Project M3

From the Overview:

* 12 units of mathematics for talented students in grades 3, 4, and 5

* 4 units per grade level: Number, Algebraic Reasoning, Geometry and Measurement, and Data Analysis and Probability based on NCTM content Standards

* Emphasis on mathematical discourse within the classroom

* Emphasis on problem solving and spirit of inquiry

* Differentiation of selected units for use with all students in years 4 and 5

* All materials to implement the curriculum will be provided including manipulatives and supplemental resources

I'm unfamiliar with it and am working with a school that is considering Singapore Math along with this Project M3 or MathLand. I don't believe MathLand is in print anymore, so I'm not sure where the school found textbooks to review. I seem to recall it was a highly constructivist program approved, then rejected in California.

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I know of this program only because of the Neag Center for Gifted Ed here in CT. The Davidson Institute has a grant to research the program.

More info here:

http://www.davidsongifted.org

/db/Articles_id_10490.aspx

(I broke up the link so it wouldn't become truncated.)

There was Project M3 funded by NSF in Missouri in the late 1990s with both the Reys involved. It stood for Missouri Middle Mathematics and was an inquiry, hands on, experimental curriculum.

There's also an NSF funded Project M2- Maturing Mathematicians.

In all likelihood this is a successor curriculum to those. It's never a good sign to emphasize NCTM.

Is the MathLand reference simply an attempt to make Project M# appear to be the compromise, balanced choice?

I glanced at the sample for the M3 Grade 3 "MoLi Stone" place value unit. It actually looks pretty good for GATE enrichment/supplement. It wouldn't be enough for a main math program, but I think if implemented properly, it would be effective in getting kids to think about the math concepts & use them to solve problems.

Am I correct in reading that the M3 units would be done in addition to Singapore? Or did you mean that the school is trying to decide between Singapore and M3?

Crimson Wife- Between! I'm going to recommend in addition to, though. I'm not seeing enough info to make this a standalone program. The school is k-8. I haven't the foggiest what were they planning to do for the rest of the grades and this curriculum.

Robin: It's possible they are clueless about MathLand and are considering it based on a teacher's recommendation...or I have misunderstood what they are really considering. They did refer to it as possibly out of print, so I can't imagine there was ANOTHER curriculum called MathLand.

I almost chortled aloud when the principal told me that is what they were weighing along with Singapore Math.

MathLand is long gone. Nobody claims it and all evidence has been erased from the web. The only things you can find now are bad reviews.

"...for talented students in grades 3, 4, and 5"

How do they pick these kids? What happens to the rest? I'm all for giving kids a way out, but once again, it puts the onus (blame) on the kids. Maybe more parents will ask why their child did not make the cutoff.

Yeah, citing NCTM is a bad sign. So are references to mathematical discourse, spirit of inquiry, differentiation and manipulatives.

Manipulatives!? I'm not persuaded they do much good in even the earliest grades, but for gifted fifth-graders? What on earth would you use them for?

Linda,

Math Trailblazers has fifth graders work with manipulatives to better enhance understanding of subtraction( and probably the other operations.) One class spent two weeks doing this. I only know this because my son observed it himself and couldn't believe it. Thank god he was already taking algebra at the middle school.

SusanS

Something we said brought out the trolls.

Must be how well we understand the NSF curricula as we borrow or print yet more money to impose it on this nation's schoolchildren.

From what I saw at the M3 website, the authors intended the units to be used as enrichment rather than as a school's main math curriculum. Something to use in a pull-out program or as an alternative for kids who pre-test out of a particular chapter in the regular textbook.

If there is only $ in the budget for one program, definitely go with the more comprehensive Singapore.

My school is using Singapore and ability grouping during a common math block so that the more capable students are moving ahead faster. It works extremely well with the higher level and average groups. Acceleration is a more effective strategy than enrichment with gifted students. The drawback to this model is that the lower level groups have a lot of kids with behavior problems in them; however, they are also making good progress because they are actually being instructed at their level so we are filling in the gaps they have accumulated over the years.

