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and another letter....
Dear UCC Students:
Thank you for your letters postmarked January 12, 2006. In your letters, you pointed out that the numbering system used for the lessons in Fourth Grade Everyday Mathematics is incorrect if those numbers are interpreted as decimals.
[snip]
In the first edition of Everyday Mathematics, we numbered lessons consecutively, starting with 1, and running through the final lesson. This system was correct in terms of counting, but made it difficult for teachers to tell which unit a lesson was in without consulting the table of contents in the teacher's manual. [...] Many computer software manuals and other types of instruction manuals use similar systems for page or chapter numbering, so we hoped that this system would be familiar to teachers.
But, as you noted, although we don't mean them as ordinary numbers, "4.1" and "4.10" look like ordinary numbers. We mean them as identification codes, similar to the numbers you see on license plates or bar codes.
[snip]
The "error" of the lesson numbering has been reported to us several times. We will definitely change it in any future edition of Everyday Mathematics. But the economics of publishing does not permit us to change it in reprints of the current edition, since every page, and hence, every printing plate, would have to be redone.
It is very exciting to hear that you are noticing and questioning the way numbering is used. We are very proud that Everyday Mathematics students would be so observant and articulate and we hope that you will continue to use mathematics to interpret and question what you see in the world around you.
21 comments:
If this weren't a math book which already confuses people, I would call it a non-issue. The question is, are you using decimal notation, or dot notation? Computer software, for instance, uses dots, not decimals. This is why you can have multiple dots, and why, for example, Mac OS X v. 10.4.10 is not the same as Mac OS X v. 10.4.1.
In a math book, I would definitely use a different type of notation. But just because it's numbers and dots, doesn't mean it's a decimal. It's not wrong, just inappropriate.
Numerical digits used as labels are not the same as numberical digits used as numbers.
The publisher tried to point this out without being rude and pointing out that these students should have teachers who actually understand the difference.
It's really sad that the kids don't have teachers who understand this.
Yes, it's clear that numerical digits used as labels are not the same as those used as numbers. However, these are fourth graders and that grade has an emphasis on decimal notation. It would have been easy enough to avoid by numbering the lessons 1.01, etc. so that they could accomodate the teachers (which appears to be the priority) without creating confusion for children just beginning to learn about decimals. The publisher even points out that they have received many letters about this issue and agree that it is something they should change in the next printing.
Everyday Math wants children to "discover" and "construct meaning" and these students did. That the publisher did not forsee this is for me in greater question than the teacher, who encouraged her students to seek clarification from the source.
The publisher was using the standard method for numbering sections, and it is not fair to criticize them for not anticipating that this could cause confusion. If authors and publishers could anticipate every possible misunderstanding, then there would be no need for teachers.
The teacher should have briefly explained that a dot does not always indicate a decimal point. Some students might already be familiar with other instances of this. For example, dots are used in library call numbers and internet IP addresses. Dots are also sometimes used as date separators (e.g. 9.11.2001) and they are used as thousands separators in many European countries.
They changed the decimal to a small diamond in the middle between the two numbers. Like the argument over basic algorithms (e.g. Lattice Method), this takes the focus away from more important problems with EM.
Well, at least they kept their word to those children which is probably why they put them on the website at all (to highlight a change to the new edition). Good PR opportunity to say that these students are thinking about decimals because of EM (like a pat on the back) and not in spite of it.
Like the argument over basic algorithms (e.g. Lattice Method), this takes the focus away from more important problems with EM.
True. And the are so many more important problems that this is merely another distration.
Just curious...besides the small diamond, has anything else changed for 2007?
Such as:
1. Lower expectations
2. Distributed mastery that never gets done.
3. The curriculum is a mile wide and an inch deep with way too much emphasis on data collection and reading graphs.
4. The new sixth grade Student Math Journal has 386 pages, most of which is review of past material. Unless teachers move really fast, they won't get done with the books. If they go at it sequentially and stop when the school year ends, the kids will miss important material.
I consider number 2 (distributed mastery) the biggest problem. EM breaks the course into units and lessons. For the new sixth grade Student Math Journal books, there are 10 units. Each unit has between 5 and 15 lessons.
Many lessons talk about topics that have been introduced in previous years. (This is the shallow spiral approach of EM.) Even so, within each lesson there are "Math Boxes" that are mostly review of unrelated topics from previous years.
It's really odd to look at. I'll give you an example.
Sixth grade, lesson 4-2, page 127 on "Comparing Fractions".
This is clearly a topic that was discussed in previous years. They don't start the explanation from scratch, but they don't assume much prior knowledge. This is a short lesson, only two pages. The kids get 10 questions to answer on the first page.
This is just review for those kids who understood the topic from before. That's fine up to a point, although in many cases, it's just wasting time. For those who didn't understand the topic fully in the first place, this explanation and practice won't do the job. Hopefully, they will see the topic later, but what mechanism does the curriculum have to ensure mastery? None, as far as I can tell. It's left up to the teacher. What if, down the road, the teacher tests and finds that some students really can't tell if one fraction is larger or smaller than another? How can the teacher fix the problem at that late date?
