Running some searches recently, I came across this April, 2004 article by Lee Sensenbrenner on Connected Math. The words remain timely more than two years later:
A seventh-grader at a Madison middle school is posed with the following situation: A gas station sells soda in three sizes. A 20-ounce cup costs 80 cents, a 32-ounce cup is 90 cents and a 64-ouncer goes for $1.25.
The first question, which appeared in similar form on a recent exam, is as traditional as any mathematical story problem: What size offers the most soda for the money?
But the second question carries the spirit of the Connected Math Program, which has developed strong undercurrents of controversy – both here and nationally – and plays prominently in one of the Madison School Board races Tuesday.
This question asks: If the gas station were to offer an 84-ounce Mega Swig, what would you expect to pay for it?
There’s really no concrete answer. A student, for instance, could argue that the 84-ouncer would cost what the 20-ounce and 64-ounce cups cost together. Another student could say that soda gets cheaper with volume, and then choose an answer based on some per-ounce price slightly less than what was given for the 64-ounce drink.
For the people fighting an impassioned battle over Connected Math, the differences between question number one and question number two are not subtle or inconsequential.
On one side, those who support Connected Math say that engaging students by presenting problems as real-life scenarios – often with no absolute solution or single path to arrive at an answer – fosters innovation and forces students to explain and defend their reasoning as they discover mathematical concepts.
The other side says the approach trades the clear, fundamental concepts of math, distilled through thousands of years of logical reasoning, for verbiage and vagary that may help students learn to debate but will not give them the foundation they need for more advanced mathematical study.
Many links and articles on math can be found here. The recent Math Forum is also worth checking out, along with a discussion of the District’s math performance.
I’m told that the MMSD’s math curriculum will be getting some attention this fall. We’ll see (35 of 37 UW Math Faculty Open Letter on Math).
My largest concern with Connected Math – having read some of the books is that we’re training the students to be consumers, not creative types (figure out the phone bill, count the cheerios, buy a soda, etc.). TeacherL made a great point recently: We can choose to be consumers or we can choose to be citizens. I know which one I think will provide the stronger future for our country.”
Please oh Please oh Please…….
Look into the Math curriculum this fall.
Johnny, Carol, Lucy, Lawrie… for every one person on this blog that complains about the Math there are a hundred that are complaining to the principal and teacher. Just ask the middle school principals! It needs your logical attention NOW. Oh please. Thanks.
Ok, I can’t help myself here Jim. Connected Math is the main reason that we have decided to send our new 6th grader to a private middle school. (Ditto Everyday Math for our 1st grader). We do not feel that it prepares students for the rigors of math in high school and beyond. I asked a West HS math teacher what she was noticing about students readiness for 9th grade math and/or algebra. She said Queen of Peace students were the most ready (they do not use Connected Math) and that for the most part, are bored while she “reteaches” basic math concepts and formulas. Madison students do not know formulas and specific strategies to correctly solve problems (where there IS one correct answer) and are highly dependent on calculators. She couldn’t speak much to student’s coming from Edgewood, since the majority either take the 9th grade requirement in 8th grade or stay at Edgewood for HS. Most Eagle students move into higher math.
I have talked to folks at Doyle and folks at Cherokee. I”m told it “ain’t going away” but that “good” teachers know how to use it and supplement it. So, you get a more solid math program if you have a teacher who is willing and able to go against the Madison policy to teach Connected Math as “the” program.
Our children can’t “wait” for Madison to take a “look” at the math curriculum since they are suffering in it now (I can say the same for science, or lack thereof). So, we’ve decided to get them a rich math program from the get go.
I do hope that the math curriculum to be changed! Maybe our youngest could get back into the district where we are paying high taxes to fund so I can save SOME money for college!!
My husband, a math professor at UW, tells me that students come to his classes unprepared in basic algebra. I would like to find out why.
However, he liked the second question above because it is a good test of numerology and logical thinking. It was a poor choice for an attack on connective math,
Not all questions in the world have exact answers.
Don’t just jump on every Connective Math smear that comes down the road.
Both math questions are important. Anyone who grocery shops runs into the second question frequently – now the grocery stores provide you with the per unit cost, which is what you’re trying to determine, so you can compare which deal is the most economical. However, that may not answer all the questions/criteria (organic, sugar content, recycled materials) you have for selecting this food item, but it does allow you to make a comparison based upon cost, which is a mathematical calculation.