Acceleration is a more effective strategy than enrichment with gifted students.Except sometimes acceleration means that kids reach a point where they run into something for which they're cognitively not ready. That's what I'm worried about with my DD, that she'll run out of elementary school math before she's ready to begin algebra. I do a lot of enrichment as a way to slow her down a bit.

I agree with Crimson Wife on this. That is why, for example, if you are using Singapore math with quick-learning kids it is a good idea to go through not just the text/workbook but also one of the supplemental books like Intensive Practice or Challenging Word Problems, both of which offer both routine (i.e. like in the workbook) and more challenging problems at the same mathematical level as the textbook. In other words, rather than going on to new topics, did deeper into the current topic. This way you keep the challenge level up without having the student zoom to the limit of his ability and founder in more abstract things they are not ready for yet. You might have bright kids who have mastered all the arithmetic in sight but just are not ready for algebra. But they can work on multi-step word problems and the like.

>>Acceleration is a more effective strategy than enrichment with gifted students.

Accelerating in a lite curriculum gives the feeling of biting into a hollow chocolate easter bunny. It does not lead to above 700s on the Math portion of the SAT nor does it lead to a background appropriate for earning a STEM degree.

I had my wakeup call when my oldest was in 5th grade and his teacher only covered 4 of the 13 chapters in the text. The other 9 chapters are now called enrichment. I had to 'enrich' at home, so that the children could become competent in measurement, fractions, decimals, radicals, problem solving, multidigit multiplication, long division, and all the other topics that are now either left out of the full inclusion curriculum or are shifted to be 3 grades later than in the past. I understand now why so many cannot pass the NY Regents exam in Math.

Dolciani is as beautiful as it was when I was a student. Art of Problem Solving and Math Counts are helpful too.

"...the feeling of biting into a hollow chocolate easter bunny."

Great analogy. I'll have to remember that.

I could get my son to do calculus if I wanted to. It's easy to learn the basics of differentiation and integration. However, our schools won't even allow acceleration up to what I consider normal grade level in K-6. But as Igm says, who wants acceleration in a lite curriculum. Bad math is bad math. I remember thinking long ago about how I would never want my son to skip grades in a MathLand curriculum.

I was at an open meeting the other night that included our school committee and one from a neighboring town. They were talking about common issues in education. I thought my head was going to explode. Many of these people see education quite differently than I, and there seems to be no way to even get them to see things differently. This wouldn't be so bad except that they feel enormously confident about imposing their views on all kids.

They proceeded to trash the importance of SAT scores and AP test grades. One woman went so far as to say that there is no correlation between teaching and SAT scores. All they talked about was hands-on project-based learning. Our town just got a grant to buy a WeatherBug Station. This might be nice for enrichment, but they want to build the science curriculum around it. There seems to be this feeling that the problems of education can be placed on the student. Students just need to be more motivated with hands-on work. It's not that the teaching and curriculum could be stinking awful, but that the students need to be more motivated. Motivation will fix everything.

I used to think that this motivation angle was to inspire kids when they eventually have to buckle down to do the serious textbook learning. That doesn't seem to be the case. They want to use it as the basis for everything through high school.

AP courses were trashed at the meeting because students apparently are only taught to do well on the test. They come out and directly say that a '5' on the AP test is not an indicator of anything. Then, someone marched out an example (from the neighboring town's high school) about how a student who had a lower AP test score proceeded to do better in college than students who had 5's on the test. Case closed. The other town's high school is very big on the project approach to everything. They offer IMP for math in high school, but (reluctantly) still offer the traditional sequence of courses.

"Except sometimes acceleration means that kids reach a point where they run into something for which they're cognitively not ready."

Can someone please point me to some published research that identifies the stages at which a child becomes "cognitively ready" for certain concepts?

I've heard others use the concept of "cognitive readiness" an excuse not to offer algebra in the 8th grade. However, it seems to me that the reason many children are not ready for algebra in grade 8 has more to do with an inadequate K-5 math education than it does with the "cognitive readiness" of 11-13 year olds.

