A guest post by Kyle Cluver:
In Conrad Wolfram’s video, Teaching kids real math with computers, he discusses the interesting topic of mathematics in education versus real world mathematics. He argues that math education is all about calculating and that this “chore” can be done effortlessly with computers. He wants us to stop teaching calculating and start teaching math. Math in the real world is done by virtually everyone that is solving a problem or looking for the answer to some question. In school, math consists of lower level questions that require a lot of by-hand calculations. Problems seem simple and trivial compared to more challenging and rigorous problems in the real world. His answer to this problem is to have students use computers more for the computation aspect and to focus on posing the right questions, translating those questions into math problems, and verifying those results to their real world applications. His model for what math is and what it should be within our education system looks like this:
One might ask, ‘why do we not do this?’ or ‘why don’t we add more computers in our education system and have students engage more in steps 1, 2, and 4?’ According to Mike Thomas’ Teachers Using Computers in the Mathematics Classroom: A Longitudinal Study, there are many more computers that can be used within schools, but they are not within the math departments. Many schools have computers within computer labs or IT rooms, but the access in the math classroom is limited. Teachers in this study also think that learning is not increased from the enhanced use of computers which could be the case in two ways. First, students could simply look up or “Google” the question and answer they are searching for in which case the students are not learning, they are simply coping and pasting answers mindlessly. Second, they are using the computers to plug and chug to find an answer. In both cases, the computers are being misused rather than being used to deepen the understanding of the math content at hand. This scenario comes back to Wolfram’s notion that math problems within the current classrooms are dumbed down and do not require students to do much when given a calculator or computer to complete all of the computations. This notion brings in the fact that math curriculums should be changing to fit Wolfram’s notion. In order to have students engage deeper with the mathematics, the problems should be more like the real world and have applications that students can see. Dan Meyer gives his personal account of how this could change in his video, Math class needs a makeover.
Dan Meyer argues that high school math classes need a makeover and that it will start with problems we are addressing in the math classroom. He points out that math problems give us way too much information that real world problems would never provide and we just take those numbers, plug them into a formula, and an answer is produced. This never happens in real life and if we want to teach our students how to solve real world problems, we need to start giving them real world problems. These problems should start with a general question about a problem that the students then use to ask sub-questions to decide what matters and what they need to solve that problem. This is where students are posing the right questions then taking information and formulating the problem into mathematics. Computers come in to do the “chore” of computation and then the answers are verified and applied back to the real world problem at hand. Meyer’s video gives an example of this process that he does with his students and it is something that all math educators should do with their students at the secondary level to promote more real math in the classroom and less direct computations.
Math classrooms are changing and for the better. More computers are being used whether they are handheld devices such as the Texas Instruments graphing calculators or actual desktop/laptop computers. These devices, according to Sue Garner and Michael Edwards in The CAS Classroom and Symbolic Manipulation in a Technological Age are being used more so than ever and are providing students with a more conceptual understanding of the mathematics at hand and are allowing teachers to ask more conceptual questions about real world problems in which students are allowed to use computers to calculate answers that the students can then verify and interpret to their real world application. Computers even offer students multiple representations of the same problem that otherwise would not be available. Computers allow students to engage in those real world problems on a conceptual level that prepares them for the ever changing world they are about to enter. Students that can formulate their own questions, develop sub-questions, use computers to do the computations, and then translate those answers into verified applications in the real world will learn more math than ever. This is what real math is and what we as future educators should be teaching our students. Students will retain the ability to formulate questions and how to answer them more so than being able to calculate them by hand once they encounter mathematics in the real world.
Thomas, Mike. “Teachers Using Computers In The Mathematics Classroom: A Longitudinal Study.” New Zealand Mathematics Magazine 43.3 (2006): 6-16. Academic Search Complete. Web. 8 Apr. 2016.
Edwards, Michael Todd. “Symbolic Manipulation in a Technological Age”. The Mathematics Teacher95.8 (2002): 614–620. Web…
Garner, Sue. “The CAS Classroom.” Australian Senior Mathematics Journal 18.2 (2004): 28-42. Academic Search Complete. Web. 8 Apr. 2016.