Our first Exposé is Math in Focus 3.
Math in Focus is an American version of the popular Primary Mathematics (also known as Singapore Math) and is published by Houghton Mifflin Harcourt. It is a popular choice among homeschoolers who like the Singapore method of teaching math, but prefer to have the bulk of the instruction in the actual text (rather than a TM). This makes it a little easier to teach (less flipping between books), and potentially less expensive. Some prefer the MiF layout over PM. This math program is also used by many brick-and-mortar schools and therefore lines up with standards.
The most recent edition of MiF (2013) is marked as Common Core aligned. I am going to be referring to the 2009 edition, which is virtually identical to the the newest edition (they have made some minor changes, but the content is the same and the pagination is even the same). It is very common for both homeschoolers and schools to use an older edition---they are readily available, much cheaper, and compatible with the current workbooks.
My examples only apply to the 3rd grade books, however part of what is at the heart of the problems we encountered with this program have to do with its incremental approach. So, it was useful for me to look ahead to the grade 5 books (which I also own) to see how the instruction progresses. Some of the concepts that are really just introduced in level 3 are more fully developed in level 5. Because of that development, the errors that are present in level 3 are less obvious in level 5 (I haven’t gone through it with a fine tooth comb, though).
In other words, if you are jumping into MiF at a later grade, you may not encounter these flaws or they may be less of an issue. Level 3 was a surprise.
A big, fat, ugly surprise.
Let me present this to you in the way that I discovered it.
I randomly opened the A book (1st semester) while preparing for this coming homeschool year and landed on page 59. The teaching examples were on deciding when to find an exact answer and when to find an estimation by rounding. Here are the details of one example that made me want to throw the book out the window (the window was open, but I didn’t want to bust my screen):
A little clipart depicts---
Dining chair $122
Arm chair $177
Computer chair $138
Now for the text of the example---
Darren has $335.
After buying 2 of the chairs, Darren has $136 left.
How much do the 2 chairs cost? (need exact figure)
Which 2 chairs does Darren buy? (an estimate is sufficient to figure out which 2)
Ok, we we are supposed to figure out that we need to find the exact difference to know how much the 2 chairs cost.
That’s easy. $335-$136 = $199. So Darren spent just under $200.
Therefore the correct real world answer to the 2nd question is:
Darren didn’t buy 2 chairs, because he didn’t spend enough money. At a minimum he would have had to spend $244 to get 2 dining chairs.
Maybe he lied and bought some candy instead?
Or maybe the salesman had an old, drastically reduced relic in the storeroom and he bought that?
But that’s not the answer in the book. Here’s how they figure it:
Dining chair 122 rounds to 100
Arm chair 177 rounds to 200
Computer chair 138 rounds to 100
$100 + $200 = $300, so he can’t have bought the dining chair and the arm chair, that would cost about $300.
$100 + $100 = $200, the dining chair and the computer chair cost $200 (uh, no, they don’t), so Darren buys (note the tense change, yes it’s in the book) the dining chair and the computer chair.
Insert facepalm here.
Here furniture salesman, how about if I estimate the cost at $200 and just give you that?
Now, to be completely fair, I thought, “Maybe this is an error and they have corrected it in the new edition.” So I checked an online sample that shows the entire text (you can see it here).
Nope, this problem is exactly the same in the 2013 edition, right down the the amounts, the procedure, and even the page number.
I checked the teacher’s manual to see if there was some explanation there that would make it clearer. Nope, there were no special notes in the manual.
Let’s take a close look at what’s wrong with this example.
The problem itself is poorly written, for one thing. Editor, where are you?
The answer to question #1 makes it impossible for Darren to have done what we are told he did. They also keep changing the tense in the problem to (first it’s that he bought 2 chairs and had x left, then it’s that he buys these two chairs).
If you stick with the problem as written, it’s akin to telling your kid to ignore the fact that it’s illogical. Please don’t do that.
Once we get past the illogicalness of the problem and how it is written, the method it is teaching is also unsound. If I am going to estimate the cost of items that are all under $200, I’m not going to round them to the 100s place in the first place.
Think about that. Rounding a $138 chair to $100 is like knocking 28% off the purchase price. Part of learning math is learning what type of rounding is appropriate in a given situation. This type of rounding is not appropriate in this situation and it risks teaching kids poor thinking habits.
There are an infinite number of ways that this problem could have been rewritten in such a way that it would make logical sense and would foster good, solid thinking skills.