I would like to see documentation of what these "cognitive readiness" markers are and at what age most researchers agree that most students have reached those readiness points in a time line or chart format spanning from toddlerhood (e.g. concept of more/less) on through teenagehood.

Can someone please point me in the right direction to find this research?

I can only point you in the other direction.

NMAP's report

http://ed.gov/about/bdscomm/list/mathpanel/report/learning-processes.pdf

says there's no evidence that children are not cognitively read by age/maturity; they are only not ready if they have not been introduced to the proper information precursors. Even limitations that are biological like limited working memory when very young can be overcome with practice/memorization.

excerpt:

Learning and development are incremental processes that occur gradually and

continuously over many years (Siegler, 1996). Even during the preschool period, children have

considerably greater reasoning and problem solving ability than was suspected until recently

(Gelman, 2003; Gopnik, Meltzoff, & Kuhl, 1999). As stated in a recent report on the teaching

and learning of science, “What children are capable of at a particular age is the result of a

complex interplay among maturation, experience, and instruction. What is developmentally

appropriate is not a simple function of age or grade, but rather is largely contingent on prior

opportunities to learn” (Duschl, Schweingruber, & Shouse, 2007, p. 2). Claims based, in part,

on Piaget’s highly influential theory that children of particular ages cannot learn certain content

because they are “too young,” “not in the appropriate stage,” or “not ready” have consistently

been shown to be wrong (Gelman & Williams, 1998). Nor are claims justified that children

cannot learn particular ideas because their brains are insufficiently developed, even if they

possess the prerequisite knowledge for learning the ideas. As noted by Bruer (2002), research

on brain development simply does not support such claims.

These findings have special relevance to mathematics learning. Research on students

in East Asia and Europe show that children are capable of learning far more advanced math

than those in the United States typically are taught (Geary, 2006). There is no reason to think

that children in the United States are less capable of learning relatively advanced

mathematical concepts and procedures than are their peers in other countries.

I am not aware of any formal research on the topic, but I'm convinced because of personal experience. When I was 17 and a senior in high school, I enrolled in calculus. I'd received A's in all the previous math courses and scored 700 on the SAT-M. I simply couldn't understand calculus. I tried a bunch of different study guides, working with my teacher after school, several different tutors, etc. Nothing helped. My teacher took pity on me because he could see how hard I was trying and gave me a C rather than the F I deserved on the stipulation that I drop the class 2nd semester.

The following year as an 18 year old college freshman, I nervously enrolled in a calculus class using the exact same textbook as the high school class. Only this time around, it made sense to me. And furthermore, I loved it. I ended up receiving an A in the first course and an A- in the continuation.

The material was the same, the only difference was that I was finally ready to tackle it.

There are probably several reasons why you nearly failed calculus the first time.

I do not believe that the reason you succeeded the second time is that you were now suddenly "ready" for calculus.

Chapter 8 of Dan Willingham's "Why Students Don't like School" might offer some insight on this issue. This chapter explains why students have difficulty understanding abstract ideas.

I think that algebra in 8th grade and calculus as a senior are perfectly normal and that all schools should have a curriculum that tries to get kids to those points, and not in a sink or swim kind of fashion. This does not mean that schools shouldn't have slower tracks or options (not dumber tracks). It means that they should not assume that these targets are only for math brains. They also should not assume that if kids can't keep up with the top speed that they are not math brains. Curricula should be rigorous, but flexible.

As it is now, if you are not on the top track, you're nowhere. One can get to trig or pre-calc as a junior, but decide to not take math as a senior. That's not a good solution either. I took calculus as a senior (I had no problems), but had to take calculus over again in college because that was before AP credit days. That wasn't such a bad thing. It reinforced my knowledge.

Another option is to retake algebra as an 9th grader even if you have had the course in 8th grade. This will keep you taking math each year, but end up with pre-calc as a senior. Another option that high schools could use to avoid empty math years is to provide a math consolidation option as a senior. This would be a course that would reinforce and solidify one's understanding in math, kind of like a checkpoint. This might be a better option than struggling with calculus as a senior.

