of kids are selected to take T-math in 6th grade. I was not surprised when they told us that only 3 of 18 6th graders are getting A's. 12 are failing. I wonder what would happen if the teachers actually taught. As it is, the only ones that seem to excel are the ones who have parents who are willing and able to spend 1-2 hours on math each night.

SteveH said...

"UCSMP Transition Math"

What are they transitioning to, the math track to nowhere? I went to the site and looked at the details of some of their chapters. It's just awful. They give this to the top 10%? If 12 of 18 of these kids are failing, then this is a clear indication that it's really the school that is failing.


"...beginning with Transition math and going through all high school math courses. They called it the 'piggybacking' method."


I've never heard of that term. What does "piggybacking" mean? When they talk about "all high school math courses", do they include the calculus track courses? Do they even have a Geometry, Algebra II, Pre-Calculus, Calculus track?

VickyS said...

I was talking last week to a friend from Italy who was ranting, as Italians are wont to do, about the American educational system, and he told me in Italy there are national benchmarks of what kids need to know in every subject (including of course math) at the end of each grade. It does not matter how the school--or teacher--chooses to get there (i.e., any curriculum or teaching method can be used), but the children are expected to master a certain body of knowledge each year.

I honestly don't understand why we can't do this in the US, at least in math and English (sorry--"language arts"). Social studies and science are more political, but give the educators federal benchmarks for content in math and English, then let the individual states, schools and teachers decide how to achieve those benchmarks.

Anonymous said...

UCSMP is the same group that developed Everyday Math for elementary school.

"They give this to the top 10%?"

Everyone takes it at some point. They look at the results of three tests at the end of each year: ITBS, NWEA, and a district developed test. Those with the highest scores in 5th grade take T-math in 6th grade. The next group takes it in 7th grade, and the last group takes it in 8th. T-math is followed by Algebra 1, Geometry, Advanced Algebra; Functions, Statistics and Trigonometry; and Pre-Calculus and Discrete Mathematics. I haven't seen any of these materials so can't comment on them. I've heard very mixed reviews from parents.

"What does "piggybacking" mean?"

Each section in the textbook has an introduction to a topic, then two sets of questions. The first set of questions is done as homework the first day, after the student reads the text. The next day, the teacher is supposed to straighten out any confusion and misunderstanding. Then, that night's homework would be the second set of problems over the previous section, and the first set of problems over the next section. I think "piggybacking" refers to the idea that they are doing 2 sets of questions each day. Sorry I didn't make that clear in my first post.

They were quite clear that the kids were expected to teach themselves the material, and that the teachers were really there to answer questions.

SteveH said...

OK. I thought "Piggybacking" had something to do with the connection between T-Math and high school math.

The high school doesn't go up to calculus; just Pre-Calculus?


"... the teachers were really there to answer questions."

They don't even introduce the material? T-Math tells them not to do that on purpose? So, rather than cover the basic questions that most students would have as a group, the teacher wastes lots of time answering them individually the next day after the kids have had a frustrating night of homework?

My son had a "technology" class like that at his old school. They were building robot kits. The teacher didn't teach anything, but just answered questions. I can't tell you how many times my son told me that he had to wait and wait to ask the teacher a question. He was stuck and couldn't go on until he got the answer. The teacher probably got the same question from five other kids. My son said that the teacher would also go work on his computer and give off "don't bug me vibes".

SteveH said...

"... but give the educators federal benchmarks for content in math and English, then let the individual states, schools and teachers decide how to achieve those benchmarks."

I assume that this is a basic states' rights issue; a turf issue. States get to decide on their own (low expectation) tests.

We (KTM) had once talked about something like (externally-defined) AP standards and tests for 8th grade. I think this might work because it's optional. However, given enough publicity, parents will begin to demand these courses and the schools will have to provide them. They will have to prove that their 8th grade algebra course meets AP (or NMP?) standards. A national 8th grade test would force the issue. They would also have to provide the curriculum to get to that course. It's a way for parents to compare schools across the nation.

Current AP tests keep high schools honest (mostly), but we need the same thing for K-8. As it is now, there is nothing keeping K-8 schools honest. They do whatever they want and then ship kids off to high school where they and their parents have to pick up the pieces.

Anonymous said...

Be careful what you wish for. There is zero evidence that centralization of anything has ever led to excellence.

Counterpoints: Soviet Union, Post Office, Public Education, FEMA, Nationalized Industries (pick one), Nationalized Press (pick one).

And, plenty of evidence that quite the opposite is true.

Points: worldwide auto industry, telecom, computers, agriculture, clothing, semiconductors, machine tools.

Nationalized standards can drive pedogogy in subtle ways, for example, spiral curriculums are derivative of spiraling state standards in my state which lead directly to the fuzzy books that support spirals. So it's not as simple as coming up with an ideal set of standards.

Plus, and this is the scary part, imagine a national effort to do such a thing and the kinds of folks who would be lobbying/participating/consulting/politicing as part of the 'team'. This scares the hell out of me because I don't think for a microsecond that the 'team' would be composed of anything but the ninnies who have gotten us to this sorry state in the first place.

