Readers of this blog are familiar with the Partnership for 21st Century Skills (P21), a collaborative of technology and education companies that aggressively advocates for reorienting K-12 education around the teaching of “21st century skills.” We’ve been on P21’s case since 2009, when three scholars who we asked to conduct an in-depth study of P21’s program found it lacking in almost every way (to watch a panel where they presented their analyses, click here). Common Core shares these scholars’ chief concern: That P21’s materials display a lack of concern for getting the basic content of K-12 education right, no matter the subject. We’ve already critiqued P21’s “skills maps” in science, geography, and ELA. They contained sample exercises in which students listened to speakers to determine which of them “sound scientific,” use globes and maps to create corporate logos, and translate Shakespeare into a text message.
Now P21 has taken on the subject of mathematics. So we asked another expert to take a look. The critique below is written by Ben McCarty, Ph.D, assistant professor of mathematics at the University of Memphis. Prof. McCarty has taught mathematics to first, second, and third-graders and to pre-service elementary teachers at Louisiana State University. In addition to being deeply knowledgeable about mathematics, he also knows what a useful curriculum tool for the teaching of math should look like. Not only did McCarty find nothing useful about P21’s new math skills map, he found the vast majority of exercises in it “ill-defined, lack content alignment, and possess a general lack of precision.” According to McCarty: “In fact, out of the 80+ examples proposed in the document, I count a grand total of 6 that I would consider relatively good math problems for the cited grade level.” Prof. McCarty’s full analysis appears below.
-Lynne Munson
Einstein once said, “Make everything as simple as possible, but not simpler.” This may seem like a pretty straightforward statement, but there’s real substance to it beyond the obvious humor. It takes sophisticated expertise and true mastery of a subject to adhere to Einstein’s sage advice and present content in a clear, concise manner without “dumbing it down.” Unfortunately, oversimplification is one of many mistakes made by the Partnership for 21st Century Skills Math Map.
In this resource, Mathematics content is gutted to make room for interdisciplinary topics, and the resulting problems are not, and in many cases cannot be, aligned to the Common Core State Standards (CCSS). In its current form the math map does nothing to help teachers with their day-to-day jobs of teaching mathematics. Moreover, the interdisciplinary approach conveys a fundamental misunderstanding about what mathematics is—a discipline that is the study of what is common to all of the sciences. The lack of content in some problems may be attributable to simple ignorance while others come across as blatant propaganda, and all for the sake of problems that fail to actually teach mathematics.
The document starts on a high note: the very first set of examples presents 3 problems that get at key concepts and teach important mathematics. However, from that point forward, the level of quality, and indeed, the level of mathematics, drops off precipitously. In fact, out of the 80+ examples proposed in the document, I count a grand total of 6 that I would consider relatively good math problems for the cited grade level. Granted, some of the remaining problems could be modified slightly to produce effective problems, but the point is this: the overwhelming majority of the examples in the P21 Math Map do not effectively teach mathematics at the intended grade level.
At first glance, I thought the Map’s lack of alignment to the content standards was a mere oversight. However, after determining that P21 leads with the most mathematically sound page in the entire document (page 6), it seems to me that the authors are well aware of the lack of content. 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.
Furthermore, consider the 8th grade example on page 26, which has students create a weeklong lunch menu with the goal of minimizing water usage (that’s the “math” part). Forget for a moment that once again the calculations done here amount to simple addition and comparisons, what constraints are we expected to use? The stated constraints are that the menu be both “appealing and nutritious.” What does that mean with respect to water usage? Finally, the 12th grade example on page 23 has students collect and display data on developing countries, as well as build a webpage 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. Sure, these examples might be interesting to students, but as mathematical exercises they are frequently ill-defined, lack content alignment, and possess a general lack of precision that flat-out contradicts P21’s claim that these problems will encourage students to “attend to precision.” Does P21 or its supporters really believe for a minute that simple arithmetic problems and routine data collection assignments will prepare students for professional careers as engineers, doctors, software developers, and the like?
