Bring Math Class to the Modern Age

The feelings of hatred, apprehension, and outright fear associated with doing math are so prevalent and extreme that they have been given a proper term: “math anxiety”. Math anxiety is largely a result of poor experiences in introductory and secondary mathematics classes. As a society, it is our responsibility to resolve this issue because math teaches critical problem-solving skills that are helpful in life, even if the specific concepts taught in class are not directly applied. A major problem in math class is disengagement. Students simply do not see the motivation for learning algebra, calculus, and the like. By integrating modern technology into curriculum, we bring a platform that students are already engaged with directly into the classroom. In other words, we are meeting students on their own level, borrowing their familiarity with the space of technology for educational purposes. Many will point to the downsides of introducing technology to the classroom; while these are valid concerns, they are not as serious as they seem upon first consideration. In any case, they are significantly outweighed by the advantages. Through the use of online free resources such as Desmos, Geogebra, and MathGraph3D, students can see a more visual, beautiful, and relatable side of mathematics that encourages them to independent exploration and allows them to reach deeper understanding.

Young people in the modern age grow up completely immersed in technology. As a result, unsurprisingly, they are significantly more digitally literate in general than those from earlier generations. The internet and devices such as smartphones and computers are introduced to children at a very young age in many cases, so technological competence comes naturally 1. Some may view this as a negative, and claim that young people today are out of touch with reality as a result. This might be a reasonable claim to make, but it does not apply as much in the context of technology for math education. Instead, using online resources simply connects students to the topics in a way they can easily understand, and the disadvantages can be avoided with the right approach. It immediately lessens the learning curve though the use of a familiar setting to students. This gives us more time to focus on the topics at hand instead of wasting energy trying to get students to focus on a 75 year old math textbook that inevitably loses their attention. In this way, technology use opens up a wide variety of approaches to instruction. Most importantly, perhaps, is the opportunity for collaboration with others. With the internet, students can work on the same task simultaneously since data is shared instantaneously between their devices. This makes the students work together, strengthening social skills that would not be practiced without this form of collaborative work. As it is easier to get young people to engage with technology, it is more straightforward to do different types of activities that strengthen important skills. When students are engaged with their learning, they form more positive associations with it. Consequently, the introduction of technology into classrooms makes math anxiety less likely, which increases the probability of future success 2.

Using technology in the classroom also makes a vast world of educational resources available to students that they would never have access to otherwise. For example, consider Desmos, the popular graphing tool, scientific calculator, and educational activity builder. Desmos lowers the barrier of entry into mathematics by providing an intuitive and functional platform that is useful for topics for grade school level and beyond. In particular, the graphing calculator performs a very important task: visualization. When you type an equation into Desmos, it is plotted immediately in a clear and natural manner. Without technology, making a graph is a very laborious and long task. A student has to correctly choose bounds for each axis, evaluate the function at a set of values, and play the game of “connect the dots” that may or may not actually reflect the true shape of the curve. This allows no room for independent exploration. In Desmos, it is easy to see function transformations such as translation, scaling, and rotation because they can be done by changing the value of a constant with a slider:

In handwritten graphs, there is nothing of the sort. It takes a prohibitively long time to produce a single graph, and it is simply impossible to see real-time changes reflected as the result of the modification of a variable. By providing a high volume of immediate and mathematically accurate results, Desmos gives students a chance to build intuition about the shape of functions. With the right guidance, this fosters understanding much more easily than spending a whole class drawing two or three graphs with no chance to explore their properties3. For every topic in primary and secondary math education, there is a similar interactive online resource that provides similar improvements upon traditional methods. Examples include MathGraph3D for multivariable calculus topics, Geogebra for high-quality visualizations of geometry, and the UCSC domain coloring plotter for the study of complex numbers. Every math course typically taught in primary and secondary school is inherently visual, and many students pass by without ever realizing it. With the incredible computing power of modern devices, online resources are able to bring these visual subjects to life, and widespread exposure to them would make the appreciation of their beauty widespread. I have witnessed the effects of taking advantage of these resources firsthand. As a teacher’s assistant for calculus, it was amazing to see how much of a difference it makes when a student can see a secant line approaching a tangent line as two points on a curve draw closer or a Riemann sum approaching area as rectangle width decreases towards zero in real time. Compare this, which a student would see in a textbook:

$$\text{Area under }f\text{ from }a\text{ to }b = \lim_{||\Delta||\to 0}\sum_{i=1}^{n}f\left(c_{i}\right)\Delta x_{i}=\int_{a}^{b}f\left(x\right)dx$$

To this (slide the slider to increase rectangle count):

In the interactive animation, you can clearly see how the rectangles are approximating the area between the axis and the curve. The formula, by itself, is completely opaque; the animation gives a clear picture of what the formula is actually describing. Without technology, a student might never gain this sort of visual understanding. Failing to use this technology forces students to attempt to conceptualize these abstract ideas in their heads, which can lead to incomplete understanding at best, and absolute misconception at worst. While that sort of thinking is good and an inherent part of math, concretizing the ideas with clear visualizations serves to provide a stepping stone to the desired generalized abstract understanding.