I don’t know what you’ve been up during the summer of 2016, but I’ve been busy doing almost nothing related to my profession. I’ve actually been learning new things, including taking up the sport of boxing. My 69 year old trainer, Bob, says I’m a “natural,” by the way, and my jabs are getting pretty good, although my hook still needs some work.

One of the things I did do this summer is do the assigned reading from my school, which was a provocative book by Christopher Emdin, called “For white Folks Who Teach in the Hood... and the Rest of Y’all Too.” In fact, I’m going to write him an email right now.

Okay, now back to this activity: in the final chapter of his book, Emdin mentions a teaching technique called “metalogues” where students share a notebook and take turns writing a sentence based on a leading question. This question could be as simple as “what did we do in class today,” which prompts the first student to make a statement, and the next student to read that and follow up on it, all of which continues until all four students have contributed. I thought this was a neat idea for working collaboratively, while giving students a definite structure to help guide their thinking.

I created these three “math-a-logues” for you to try out with your students. I would enjoy hearing back from you about how your students did on these problems, and hopefully getting some samples of how they worked on them. There are three different topics: one is order of operations, which would be appropriate for 5th graders and upwards, a problem on adding two fractions with unlike denominators, which would be good for 4th graders and up, and a final problem on multiplication, which would be good for third graders and older. I’ll work on some ones for younger classes, but these are the ones I thought of for now.

I also included answer keys, but remember to give kids some latitude as to what they write. For example, in the order of operations problem, the students don’t have to put in the parentheses, although it is a good practice because it makes solving the problem easier. Hopefully you’ll have some pairs that do put in the parentheses, while others don’t, which could spark a very useful conversation about the necessity of putting them in.

Similarly, the word problem with Ellen and Mike can be done in different ways: whether you calculate Mike or Ellen’s box first or second doesn’t make a difference; the important thing is that your students read and understand what the previous response was, and then construct an appropriate “follow up” to that step. I am confident that this is a nice method for helping students not only communicate better, but also carefully consider what the other student is doing.

Finally, the fraction problem offers students the opportunity to discuss what happens when somebody chooses a direction that you didn’t anticipate. For example, one student may decide that the common denominator should be 12, while another may choose 24 instead, which would require the additional step of simplifying the answer at the end, or even simplifying it while it is still in the equation stage (that is, change 16/24 + 6/24 to 8/12 + 3/12, and then leaving it to the next student to get the final answer.)

Please, PLEASE let me know if you have any ideas where this could be taken. I’ll handsomely reward you with some free product as well as a puppy!