Students might not be ready for new material for lots of reasons. It shouldn't really matter why that is, but schools need to offer proper alternatives. For math, it shouldn't reduce to either the IMP track or calculus as a senior.

One other point. It was in my junior year (trig) that I finally felt that I really "got" algebra. I could do anything and not slow down or get confused. I wouldn't call this maturity or being ready for the material. I would call it mastery. I suppose that the math curriculum should have brought me to that point more methodically, but perhaps I just had to figure out and fill in all of my gaps and near-understandings. I'll wager that this made a big difference in why I did well in calculus.

I would argue that a valuable alternative to Calculus your senior year is AP Statistics. I think this is especially true for people that are thinking about going into the social sciences in college.

Or you can do what my sister did: Take Calc AB, BC and AP Stat. She was in a track that led to Calc as a Junior.

"... senior year is AP Statistics"

I forgot about that. I never took a course in statistics, but I had a lot of it in many of my other courses.

"She was in a track that led to Calc as a Junior."

Wow! I didn't know any school had a track like that. The question here, however, is what happens if someone wants a rigorous sequence in math, but wants it at a little slower speed. Also, how can you determine if things are not going well, for whatever reason? Are there other options, or do you just push right on to calculus? Statistics might be a good alternative, but it won't necessarily fix understanding issues that need fixing.

Many at KTM have commented that getting a proper foundation in math is more important than getting to calculus in high school. There is some truth to the problem of teaching to the test (i.e. bad teaching). That's why the idea has such traction with people. Of course, the solution is not one of the fuzzy, integrated math curricula that educators push, like IMP.

Isn't the premise of NSF math the idea that the AP calculus track is fundamentally flawed? I'm open to alternatives, but you have to define some basis for comparison. That's tough to do when you trash objective testing for fuzzy ideas like critical thinking and portfolios. NSF dislikes the content of AP-track math, not just the approach to the material.

Does anyone have any idea or data on the fallout of students from the AP calculus track? How many of the students who start out with geometry as a freshman end up not getting to calculus as a senior? How many stop while on top and how many stop because they hit a course where they fail? My belief is that kids fail because too many gaps and misunderstandings finally catch up with them.

I understand the reasons why some don't like AP classes and tracks, but the alternatives offered are too terrible to think about. Schools can either blame the teaching or they can blame the curriculum. If your philosophy leads you elsewhere, then it's very easy to claim that a new curriculum approach will solve the problem. As with Everyday Math, when your pet curriculum begins to fail, THEN you can start talking about the need for better teacher training.

AP as a Junior was a track at a school that was only for students that scored in the top 3% on the ITBS. There were actually a few students that took Calc as a Sophmore. They did it by covering a year and a quarter of a class each sememster. If you were in the track that only covered a year at a time, you could catch up over the summer and go up a track. I'm not sure if there was an option for shifting down a track.

I definetely agree that there are not great opportunities for the students that don't get into these programs.

I also think that there have been some changes since my sister and I were in school (I graduated in 2001, she graduated in 2005). The area districts are just now embracing Everyday Math and Terc.

--Many at KTM have commented that getting a proper foundation in math is more important than getting to calculus in high school.

Actually, I don't think I've ever read that here. I personally have said that getting a proper foundation is more important than getting AP credit for calculus in high school (because you still need to take calc again in college to learn it to mastery), but I think what's been said most often is this:

in nearly every school out there (perhaps excepting the TJs and Stuyvesants) you cannot get mastery of math without being on the AP calc track, because that is the ONLY track that leads anywhere in high school, since it is the only track that has any rigor on it at all.

It's not the AP class itself is necessarily all that rigorous; it's just usually that track has the least watered down curricula.

Fall off that, and it's over. You're remediating high school math in college, and all STEM subjects and most social sciences are closed off to you permanently.

The problem with 8th grade algebra being delivered top-down by states is that a) the schools can't teach it properly in 8th, so they don't, and so it isn't mastered then; b) because it's required in 8th, high schools can't teach it again for credit (so students don't take it or are already a year behind), and so it isn't mastered then c) the typical replacement high school track of geometry-alg2+trig-precalc-APcalc hierarchy is too long and drawn out to lead to rigor. It could be demanding, but it isn't. No demands anywhere after you've failed somewhere in middle school.

