I teach graduate math methods, and I try to include instructional technology into the curriculum. Most of these students have familiarity with technology, but upon closer examination I find some are thinking primarily of communication technology – email, social media, or searching on the web. They don’t think of technology as a tool to fundamentally alter instruction (extend and/or enhance).
In class a few weeks ago we looked at Wolfram|Alpha (www.wolframalpha.com). This is a ‘browser’ that can solve equations, evaluate expressions, and obtain other numerical information from a wide variety of fields. “It works by using its vast store of expert-level knowledge and algorithms to automatically answer questions, do analysis and generate reports.” My students discussed the opportunity to use the information generated from Wolfram|Alpha to engage students in mathematical thinking. For example, to engage one of my students, we entered his name, Jake, into the Wolfram|Alpha engine and was rewarded with a great deal of numerical data such as:
This instructional activity generated (too much?) engagement as almost every student in the class entered their own name at the website on their laptops and mobile devices. Afterwards, we were able to find the following ‘topic activities’ presented by the data; ratios, interpreting graphs, percents, frequencies, and many more. I’m sure many of the readers of this blog post can ‘see’ questions that are generated by this type of data.
While these topics can be engaged with traditional data sets, this data was personal and ‘fun’. Try it! Try ‘asking’ this search engine some of the hundreds of questions suggested in the Wolfram|Alpha tour page (https://www.wolframalpha.com/tour/). Access to this website is free, or it’s an inexpensive app for your mobile devices. By the way, Wolfram is a well-known and respected developer of very powerful mathematical software (e.g. Mathematica), so you or some of your friends may recognize the name.
Here are some examples generated in my course.
We entered the name ‘Jordan’ into this computational engine (as I recall the default was the Jordan River, so we had to select ‘use as a given name’), and we received the following charts; the students in the class asked the following questions (in italics).
If 4646 people per year are named Jordan and this fraction is 1/388, then how many people are named (born) each year?
What percent is equivalent to the fraction 1/388?
Why is the rank different in the two charts?
How should I ‘make sense’ of the most common age data?
Why is the data concentrated on the left (right tailed)?
In class we discussed another example generated by this engine by entering IL vs IN. The amount of data generated was overwhelming (as characterized by one of my students). Here’s an example, again with questions which will engage students and exercise mathematical thinking.
Which state has the greater population?
What state has the greater population growth? (Note: is .4 greater than .15?)
What do the ratios represent?
What might account for the growth of Illinois vs Indiana even though it appears they had the same population in 1850?
How much greater was Illinois’ population in 1950, 2000, and now?
Estimate the population ‘slope’ of these states?
I’m sure many readers can find other data through Wolfram|Alpha in a variety of subjects (which can be ‘coordinated’ with other schools subjects such as geography, history, nutrition, science, etc.). Feel free to respond to this blog with your own examples from experiences with this engine; we’ll publish a few.
Finally, I’m sure there are many other web-based sources of data which can be used to engage students and stimulate mathematical thinking. Respond to this blog with your own favorite and, perhaps, an example of how you use it.
One thought on “Thinking from Data”
This is an amazing method to generate enthusiasm in the classroom about numbers and data. As math educators, we need to ask students about numbers and what they mean to the student, for example, the number 13 is 10 and 3 in addition or 17 minus 3 in subtraction. 13 is a prime number, which needs to be explained and discussed in class. A student may express 13 as an “unlucky” number in which the class can analyze the background and origin of “unlucky” numbers, which can expand into the social sciences and literature. This style of education promotes and encourages the love of learning within a student, a quality that has been destroyed in our students and needs to return to our classrooms.