When connected math was introduced into the MMSD math curriculum, I was concerned not because it was connected math, per se, but I was concerned there did not appear to be an ongoing evaluation/feedback component in place with yearly goals in place. I don’t remember a pilot and evaluations of a pilot with discussions among the district’s math staff (at all levels) and other math professionals about changes in student achievement. During the three years my daughter was in middle school, I was not asked about the math curriculum – did I feel my daughter was getting a strong foundation in mathematics, did I need any help understanding the math being taught so I could help my daughter. I did not hear anything about any ongoing assessments/discussions among math professionals – mmsd admin, mmsd teachers, uw professions, parents. I want to be very clear to say the math teachers were always willing to help my daughter if she had any questions. The teachers would be available to provide needed help, and I sincerely appreciate their talent and hard work. But, do they have the best tool, combination of tools to teach math to students? Ongoing process and impact evaluations, discussions, changes, goal setting are key. State law requires ongoing evaluations of K-12 sequential curriculum.
To me, it’s not simply about Connected Math – yes or no. It’s about learning math – what’s do children need to know, what sequences of learning need to be followed, what must you know before the next step, etc., are our children successful math learners?
I’m also concerned with the appearance (reality?) of the UW math department being out of the loop/discussion re the math curriculum for the largest school district in the area. What input into the math curriculum do our Madison math teachers have? How much discretion do teachers have in using an approach they feel will provide students with the most rigor and academic achievement? Is it one size fits nearly all? I know there is differentiation in levels, but what about teaching approaches and other curriculum models.
Do teachers have the ability and flexibility to teach to the standards using the approach they believe is the most successful for their students. Maybe a little, but in practice, I would think that would be hard in such a large institution and get complicated with purchasing materials. With staff and other resource limitations, I would like to see some sort of Math Council that reports to the Performance and Achievement Committee of the School board that oversees student achievement.
You simply must have the basics down.
To me, mathematics is like a language, a different way of communicating. When I learned a language, I needed to learn basics of verbs – conjugation, tenses. I needed to learn vocabulary. Then, I needed to learn and to practice how to put this information together.
From my experience helping my daughter with algebra, basic algebra, at the introductory level begins with integers, fractions, order of operation, exponents, etc. You have to have this information down in order to be able to learn, to understand, and to compute algebraic problems. Each of these areas, have their own rules, so when you combine say fractions, exponents, parentheses in a computation you have to know the order of operations and the rules for each of these areas of math.
Also, you have to know how to do the computations following the rules but also be facile with trial and error and/or estimation. Then you have math problems, which ask you to think about how you would take all this information and apply this information. Simple problem: if a rug costs $800 and costs $20/square yard, what is the length of the room if the width of the room is 15 feet. You need to know the equation for area, determine what parts of the equation you know (area and width), recognize units are different, convert, etc.
Clearly, one needs to know a) rules for different aspects of math and the terminology, b) how to do basic computation and c) how to apply these rules and computations to solving problems, which have their own logic.
I’m not a math professor or a math teacher, but I am an adult who took many years of college math and statistics. I worked with my daughter with the connected math materials, which I did not find very useful. These materials were not clear to me, did not provide the basics clearly and I was hard pressed to find definitions of various math terms and concepts many times.
If I was unclear how to explain a math topic – sure I could solve the problem, but to work with my daughter I needed to review the steps so I could explain the concepts and steps, etc., I would go to the internet and Google the topic.
To do math, it seems to me you need the basics and you need to know how to use this information solving problems. Another simple problem: You have $1,000 and have earned $300. How long did it take to earn this money at 3% per year (simple interest, not compounded)? You don’t necessarily have to say – what’s the equation for simple interest? You do have to know that you have to take 3% of $1,000 and that gives you the interest you have earned for one year. If I know the total I’ve earned, $300, and what I earned in one year, then I can either a) divide $300/$30, b) trial and error – multiply $30 by 3, $30 by 10, etc.
I’ve volunteered as a math tutor since my daughter was in Kindergarten. Fifth grade is one year that stands out to me. I was amazed how many children did not know their multiplication, division, addition and subtraction math facts by the end of fifth grade. Not having this basic information down cold, slowed them up when working on fractions, decimals, and freeing their minds to think about the logical steps to follow in a math story problem.
I would like to see our School Board set more specific goals for mathematics based upon input from professionals – mmsd admin, uw professors, teachers, parents who work in the field. The tests students take would allow more specific goals to be set. It’s necessary but not sufficient to have math goals for algebra and geometry in high school, but I would suggest simpler more concrete goals for each grade. We have the standards for each grade, measurable goals can be developed from these standards and refined as we learn from setting goals. If the goals aren’t being met, perhaps the tools/approaches being used are incomplete, inadequate, might be part of the reason. Our teachers, math professionals, students, parents need to be part of this loop. It’s not simply a question of Connected Math – it’s about learning and being able to use math as children and adults in our everyday lives.
Barb,
You mentioned the need for standards or goals. If you visit the site below from the state DPI you will see the “math standards” for 4th grade “Mathematical Processes Performance Standards.”