Crimson Wife - in New Zealand when I went through school we started to learn calculus at age 15 in ordinary, non-accelerated maths classes. (A small number of students took Maths With Applications, known by us students as Veggie-Maths). We started off with the concept of limits, and only later on moved to the short-cuts of differentiating and integrating.

It took me about 3 years to really grasp why differentiating and setting to zero really worked (the teacher told us and I memorised the explanation and reproduced it faithfully on exams, but I didn't really get it), but I could get answers with calculus fine.

If my struggles with calculus my senior year of H.S. were simply a matter of my not having the fundamentals down, then why did it suddenly resolve itself the following year? I didn't spend the interim boning up on math. On the contrary, I took an elective in law 2nd semester of 12th grade and spent the summer in France working as an au pair. If anything, the break should've made the return to calculus harder for me.

I don't think the issue was bad teaching by my high school calculus instructor either because none of the tutors or study guides I tried made any sense to me either.

The only explanation that makes sense is that my brain matured in the year between my first attempt at calculus and my second.

This is an example of distributed practice. You worked with calculus for one semester. You had a break for a semester and then you worked with the same subject matter (with the exact same book, no less) a year after first working with it.

This isn't a matter of your brain "maturing" in the interim. It's a matter of your brain recognizing something that it had dealt with before and determining that it must be important enough to retain.

A while back I read "The Non-Designer's Design Book" by Robin Williams (not the comedian). In the first chapter, entitled "The Joshua Tree Epiphany", the author describes how she received a tree identification book as a gift. She cracked open the book and read a brief description of how to identify Joshua trees. After looking at the pictures and reading about the tree she concluded that Joshua trees must not grow in Northern California, because it was a strange looking tree and she would certainly have noticed it if she had seen one before. Later she stepped outside the house and immediately noticed that most of the houses immediately surrounding hers had Joshua trees in their front yards. In fact, fact 4 out of 5 houses in the neighborhood had Joshua trees in their yards.

She had become concious of Joshua trees and now recognized them everywhere.

In your case, your brain began to "recognize" the calculus.

Crimson wife, the problem with your hypothesis that your brain needed to mature is that it doesn't make sense given that NZ schools routinely start teaching calculus to 15 year olds.

I dunno, I'm with Crimson Wife on this. I always did well in math, took Calculus in 12th grade, did well on the AP. But I always felt like I didn't really get it -- I just memorized and practiced and did what I was told.

The next fall in college, I didn't take math, but I found that I could help friends with their calculus -- that it now made more sense to me, I could understand what those things I memorized meant.

I swear that math fell into place for me from about the age of 17 -22 -- during which time I took few math classes. But suddenly, the abstract concepts suddenly were clear, the different ways of doing things that my mother had always harped on (which I hated to hear) made sense, rather suddenly.

The ending to the story is that now, many years later, I'm teaching middle school math and heartily agreeing with the non-constructivist approach that seemed so appealing in writing and as the parent of very math-adept children.

Now, I'm all about the content. No one can construct and discover about topics without the basic knowledge to build on. Doesn't happen. Does lead to a lot of guessing and a lot of thinking that any answer will do.

Wow, too fast typing, not enough editing.

Clarification: constructivism sounded best when I was reading about it and when watching my own children who picked up math quickly and easily.

In a low achievement, high poverty, urban school, it looks like chaos. It looks like students who can't estimate what half of a number is. Who will just add the numbers in any word problem, because that's what pops into their heads to do.

Cassy T my name is Robert Moore. I am working on a curriculum committee that is helping Supt. John Covington revitalize the Kansas City Missouri School District.I love reading about Singapore Math and I want to see it taught in Kansas City.I was wondering is there any studies showing it to be effective in the inner city school districts your help or anyone else that has knowledge about implementation of Singapore math please contact me at rlmcbc@yahoo.com. I love this blog

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