Category Archives: real world learning

Unauthentic, Imaginary World Math

Photo by Cowboytoast

“Real world” and “authentic” are two of many educational buzzwords overused right now. What if instead of making sure that everything has a truly “real” context we give students a creative opportunity to explore the “unreal.”

The inspiration for this post comes from a new blog by Randall Munroe, author of xkcd, called What If?. In this blog he answers hypothetical questions by doing the actual math to answer them. So far he has shown things such as how much force does Yoda have? and what would happen if you gathered a mole (unit of measurement) of moles (the small furry creature) in one place? These questions are not real or authentic but the math and science is.

But these questions are fun and interesting! Students love to talk about fantasy and science fiction such as zombies and vampires.

So why not expose your students to a few of these kind of questions and have them try to “prove” their answer. Afterwards show them what Randall Munroe came up with. Then have students come up with their own questions and write out their reasoning and solutions. This activity would tap into their creativity but also demonstrate their mathematical computations and more importantly their mathematical reasoning. It also would be a literacy task in math. Finally and most important in my opinion it may also be an avenue to engage a student’s passions in math class that Jeff de Varona has been asking about.

Lego Robot Erase

My students, Cullen, Jordan, and Jordan designed, built the robot, and implemented this program where the robot follows a black line and then erases it.

Math from Canada

My student teacher, Kyle Webb, in Canada sent us a video problem to solve. Check it out on his blog.

We solved and sent a screencast back to him. This was my favorite thing that we have done this year so far.

Wood chips

I should have wrote this before my last post to better describe how my math class has been going. We are currently working on a basic geometry unit of area, perimeter, volume, and surface area. I was excited because this would be “easy” to teach with out a textbook.


I started off by explaining a problem I had of needing to know how much wood chips I needed to cover some landscaping that I did with a class last year. We discussed what we needed to know to figure this out and then went outside and measured the circle. They told me we needed to know the length and width of the circle so I had them measure where they told me those were. I did not try to correct their improper terms. We came up with 7 meters and 6.9 meters. One student noticed that they were approximately the same. We ran out of time for the day.

The next day we started in class and discussed the wrong use of terms. I had them search and find the area of a circle and we talked about what the formula means. Then I asked which of our measurements was right. They argued that 7 meters was correct because it was a whole number. We finally concluded that we did not know which one was right and that we had to go outside and take more measurements and then average them. We also talked about the fact that the circle was eye-balled when created and not perfect.

We ended up solving the problem and then solved two more wood chip problems for some rectangle gardens. Through out these lessons I asked lots of questions and guided their learning but did not give out any information. The students either came up with the answers themselves or surfed the web for them.

My evaluation of this teaching method was that I did not see the high engagement that I had hoped for by the class. My top students were with me and the bottom students seemed to be daydreaming or not really participating. I don’t have a great story of the student who always fails getting excited and being successful.

Next I needed to cover parallelograms and triangles which are harder shapes to find in the real world. So we did some visual proofs together in Geometer’s Sketchpad so they could play around and see why the area formulas work.

Again I have to give the district unit test so I gave them some practice problems with area and perimeter of parallelograms and triangles. They were totally lost. They could not remember the formulas or even use them when I gave the formulas to them. I ended up going around the room and individually teaching how to use the formulas.

We measured a bunch of food boxes and found their surface area and volume. I demonstrated how to use the formulas on the board and the majority of the class still needed me to re-teach individually.

So in response to the comment from Matt Townsley on last post about teaching at a deeper level. I have tried (I am not giving up!) but in the end I have to prepare the students for the district test. That is why I found ThatQuiz to be a useful tool for students to check their work on the basic problems that they need to know. I know it is not technology integration but doing the same old thing just on the computers. I do think the immediate feedback to students of whether or not they found the right answer is helpful. And unfortunately these are exactly the kinds of problems on the required tests.

All right push me back some more readers 🙂

Standardization Kills Real Learning

I have not written about my math class much yet because I have been frustrated. My goal was to use the textbook as little as possible and to use authentic learning sources. The reality is that my scope, sequence, standards, and assessments are all mapped out for me with little wiggle room.

My first unit was on factors, multiples, and prime factorization. The more I think about these topics I find them to be quite abstract and separated from the “real world.” The best real world example I could come up with was matching up hot dogs, ten in a package, with buns, 8 in a package, for multiples (Thanks to Becky Goerend for that tip on Twitter) to which another teacher responded, “I just let the extra buns rot in the frig.”

This kind of example and others like it in the textbook just feel like the contrived story problems that drive students nuts. No one actually takes the time to figure out the right number of hot dogs and buns because nobody wants to buy 40 of them unless they are having a pretty big party!

I could have used multiples today when we bought candy for my son to bring as birthday treats for his class to make sure each student got the same amount. Instead we bought enough for each kid to have one package and we will eat the leftovers 🙂 This is where math becomes too abstract and irrelevant to students because the questions that are asked in the book would never be worried about in the real world.

Although I do not have to use the textbook, each of our ten unit assessments (read tests) are already created for me by the district. I am required to use these tests. So on top of preparing (read teach to the test) students to take the MEAP next week (Michigan’s assessment for NCLB) I feel that I have to teach to the test for every unit. I can not make an alternative assessment such as creating a mathcast or some other portfolio type project.

The push in this country to standardize everything in education to guarantee that each student receive an identical education is a fallacy and just plain ridiculous. It is time for the pendulum to swing back to professional teaching that is creative and individualized. We need to trust teachers to teach the right content at the right time for each student instead of trying to teach everybody as if they are in the same place at the same time. We need to start treating students as humans who are naturally curious, intelligent, and motivated by authentic learning experiences instead of as lab rats.

I am tired of hearing about how we are behind all of these other nations based on some test. The United States is still the creative center of the world. Last time I check the elite of the world stil come to our universities. This will eventually change if we continue down this overkill of standards and cookie cutter assessments that kill curiosity and creativity in our kids.