Baseball and Not Baseball

What I Learned This Week

MichMATYC 2017

I spent much of my time in inquiry based learning sessions again. These were run by Chrissi Von Renesse, Kyle Petereson, and Brian Katz. They ran the sessions using IBF techniques which is what I always like about IBF sections. They do not lecture about IBF.

Despite the fact that this is an overall philosophy I want to list some things I will add to my teaching in the winter based on this session. Sometime later this semester I will merge this with the Small Teaching and AMATYC ideas and make a set of goals for the next year.

  1. Welcoming Activity: Have students introduce each other. Give a trivial distracting questions (favorite food, favorite color), have students tell something they are good at. Have students tell how they got good at it. Write the answers to the “How” questions on the board. Make obvious connections to working to learn math.
  2. There is a PRIMUS (magazine that two of the session-runners edit) special on Quantitative Reasoning. I should try to find that.
  3. I think I remember this from last year- make my introductory problems have a high ceiling and low floor so that I can give time for some groups to finish without boring other groups. I think the QR course I am teaching in the winter is the perfect place to try this.
  4. I may add relevant puzzle problems from time to time for fun. (This was actually from a lecture).

Some of us got to do a teaching demo and receive feedback from out peers. This was valuable. My biggest praise was allowing sufficiently long pauses after questions for people to think (and not answering the questions myself.) One critique was that although I did sit with groups to discuss their math, I also sometimes loomed over peoples’ shoulders which can be disconcerting. I will try to watch for that.

The three IPA’s at Unruly Brewery I tried were all good, but none are spectacular. I can’t find the name of the one I liked best on their website, but it was the one the bartender recommended. The attached pizza place was also good (Rebel Pies), but the $22 pies might keep me away. (Well, that and the three hour drive). I would visit as a local to try some of their other varieties of beer from time to time.

Old Nation: M-43

I just noticed that I did not review M-43. It is very citrusy through hops, not clear and delicious. You should have some. The only drawback right now is the price. It can cost over $3 for a 16 ounce can.

(Before it became widely available in Detroit I stopped at their brewery on the way home from Lansing to get some once.)

Small Teaching Chapter 7

Chapter 7 is about using emotions to motivate. You can use a story, or an interesting problem at the start of class to engage the class. You can periodically remind students of the big picture. I do both of these, but could remind myself to do these things more often.

The author also mentions that negative emotions may work better, but may cause other problems. I think he missed an opportunity for a Star Wars metaphor.

Small Teaching Chapters 5 and 6

Chapter 5 is about practice. Students should practice in the same way they will perform. Students should also practice to commit certain basic facts to memory, so that their working memories are not overwhelmed when doing more advanced practice. Students should also be mindful, or they may repeat errors instead of learning something new. Teachers should provide feedback on the practice as soon as possible and should do some practice in the classroom. Chapter 5 did not teach me much. I guess it reminded me to do more quiz-like activities to close class and it reminded me I should give some short writing prompts with instant, rather than delayed feedback.

Chapter 6 is about self-explaining. It opens with a result that I thought might just show correlation. Students who explained a task to themselves as they did it learned it better. Of course if you understood it better you are also more likely to be able to self-explain. There was a useful idea for math class, however. You can ask students to tell why they chose the process, or step that they chose. Then they will focus on the theorem, or big-picture idea in the class as they do any problem. I might add some of these questions to my worksheets in the winter.

Chapter 6 also said that backward fading, which I would call scaffolding, does seem to work in math. So, starting with steps defined and removing the reminders on later problems may help. I often already do this.

Finally, think-pair-share activities with Plickers (or other clickers) is useful. I do this from time to time and might want to start doing it more.

Small Teaching: Chapter 4 – Connecting

You can help students make connections in the material they are learning with knowledge dumps- to remind students what they know, and let you know what they know, frameworks- such as partially completed notes where students can complete the details, but the big ideas are already there, and concept maps.

I sometimes use the knowledge dump when introducing slope. Many students remember pieces of that topic. Our current Math 081 book is a work text so it essentially has a notes template. I think it sometimes does not connect the big ideas so I try to do that on review days. I also mention how topics interleave as topics like proportion are revisited 3 to 4 times during the semester. I have done concept maps as parts of reviews as well.

For me the most useful part of the chapter was a reminder to at least periodically show how all the big ideas in the course are tied together.

Letter to Mike Pence


p style=”text-align:left;”>Mr. Mike Pence
1 Observatory Circle
US Naval Observatory
Washington, DC

Dear Mr. Pence:

I am somewhat sure that you are not a simpleton. I am fairly sure you understand that national anthem protestors are trying to encourage an improvement in laws, policies, and procedures in this nation so that both law enforcement personnel AND the communities they serve can feel safe when they interact.