EM is not mastery followed by ongoing practice. It is spiraling mastery with no way to make sure that mastery gets done. they just hope that if the kids see the same stuff over and over it will happen. This brings up the second page of the lesson on "Comparing Fractions". It has almost nothing to do with comparing fractions. It's simply an out-of-context review of past skills that is just arbitrarily placed in this lesson. On the second page (EM calls these "Math Boxes") they have the students do a stem and leaf table, they have them do some tasks like adding -21 + 12, and they have them say whether angles are acute, right, obtuse, reflex, or straight.
Review is nice, but this lesson is like two different reviews in one. What if a student is still having trouble with identifying types of angles. Is the teacher going to stop the flow of teaching (remember, we're talking about comparing fractions here) to review types of angles? What if kids are having problems with adding negative numbers? The teacher has to stop and explain that.
In this one two-page lesson, EM reviews a subect from previous years (comparing fractions) and then has the kids review in the Math Boxes: find the greatest common factor, find missing numbers for two fractions, do a stem and leaf table, adding negative and positive numbers, and identifying angle types.
EM does this over and over and over. I get the feeling that for the new edition, they took the old edition and just crammed in lots of review practice just to make people happy.
You have to try and keep all of the kids on the same page. You can't have a curriculum that allows kids to go at their own speed and hope that distributed practice will ensure mastery. I can't imagine any teacher liking EM unless they just don't worry about mastery. Perhaps they see some kids learning the material and can't understand why other kids cannot.
I don't have the old version of sixth grade EM to compare it with, but this Math Boxes issue seems much worse than the Math Boxes my son had in the old fifth grade SMJ.
Wow.
Your review deserves a post of it's own. Thank you, it was exactly the kind of description I was hoping for.
My daughter is going into 5th and it will be her second year of EM (2004 edition). In sixth grade they switch to Connected Math.
OK. Let's look at Singapore Primary Mathematics 6.
Two textbooks and two workbooks.
424 pages and no Math Boxes. The practice or review of material is done in context, and they don't waste much time on data collection and graphs.
There are 11 chapters or units, each covering only three topics or less. Obviously, this is not a hit and run type of curriculum.
Let's look at an example topic. This is topic 3-1 on "Rario and Fraction". There are step-by-step explanations and examples. I'm not particularly fond of their silly comic strip sort of characters with bubbles over their heads for sixth graders. However, they explain the subject with many examples (and bar models!) over eight pages before they give some practice problems.
I'm not a big fan of splitting the text book and the workbook. They give some practice problems at the end of the topic in their textbook, but you have to go to the workbook for more examples. I think it's the modern idea of textbook publishing - at least one of the books is written in by the student so that schools have to keep buying more books each year. Everybody does this now. I just don't like having to flip between one book and another for the same topic.
However, Singapore Math dives right in and teaches the topic. They assume that the student will do enough problems to master the topic. All kids will be on the same page. All kids will be tested together so that the teacher can fix problems before they get worse. Everyday Math just assumes that if you spiral through the material enough, then everything will be fine.
OK. Let's look at Everyday Math sixth grade for how they teach ratios and fractions. They talk about the subject in Unit 8 on Rates and Ratios, page 278 out of 386 pages for the course.
On page 278, the beginning of Unit 8, at the top, is something called a "Math Message", followed by:
"1. A computer printer prints 70 pages in two minutes. How many pages will it print in 5 minutes?"
No explanation. No discussion. No sample problems. OK, I guess I have to go to the "Student Reference Book". This book does not follow the Student Math Journal. I have to look in the table of contents. They have a section on Rates, Ratios, and Proportions that goes from page 108 to 124. The Ratio portion is just a few pages. EM does not use bar models for explanation. The problem is that the reference book is not directly covered in class. It's just a reference book.
I have to go to Lesson 8-6 to get to ratios. There is no discussion or explanation (you have to go to the reference book). It says at the top of the page:
"Math Message
Work with a partner. You may use a deck of cards to help you with these problems.
1. There are 2 facedown cards for every faceup card. If 6 of the cards are faceup, how many cards are facedown?"
This is not teacher-led. There is no way in heck that you can cover the material in this course if you teach that way. The students have 9 questions and a few sub-questions to answer.
Incredibly, the next page contains "Math Boxes". The first question is: "If 9 counters are 1/6 of a set, how many counters are in the set?" Another box requires you to plot a pie chart. Another box has the student convert from Centigrade to Fahrenheit, given the formula. This has almost nothing to do with ratios.
Then, the next two pages (this is still lesson 8-6!) they have ten "Ratio Number Stories". This is problem number 7.
"Mr. Dexter sells subscriptions to a magazine for $18 each. For each subscription he sells, he earns $8. One month, he sold $900 in subscriptions. How much did he earn?"