I’ve included its entirety below the site.
http://dpi.wi.gov/standards/matha4.html
“By the end of grade four, students will:
A.4.1 Use reasoning abilities to
perceive patterns
identify relationships
formulate questions for further exploration
justify strategies
test reasonableness of results
A.4.2 Communicate mathematical ideas in a variety of ways, including words, numbers, symbols, pictures, charts, graphs, tables, diagrams, and models*
A.4.3 Connect mathematical learning with other subjects, personal experiences, current events, and personal interests see relationships between various kinds of problems and actual events
use mathematics as a way to understand other areas of the curriculum (e.g., measurement in science, map skills in social studies)
A.4.4 Use appropriate mathematical vocabulary, symbols, and notation with understanding based on prior conceptual work
A.4.5 Explain solutions to problems clearly and logically in oral and written work and support solutions with evidence”
When you couple this thin soup (It got a D- rating recently from the Fordham Foundation’s evaluation of state standards) with educators willing to facilitate fuzzy pish-posh like connected math, you have a prescription for mediocrity or less.
When asked about the textbook, then, the educator or administrator will be able to say “our textbook is aligned with state standards.”
Nevermind the fact that a recipe book for chocolate-swirl bundt cake would be aligned as well.
Barb, Are you aware of any MMSD administrative system that currently allows teachers, professionals, students, and parents to be “part of the loop” on any issue?
I’m not. The board created the attendance task forces and the equity task force; based on what I’ve seen and experienced, however, the administration does not welcome input from anyone or any body other than staff at the Doyle Building.
Has the administration (or the board) yet agreed to set up a community committee on fine arts, a request you’ve been making for the last few years?
Maybe I’m mistaken, and you know of some process that allows “outsiders” to be part of the loop on an issue, particularly an academic issue, in the district.
Reed and Ed,
Goals: The standards are general; test scores are more specific – basic, proficient, etc. Within the tests, there are sections of different concepts being tested. I would like to see the Board set specific high level goals, the administrators take those higher level goals and make them more specific and measurable by grade, or some other appropriate grouping. Is it unreasonable for the board want to see x% improvement in overall test scores each year, or within groups, etc.? I simply feel mmsd needs more than 9th grade algebra and 10th grade geometry for board priority goals in the area of math.
I don’t know of any academic councils that involve various professionals, parents, etc., providing oversight and feedback. Perhaps the performance and achievement committee could explore this. I’m on the Partnership Committee this year, and we will be looking at MMSD partnerships with parents and improving/strengthening partnerships between the district and parents through various listening/focus sessions with parents around the district.
Re., fine arts, not much to report here. After more than 7 years of cuts in fine arts, there is no strategic plan for fine arts education, I know of no forward looking initiatives underway that include the community. There is a “pilot” for elementary strings next year for one school. Both Shwaw Vang and Lucy Mathiak are interested in this.
in my previous comment reference to mr. vang and ms. mathiak’s interest was not in the pilot for elementary strings but in community involvement/engagement in fine arts education issues. i expect to see any initiative of this sort begin in mr. vang’s performance and achievement committee.
support for a pilot music choice in grade 4 was from mathiak, vang, robarts and kobza.
With four kids in Madison schools, I feel I know why kids struggle with algebra. Although I honor aspects of the “constructionist” approach, math curricula such as Everyday Math do not offer enough practice after the student constructs the concept. It’s important to understand that 5 X 6 is 5 sixes or 6 fives. But if at age 12 you have to count 5 sixes to solve 5 X 6, you are unable to handle the arithmetic component of algebra problems. The “spiraling” curriculum had too few problems in any one area for my children to feel they had mastered anything.
The calculator dependency is nuts; last year we homeschooled, and I found my 7th graders couldn’t divide a 3-digit number by a 2-digit number without a calculator.
We supplemented with Singapore Math, which offers a logical, stepwise approach to math concepts with both understanding and mastery emphasized. When people argue about “concepts” vs. “drill” I wonder why in the world we can’t have both.
Kay Cahill
There SHOULD be balance. I have, after wrestling with it for awhile, become a big fan of many of the key tenets of a constructivist approach. I have definitely become convinced that teaching standard algorithms should not be a first step in any operation. I also believe that assigning 50 of the same problems (as homework, for instance) gives students 50 opportunities to practice making the same mistakes over and over until they are really good at…..making that mistake. Direct Instruction (big D, big I 🙂 ) also discourages homework or “seat work” for the same reason. The idea is that once you “have it”, you don’t need to do it over and over again; and if you don’t “have it”, you need more guidance than seatwork/homework provides. However, that should not mean that students are not engaged in multiple opportunities for practice, and I think that, just as in reading debates, we tend to overgeneralize ideas on both sides. It IS possible to provide adequate practice without undermining the approach to teaching–but we can’t be lock stepped into the scope and sequence of a published curriculum to meet students needs. We have to assess what is needed and provide that to appropriately pace for each student.