That is why it shocked me to see you take such a strong stance in support of the killing of civilians in this country by leaving the Colts game on October 8. I would be curious why anyone with empathy, or intellect would support the continued slaughter of innocent citizens without at least some reflection on whether this can be avoided.

Clearly, one reason you might do this is that you value the lives lost less than the political advantage you feel you gain by trying to create a straw man argument about supporting the military, or by portraying this as an either support police, or oppose police issue while ignoring the fact that solutions that protect police and the people they serve might exist. I hope that we have not elected someone so lacking in both thoughtfulness and empathy to the second highest position in the nation. I fear, however that we have.

I welcome your response.

Yours truly,

Jeffery C. Morford

Small Teaching Chapter 2: Prediction

EDIT: WordPress now requires the publish button to be pushed twice- that is why this seemed to have disappeared. It may appear now- if I remember to push publish twice.

In Chapter 2 Small Teaching discusses the power of having students make predictions about upcoming material. Interestingly when I started reading I predicted that the reason this might work is just that students are engaged with the material. I am a fairly good student when I want to learn something and I used the skill naturally.

An important element of having students make predictions is quickly correcting misconceptions. When that is done, incorrect predictions do no harm. Two things that might explain improved learning when using predictions are that it primes certain connections in the brain to receive and connect to the answer when received, and it helps students recognize gaps in their knowledge. I use the first of these in Math 131 when I have students predict the answer to a pre-lesson question (What percent sunlight is left 50 meters underwater?). I use the latter when I ask students to simplify 8 – 3 + 4 to check for a common misconception in order of operations.

One challenge for using this in mathematics is that it relies on activating prior knowledge. Students need a hook upon which to hang the answer. When working abstractly in mathematics this might be a challenge for the novice learner. On the other hand this could be a signal that it is very important to do math in context with novices.

Small Teaching Chapter 3: Interleaving

I will have to try to find my Chapter 2 post. It is probably on another blog where it does not belong!

Chapter 3 is about interleaving- learning part of a topic and then revisiting to learn more, or periodically reviewing a topic. Simple ways to achieve this are to adjust how you cover learning blocks so that half is in each of two classes, or so that assessments are cumulative over a course.

Cumulative assessments left me wondering if some topics would be over emphasized and others under emphasized by the assessment system, but Lang acknowledges this and suggests only using a small portion of each assessment for the review questions, or using only a fraction of the assessments for review if each has only a couple questions.

This certainly shows that review sheets and mixed reviews mid-chapter in a math course are worthwhile tasks.

Small Teaching Chapter 1: Retrieval

In Chapter 1, Lang talks about the power of retrieval. I was aware that students need to practice remembering and using information in the same way they will be tested on the content. I was unaware that simple exit quizzes in the last few minutes of class seem to have an impact on recall rates 30 days or so after the lesson. While I periodically use “exit problems” which are a lot like the activity Lang describes, I think I will make it a regular part of my classes in the winter semester (and as much as possible now). Lang also mentions the use of entrance problems, where you ask students to summarize what they learned in the last class.

Two less surprising results are that short answer questions are better than multiple choice questions and that frequent quizzing is better that simple review of notes for student performance.


In all classes use an exit question in most classes.


Introduction: Small Teaching

I should have remembered that I have a blog when I went to Miami because I attended a Marlins game. It is almost peak professional development season (state and national conferences for two-year math teachers in Michigan happen in October and November) so I did remember about it.

I will be reading Small Teaching for a book discussion group on campus. I will probably post my notes about it chapter by chapter so I can reference them in the discussion.

Things started out poorly. The content might turn out to be great, but there is a terrible opening metaphor. James M. Lang, the author, compares making small changes in teaching to small ball in baseball. The only thing they have in common is the word small. Small ball is a strategy overhaul. Generally it reduces run scoring and thus winning. The Royals in 2014 either won in spite of small ball, or employed small ball because they did not have the personnel to hit for power. A better analogy would be a hitter changing his stance, after a prolonged decrease in average, or power. Or, hitters like J. D. Martinez changing their swings to hit more fly balls and increase OPS. These are small changes that can bring big results which is what the book promises.

In the introduction Lang promises ideas with foundations in learning sciences that have made an impact in real-world teaching. Some ideas will be brief, or one-time classroom activities. Some will be structural changes. The author sets a high standard for the book. The small changes should be viewed as a major strategy and not just an alternative in place of dramatic change. I will read with a goal of seeing if this standard is met.