The new math skills map produced by the Partnership for 21st Century Skills (P21) does not help teachers teach Common Core State Standards (CCSS), writes Ben McCarty, a University of Memphis math professor, on the Common Core blog. McCarty, who’s taught mathematics to first, second, and third-graders and to pre-service elementary teachers, says P21’s exercises are ill-defined, imprecise and not aligned with content.

Art from Bigstock.The 8th grade example on page 12, for instance, engages students in a wonderful discussion about the health content of a typical fast food meal, but mathematically, students are only computing percentages and comparing them to daily values. That’s it. This activity is well below the 8th grade content standards in the CCSS.

Worse still, the 4th grade example on page 21 has students tallying the number of various types of media messages they are exposed to on a daily basis. Based on the description of the activity, no analysis is done with the data beyond basic counting–a Preschool/Kindergarten skill.

. . . Finally, the 12th grade example on page 23 has students collect and display data on developing countries, as well as build a web page to display the information. The students don’t generate the data. They don’t do calculations with the data. They merely read about a poor country, and publish data on it.

“Simple arithmetic problems and routine data collection assignments” will not “prepare students for professional careers as engineers, doctors, software developers, and the like,” McCarty writes.

Sounds like the students would actually learn more out of a math for dummies collection than the nonsense which is being foisted at them (ugh)…

The CCSSM provide real world examples for students to see the relevance of math. Mathematics is more than following procedures. It requires students to think and problem solve. The examples above are simply situations in which math can be used to solve a problem. As with anything, teachers are required to make the connections for students, and enable them to think about how math can help solve problems. When we oversimplify education we run the risk of devaluing the importance of educators.

The CCSSM is valuable in that it levels the playing field across the country. It allows states to share resources and therefore develop valid and reliable tests that can assess student understanding. It sets the standard that math is more than a rise of steps to follow, but a way of thinking and reasoning.

After an era of too many children left behind, we are finally taking steps to teach students to think. Give CCSSM a chance. Give our students a chance. In time, I believe we will find that we really are making a difference and CCSSM helped us do so.

Mathematics is more than just number-crunching, but even when numbers are absent it still has a level of rigor, logic, and relevance I fear these standards omit. Consider the initial non-trivial case of the Ramsey problem, often stated as “If there are at least six people at a party, then either there are three people there who already know each other, or there are three people there who are mutual strangers, and six cannot be replaced by a smaller number.” The proof of this does absolutely no calculation, but it uses logic and mathematical visualization crucially.

Why not five? Put five people in a circle, and suppose each person only knows his neighbors. Demonstrate that the condition is not satisfied.

Why six? Draw the complete graph on six nodes K6. Each node represents a person at the party. Now, color the edges. Use red for the edge connecting mutual acquaintances, and blue for the edge connecting strangers. So, we have graph theory, and graph coloring problems.

Now, worry only about the colors, not about matters of people–removing irrelevant ideas. We are looking for a monochromatic triangle.

Choose an arbitrary node. Call it u. In general, no node is different from any other, so don’t waste time looking for a particular one.

Look at the edges leading from it. There are five, each either red or blue. So, it has (at least) 3 red edges, or (at least) 3 blue edges. That’s the pigeonhole principle, or the simplest of inequalities. Without loss of generality, assume it has 3 (or more) red edges. The choice of red and blue was arbitrary, and I could swap them if I wanted to. This is probably the most difficult step for the novice.

Look at the nodes on the other side of the red edges. Call them v, w, and x. If any of them are collected by a red edge, then they and u form a monochromatic triangle. If not, v, w, and x have only blue edges connecting them, again a monochromatic triangle. And that’s the proof.

So far, that had very little arithmetic. But, what is the generalization? This couldn’t b an important problem all by itself. The answer is this:

For any two natural numbers r, s at least two, there is a number R(r,s) such that any complete graph of that size colored with red and blue edges has an all-red Kr subgraph or an all-blue Ks subgraph. It is extremely hard to calculate the number R(r,s). The proof of this would only be for honors students.

Most of the applications of the theorem are in computr science.

I agree, math is something much deeper than simply following an algorithm and finding an answer. Kids need to work with numbers enough to get a real feel for them and their properties.

When an adult hears on TV “this condition afflicts about 1 American out of a million”, they should just know, without any serious effort that we’re talking about a few over three hundred people. That simple leap should be almost automatic.

Say all the nasty things you want about “drill and kill”, but I came out of high school (back in 1979, sigh) with a nice feel for numbers that has benefited me my whole life. My calculus teacher in high school, Mrs Calahan, was just about the best teacher I ever had.

I remember ‘drill and kill’ from my junior high days, my old math and science instructor Miss Watson (who is still a dear friend) gave me the skills to allow me to have the career I have today 🙂

Combinatorial reasoning and advanced logic (the highly abstract stuff Eric is talking about) are islands sitting in the center of a lake of drills, repetition, and suffering.

Maybe 1 in a few thousand people is lucky enough to be born on the island. The rest of us have to swim.

Many curriculum designers nowadays think that looking at pictures of the island is the same thing as being there.

Right; it’s called math appreciation.

I remember that course being available when I was in high school…never took it, was too busy hurting my brain with Algebra I/II, Analytic Geometry, Trig, etc…