But as it is written, there is a disconnect between the theoretical and applying arithmetic in real world applications. In a theoretical world, it might be ok in some instances to round a dollar amount to the hundreds to get a ballpark figure on what can be purchased. But in the real world, you cannot spend $200 and purchase two items that together cost $250.
That’s just plain sloppy thinking and sloppy teaching.
This is just one of many similar issues my husband and I found with this text. And we just randomly flipped, we did not go through it systematically.
Over and over there was a disconnect between the theoretical and real world applications. That’s disturbing when you consider that one of the big goals of teaching kids how to do math is so they can use it in real life.
What’s at the heart of this sloppy teaching?
Are the textbook writers trying to lead our children astray? Do they want to encourage the type of lazy, imprecise thinking that will cripple our children when it comes time to do things like make a budget or decide whether they have enough cash in hand to buy the groceries in their cart?
Some people seem to think so. They say that the curricula writers want our kids to be stupid.
But I don’t think so. I can’t see into the hearts of these people, obviously, but after comparing level 3 of Math in Focus to level 5 and seeing the progression through concepts, I think the answer boils down to: over-incrementalization (I made that word up) of instruction and premature introduction of abstract concepts, which in turn leads to oversimplification of those concepts. Oh, and bad editing.
In defense of the book’s author, I can kind of see what went wrong here and why. It’s likely that there was a list of concepts that needed to be taught at this level (standards) and a list of specific types of problems that needed to be practiced (Estimation with money! Rounding to the hundreds! Knowing when to find the exact number or to estimate! Check, check, check!), and the need to address specific topics at a specific grade level got the upper-hand.
It’s possible that what’s at issue here is how we are teaching math in this country.
Perhaps there is too much emphasis on standards and not enough on logical progression of skills?
Someone’s liable to slam me for that. But let me give you an example: how important is it for a 2nd grader to learn to tell time to the 5s if she learns all of how to tell time by the end of 3rd grade? What if I wait until 3rd grade when she is fully capable of learning it all and that’s it?
Here’s another example we found in the Math in Focus books:
The level 3 lesson on “front end estimation” only takes into account the first digit of the number and it’s place value, whereas the level 5 lesson makes adjustments based on the rest of the number. That’s a difference between front-end estimating 989 as “900” (level 3) and “1000” (level 5). Pretty significant difference, right?
Over-incrementalization, y’all. We’ve got to wait two years to find out that our original front-end estimation wasn’t really quite right. Here’s how to make it more right.
What if…oh forgive me…but if we think kids won’t/can’t really understand the whole of front-end estimation until 5th grade, why not wait until 5th grade to teach it?
I realize that’s hard in the public school system, having a different teacher for each grade, and the general mobility of the population…but the reality is that if you use Math in Focus in 3rd grade and then a completely different book in 5th grade, you just might never fully understand front-end estimation at all and grow into an adult who tells someone that something that costs $2.89 at the local store is $2 (almost a third less than its actual cost) and not understand why they are annoyed when the $5 they brought to buy 2 isn’t enough (based on a true story).
Of course, there are some who will say, why teach it at all?
(warning: ramble alert)
Front-end estimation, as I see it, tries to distill a logical thought process down into specific baby steps for kids to follow. Interestingly, it’s the type of strategy that someone who has a solid foundation in arithmetic may come up with on her own to simplify figuring stuff out in her head.
It’s shower math. It’s ruminating over your homeschool budget as you try to go to sleep math. It’s wielding an overfull cart and 3 crazy children through a grocery store math.
It’s the type of math that someone who is comfy with figuring stuff does. That’s an admirable goal for our kids---getting them comfy with math, yes!
But, the catch here is that you don’t get comfy with math by learning short cuts or strategies---you use short cuts or strategies when you already know what you’re doing and are comfortable with it.
You may be able to teach that type of thinking explicitly. But it may make more sense to lay the foundation and present opportunities for using those skills so that kids can discover patterns and strategies as they become more and more well-versed in how to figure stuff out.
Because what do they do when the short-cut doesn’t work and they don’t understand why?
(end of ramble)
In the end, we decided that Math in Focus was not going to be a good math program for our family simply by virtue of the fact that it might lead our kids into sloppy thinking. I would either need to skip some of the material or modify it---and sometimes it’s just easier to either start from scratch or use a program that doesn’t have obvious problems.
So we are looking for math program that doesn’t have that same disconnect between the theoretical and reality.
What do you recommend?