P21 has chosen to focus more on projects than problems in their curriculum. Indeed, a few of the projects are quite good, and would be valuable for students to spend several weeks or a month working on. A few of the projects actually go so far as to introduce students to some graduate level mathematics. A 12th grade example on page 19 has students explore knot theory. This is a high-quality task, even if it can’t be aligned to any of the content standards of CCSS. However, if the point of the math map is to help teachers plan, it should be observed that very few of the problems put forward by P21 are very helpful for this. In fact, there is very little guidance within the P21 Math Map to assist teachers in building their day-to-day lesson plans, and the map does not provide any structure to help them plan out their year. Instead, snapshots are presented which show a few examples of problems that teachers could use in their planning.
Even if these snapshots were good, solid problems, the P21 document only presents examples at the 4th, 8th, and 12th grade level. Are the rest of the grades not worth addressing? Of course, the real problem goes deeper than this, as the snapshots fail miserably to shed any light on how to make such projects fit into an actual curriculum. For instance, the 8th grade example on page 16 has the students investigating potential causal relationships between crime rates and other factors. This example certainly fits with 8.SP.4 of the CCSS. However, the collection and presentation of the data represents large investments of time, and all for the sake of a minor mathematical issue that addresses only one content standard.
Beyond their disappointing lack of usefulness in teaching the CCSS effectively, P21 problems are often over simplified and appear to be written with an obvious bias or agenda in mind. Simplification of an interdisciplinary problem to motivate and model abstract mathematical operations is an accepted practice in teaching mathematics. For example, engineers do not solve actual “spring problems” in their work, but they often do solve problems like spring problems. The intuition gained from studying simple spring models in college helps them create the 2nd order differential equations needed to solve real engineering problems. However, many examples in P21’s document are not used to discuss simple, general models or features common to all disciplines—one of the main values of learning mathematics as a discipline. Instead, the problems focus on the discipline itself with mathematics as an afterthought. For example, the 12th grade example on page 14 has students engage in a discussion about the allocation of seats in the US House of Representatives. This is a great discussion to have, but I have to ask, was the problem chosen for its value in teaching a mathematical topic, or has a little math been used to justify a civics discussion within math class?
I suppose one might argue that education should include an emphasis on solving a wide array of unrelated, domain-specific problems. In this view of education, however, simplification of the issue being discussed can be irresponsible. Oversimplification of the issue can run the danger of becoming propaganda—where information is presented, or withheld, in order to influence someone to reach a pre-determined conclusion. For instance, the 8th grade example on page 14 invites students to investigate the “cost effectiveness of buying a hybrid versus a non-hybrid car.” This activity is certainly interesting and relevant today, and it even involves some linear functions. However, the description of the students’ work focuses only on fuel economy and upfront cost. While these are major factors, they are far from the only ones: maintenance costs, longevity, and battery replacement immediately come to mind. All of these affect the cost comparison, and should be addressed if we want to claim this problem teaches “financial literacy.”
The problem also claims to teach “environmental literacy” (even though it contains no thought-provoking questions about the environment). I can only assume that they mean to somehow measure and compare the environmental impact of a hybrid versus non-hybrid car. If that is indeed the intent, then the one factor that is considered, namely, fuel economy, is only one of many relevant factors, such as: the environmental cost associated with producing a vehicle in the first place, differences in longevity between hybrid and non-hybrid cars, differences in the environmental impact of the batteries used in such cars, and the generation of electricity to charge the batteries of some hybrids (most of which involves burning coal or other fossil fuels). All of these factors have a significant impact on the environment. With this example, it appears that the P21 authors have oversimplified (by choosing only one yardstick—fuel economy) for the sake of having students conclude hybrid cars outperform conventional cars.
No matter how much the world around us may change, mathematics still works. The same principles of mathematics that Pythagoras and his contemporaries were discussing 2500 years ago still apply today. This is the power of mathematical abstraction: that the mathematics of ancient Greece is still incredibly useful in our modern world. To be effective in the 21st century, or any century, students need a strong knowledge of the content that P21 seems intent on ignoring. The lack of content found in the examples presented in this article should not be viewed as exceptions. These examples were chosen because they illustrate flaws that may be found throughout the P21 Math Map. While the document contains a few decent examples, any teacher reading P21’s map should exercise a healthy amount of skepticism and ask themselves if the mathematical content of the problem is worth the time involved. I would encourage teachers to look elsewhere.
Ben McCarty, assistant professor of mathematics, University of Memphis.