This is as hard as it gets.
For Singapore Math, Practice 3B, page 33, number 5.
"Mary mixed syrup, milk and water in the ratio 2:3:9 to make a drink, She used 6 cups of syrup. How many cups of drink did she make?"
You can open up EM anywhere and it looks like math. The problems are their shallow sprialing of the subjects, their emphasis on less important topics, and their idea of distributed mastery. The "Math Boxes" are just awful!
I love those decimal letters from kids!
Kids are hyperspecific!
That's hyperspecificity in action!
It is spiraling mastery with no way to make sure that mastery gets done.
I'm thinking the fluency people probably have the answer to this, which is timed worksheets.
I've always defined mastery as 80 to 90% correct - but as one of the fluency people point out, "percent correct" divorced from speed doesn't distinguish well-educated children with mental retardation from mathematicians.
This is dot notation. It's just not a problem.
Computer software uses this notation for versioning.
I can understand scrutinizing everything Everyday Math does, but once in a while, we're bound to run across something that's really not an issue after all.
This is one of them.
No, it's not a problem, just a "distraction" from the real problems that plague EM. If this were the only "problem" with EM we'd be in really good shape.
I did find the student's letters terribly endearing, however, and having gone through EM with a fourth grader this year it just struck a chord, I guess.
I thought I posted a comment someplace here at KTM about EM math boxes (it began something like: Everyday Math Boxes--RANDOM!) but I can't find it (anyone know how to search comments?).
Anyway, to partially reconstruct it, I did some research on Math Boxes and this is from the official EM site:
Math Boxes, originally developed by Everyday Mathematics teacher Ellen Dairyko, are an excellent way to review material on a regular basis.
In Everyday Mathematics, Math Boxes are one of the main components of review and skills maintenance. Once this routine has been introduced, almost every lesson includes a Math Boxes page in the Math Journal as part of the Ongoing Learning and Practice section.
Math Boxes problems are not intended to reinforce the content of the lesson in which they appear. Rather, they provide continuous distributed practice of all skills and concepts in the program. The Math Boxes page does not need to be completed on the same day as the lesson, but it should not be skipped.
Math Boxes are designed as independent activities. Expect that your guidance will be needed, especially at the beginning of the school year when some problems review skills from prior years. If children struggle with a problem set, it is not necessary to create a lesson to develop these skills. You can modify or skip problems that you know are not review for your children. Lesson activities revisit skills throughout the year. Math Boxes also provide useful assessment information on review skills.
Well, thank you, Ellen!
I agree 100% with everything Steve has said about this lousy teaching tool. "If the kids struggle, it is not necessary to create a lesson to develop these skills." Ack! What kids do learn from this type of instruction is that learning/achievement/mastery is neither necessary nor important. Just doing it is apparently enough.
The kids do tons of these "Math Boxes" (one page sheets with random problems blocked off into "boxes"). For the teachers it's a no brainer--what can they do besides just look it over, if they even do that? In our class the kids just exchanged papers and corrected them and returned them to the other kids that was the end of it. The teacher often did not even look at them. Big whoop as my son would say.
At least it's not a group activity...yet.
:)
Big whoop, indeed.
Vicky,
I saw your comments after I posted my comments here. I forgot where your other comments are. I guess I didn't realize what was happening when my son was doing fifth grade EM last year, but I just pulled out his old SMJ from last year and opened it up to Volume 2 and found the same thing going on. I also saw again that the teacher just went sequentially through the books and stopped when the school year ran out.
"In our class the kids just exchanged papers and corrected them and returned them to the other kids that was the end of it. The teacher often did not even look at them."
That's exactly what happened in my son's class. No assessment or correction. That's why the teacher had to form an after-school math group to help kids with everything they were supposed to learn in previous years.
First, there is this in Ellen's comments:
"If children struggle with a problem set, it is not necessary to create a lesson to develop these skills."
Then, there is this:"
"Math Boxes also provide useful assessment information on review skills."
If children struggle, you don't have to do anything about it? Perhaps this means that the teacher doesn't have to worry about assessment and correction with the primary lesson because the child will see the material again in many Math Boxes.
But you have to assess and correct at some point, and sooner is much better than later. For EM,
I completely understand why children would be confused with the way the sections in their textbooks are labeled. They are correct that 1.1 is equal to 1.10; however, as adults, we understand that the "." represents a dot and not a decimal. In an effort to improve our children's mathematics skills, schools have encouraged teachers to integrate mathematics across the curriculum. Students should see a connection between what they learn in each of their classes and should be able to find similarities in real-life situations as well.
The confusion lies when a child is trying to do this very thing...and ends up with an explanation that 1.1 in decimals is different than 1.1 used in the texted. This can be discouraging to a child. Since this is a mathematics series, I feel that special attention should be given to sensitive topics such as these. The textbook series should rethink their labeling method and maybe use 1A to represent Chapter 1 Section A, 1B to represent Chapter 1 Section B, and so on.
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