Instructivist said...

[Plus, and this is the scary part, imagine a national effort to do such a thing and the kinds of folks who would be lobbying/participating/consulting/politicing as part of the 'team'. This scares the hell out of me because I don't think for a microsecond that the 'team' would be composed of anything but the ninnies who have gotten us to this sorry state in the first place.]

It might be worth it just for the sheer spectacle of having a motley crew of quacks, charlatans, snakeoil salesmen and mountebanks all in one place.

On the other hand, a national effort was able to put a man on the moon. Shouldn't it be possible to put up decent standards to be followed at least on a voluntary basis. There is no need to reinvent the wheal. Good standards already exist, e.g Core Knowledge, CA math standards, etc.

Instructivist said...

If algebra in 8th grade, then what should the HS sequence look like?

+++++++++++++++++
Correction: wheel

TerriW said...

On the other hand, a national effort was able to put a man on the moon.

But there was a national pride issue driving all of that. Maybe if China sent a man to Mars we could get decent math curriculums back into the schools.

Catherine Johnson said...

Haven't read the comments here yet (MIRED IN CHICKENS!!!) but The Race Between Education and Technology is the book to curl your hair where all of this is concerned.

Basically, for 3/4 of a century America raced ahead of the rest of the world due to universal education -- universal education in the liberal arts disciplines, not vocational ed, which is what the rest of the world was doing.

All of that stopped in the late 1970s.

We've had rising inequality ever since.

Catherine Johnson said...

Also, the fourth graders at my school are being taught pre-algebra by using Dr. Henry Borenson's hands-on math equations.

How'd that come about?

And what's it like, anyway?

SteveH said...

"Be careful what you wish for. There is zero evidence that centralization of anything has ever led to excellence."

How did AP testing get started? I took calculus in high school before the AP appeared. Why didn't high schools ignore the trend? My guess is that it made a difference on college applications and then parents expected it.

Anonymous said...

re: Moon

Remember, at the time, NASA was like a military operation and was very much the tip of the spear regarding space travel. At that time it was an innovative organization.

Now fast forward. What was the date of our last moon landing?

NASA has evolved to a stately dino much like public education. It still gets things done but the bloom is off the rose.

Unknown said...

A national effort to improve P-20 mathematics content is a little scary. The possible ill effects are evident in the amount of effort (money) that has been funneled over the last 20-30 years into what have proved to be mediocre programs.

But, as Instructivist said,
"On the other hand, a national effort was able to put a man on the moon. Shouldn't it be possible to put up decent standards to be followed at least on a voluntary basis. There is no need to reinvent the wheal. Good standards already exist, e.g Core Knowledge, CA math standards, etc."

I think that transparency is the key. By developing a better "delivery system" which focuses on content and success of students, not on teacher workshops or any particular trademarked program, our current systems will improve.

PaulaV said...

Catherine,

Regarding Borenson's hands-on equations, I have no idea how it came about. Last week when I was copying papers for another fourth grade teacher, I noticed her class was using the lessons. Lo and behold when I asked my son about it, he said his class was also using it.

I have no idea what the "hands on equations kit" is or how it is used. My son said it is supposed to be pre-algebra. While he thinks it is easy, he still doesn't understand why he is learning "pre-algebra" this way.

Anonymous said...

After reading these comments, I googled borenson. Have you been to www.borenson.com? After going there, I'm pretty sure these are the problems that my third grader was doing in school this spring. She had worksheets of single-variable algebra problems (basically solving for x). Looking over the completed sheets she brought home, I was puzzled. She had all right answers, but the only work shown was to plug the answers back in to verify that they worked. My daughter explained to me that they had used the hands-on manipulatives to actually solve the problems. Then, they plugged the answers back in to verify.

I think the hands-on manipulatives are pawns that represent the variables (x = 1 pawn; 2x = 2 pawns). There must be some other pieces that represent constants. Then, with these pieces the students solve for x according to laws of equality. So, you can add some constant to both sides of the equation, or you can take away a pawn from both sides of the equation, etc. I like this idea a lot. I had experimented with similar manipulatives using magnets marked "x" or "1" or whatever. I think it drives home doing the same operation to both sides of the equation.

I realize this is not a full-blown algebra course, but I think this type of problem solving is algebra--not just pre-algebra. I am thrilled that my daughter saw it in third grade. One reason that she could is that our public school does ability grouping for math. My daughter's group had finished the school year's worth of Saxon math by December. The top group could go that fast. Then, there was time to move ahead (thank you for not just "enriching") to topics like this kind of algebra.

I like it.

Dan K.

PaulaV said...

Dan K.,

Your daughter had a year's worth of Saxon. My son has had a year of TERC math investigations and worksheets pulled from various math workbooks. If it were not for Kumon and hours of tutoring by my husband, I doubt seriously my son would be able to understand the hands-on equations.