## Mathematics education today: Musings about CCSS-M and KhanAcademy

I am definitely biased. As a professor of mathematics education, I have fairly strong opinions about the mathematical education of children.

Two of perhaps the most current, publicized, political, and divisive issues around math education in the United States are the Common Core Mathematics Standards (CCSS-M) and Khan Academy. Both have certainly entered my everyday conversations lately.

The CCSS-M standards are currently being blamed for all that is wrong with mathematics education today. At least from adults who had a different experience of mathematics during their own childhood education. But this is flawed for at least two reasons. First, standards do not dictate how mathematics is taught; they represent, rather, what the goals of its teaching should be. In the CCSS-M, these rightly include conceptual and procedural aspects. Whether a student learns to understand these mathematical ideas by rote repetition and algorithms, familiar to many adults of today, or by the “loosey-goosey” “let the student reinvent everything” approach of more recent reforms, the standard remains. Standards do not dictate pedagogy: they outline the *goal*, **not** the *process*, of mathematics education. Much the the chagrin of politicians and parents who vent, blame, and claim otherwise. Second, the mathematics that is more familiar to parents (e.g., practicing the multiplication algorithm repeatedly), which certainly has value, also has serious drawbacks (e.g., do you really understand why the “0” gets added in subsequent lines?). Many of these claims revolve around a sense that practice learning to do a problem the “correct” way builds numeracy. Indeed, lots of practice with almost anything helps build ability and fluency. But to say that the “old math” teaching approach was better at producing more numerically-literate citizens than the “new math” reformed approach is equally incorrect. This issue is illustrated perhaps no better than by the following Khan Academy video. (Type in the password: mathematicalmusings)

In the video, Sal Khan walks students through several addition problems, one of which is the sum: 99+88. This morning happened to be the first time that I ever watched one of the elementary videos apart of the Khan Academy with my 2nd grade daughter. This nine minute video was the first. As we had done with the previous problems, I paused the video to let my daughter try to answer the problem first. As we played the video again, we talked through the “addition algorithm” Sal Khan had been using in the problems – a notation that was unfamiliar to my daughter, until today. When we got to the problem, 99+88, my daughter quickly said, “Oh that’s easy. 187.” I replied, “Great. Now remember your answer. He’s going to take a long time to solve the same problem.” We proceeded to watch the laborious and insidious application of the standard addition algorithm to produce this answer. Watching Khan talk through the algorithm was like watching someone bring a bazooka to shoot a fly. Totally. Unnecessary. This, in fact, is the problem: nothing more demonstrates lack of numeracy than applying the algorithm to solve that addition problem. It is totally unnecessary, unpractical, and, in fact, undesirable. So while my daughter might have taken more time to complete some of the previous addition problems, with a mistake or two mixed in, I at least have some confidence that she is, in fact, developing a degree of numeracy in the process.

This also brings me to the second issue, of Khan Academy. Sal Khan is perhaps one of the most influential teachers of our time, at least by the metric of the millions of students and people who have watched his videos. And Khan Academy has noble goals: a world class education, free, for everyone (with a computer and Internet). He is a pioneer, exploring the possibilities of digital education at large scale – one that uses technology, diagnostics assessments, and gaming techniques, amongst others, to accomplish that end. And the intent is powerful: trying to individualize instruction for each learner to meet them where they are at, mathematically. With that said, however, these “educational lecture videos”, which are a static form of instruction, are worrisome – they do not allow for interaction. (Not to mention a boiling down of mathematics to be some learned procedure.) Take a look at another portion of the same video. (Type in the password: mathematicalmusings)

In about the middle of his explanation, my daughter interrupted and looked at me: “Dad, that’s wrong. Right?” In fact she was right. (8:20 mark) They did not sum to “9”. (“9 is just 9 pennies, no dimes” to be precise.) They summed to 900. And this was extremely evident to my daughter – despite the additional notation on the right. She had a sense of place value to justify her thoughts. And she was right. But, like any child, an authority figure like an instructor always has authority. So she wasn’t sure. Without me being there – and immediately understanding her issue – she might have believed she was in the wrong. This is one of the fundamental issues of “static” education: it cannot respond to students, no matter how many times a video is rewinded or replayed. The explanation doesn’t change. And she was right. But she needed clarification. The educator inside me cursed Khan for so stupidly writing 1+3+5 and not 100+300+500 – amongst other things. This may perhaps be part of the point, but the larger point is one of the paradoxes of such efforts. The goal is the individualize the learning and mathematical experience for each of the millions of students, but we simultaneously try to accomplish this goal through one standardized educational program with fixed components. One that is static, and non-responsive to these millions of students – or their questions.

We have lots to learn about education. But claiming that the CCSS-M are responsible for the demise of mathematics education in our country, or that Khan Academy is providing a world class mathematics education are troubling. That’s neither to say the CCSS-M are perfect nor that Khan Academy has no value or educational potential. In fact, to me, both of these point to the same place: teachers. They will bring life (or not) to our country’s mathematics standards, and provide the interactions (or not) that help our children learn. Specifically, we need to place appropriate value on preparing educators who are mathematically ready for and able to take on the challenges of educating our youth in the classroom.