Nick: Reflections and Inspiration for Improvement

Nick is an associate professor at Stephen F. Austin State University. 

I have a problem with grading. Actually, I have lots of problems with grading, but I do it because student feedback is important. With grading it can be a problem that I tend to focus on all of the stuff that my students get wrong. By this I mean that I notice everything that they miss. The worst part of this is that I tend to not pay attention to all the stuff they do well. We actually have a rule in our house when grading exams; complaints are limited to one minute until the exams have been totaled and reexamined. This phenomenon is a lot like implicit bias, in that recognition and attention to changing conscious attitudes are vital.

The same kind of thing often happens to me when I reflect on my teaching between semesters; I see only the things that I think I can do better. Again I try to combat this with some conscious statements about the things that went well. This past fall semester I had the heaviest teaching load of my time at SFA. I had three sections of freshman level trigonometry (all at capacity) and a section of multivariable calculus. My fall semester is seems at this point like things were either the best or the worst and not much in between. This goes not just for my teaching being split like this course to course but also to each student. More specifically, I feel like one of two things happened: 1) I really reached a student and was able to engage them in meaningful and profound ways about their education or 2) I was unable to connect even at a superficial level.

As a whole, each of my three trig sections was a different story. My first section met MWF, which I point out because I almost exclusively teach on Tuesdays and Thursdays. Having more meeting times ended up being a great help in this section, not because we had more in class meeting time (we didn’t), but because I had more opportunities to make adjustments to the many facets of the course. For instance, students don’t know what they don’t know, so they need lots of opportunities to discuss and ask questions. I think that being able to make these adjustments had a profound effect on the students in this course. In total, this section was the most engaged group of students I have ever taught or observed. It was truly awesome to go to class toward the end of the semester.

A colleague visited this section and was overwhelmed (in a great way) by a many of the things we did in class. Going into this visit, I had mixed feeling about how things were going. After discussing what I was trying to do in my classes and what was actually getting through to students in the post-observation meeting, I had a better picture of just how far the students in this section had come (at least the ones that showed up). It was another success in a course that I was very happy with the outcomes.

Attendance was an issue for me in all of my trig sections, but no more than in traditional classes. I thankfully had another faculty member who was not annoyed by my monthly visits to her office about the various issues that come up in this freshman level course. While she does a traditional lecture course, it was good to know how things like content and attitude compare to the student-centered approach that I took.

In the spirit of not trying to dwell on the places that need improvement, I am only going to talk about one of the things that did not go as well as I wanted. I really missed a lot of opportunities to effectively engage students who are from underrepresented groups in STEM fields. I set that as a goal for my semester and a lot of the student-centered stuff we did not seem to have much of an effect on many of these students and their habits. Let me clarify; when they got past the different learning environment, they flourished, but I was not able to encourage that regularly enough and get them to internalize the habits that would make them more successful in their academic and professional lives. It is not that I didn’t have some cases that I shouldn’t see as having a great impact on my students’ lives, but I had too many misses for me to be happy with how things went. This was especially hard on me because I spent a lot of physical and emotional energy on trying to make improvements in this area.

My multivariable calculus course was a lot of fun and very easy to see the gains that many students made to their habits of mind and their approach to their education. It was especially good to teach this course alongside a young faculty member. With this new faculty member, I found it really helpful to discuss how our students were doing and what we are trying in class. I think I was able to offer more questions that show what our students don’t understand (the notation is always very difficult for students), and he kept me from reverting to mechanical questions about the content and skills. I think it was especially important as a reminder for me to remember that we should not be doing our teaching in isolation, just as we would not expect to do research in isolation.

I am headed to Atlanta right now for the JMM and I look forward to the ideas and energy that I get from interacting and working with some many people who really care about improving the facet of our jobs with the greatest impact, teaching. As always, feel free to let me know if you have any questions or comments.

 

Nick: Preparing for the Fall Semester

 

Nick Long is an associate professor at Stephen F. Austin State University.

When a bank robber was asked by a reporter why he robbed banks, he replied “That’s where the money is.” It wouldn’t make sense to try to harvest wheat from a forest, so why would I ask my students to do work that isn’t suited to them getting what they need. When considering different activities for my fall courses, I tried to ask myself , “Is this where the learning/growth/effective feedback is?”

This fall I am teaching several sections of a freshman level trigonometry and multi-variable calculus. I haven’t taught either class in a while, so it was nice to look at them through the IBL lens. One of the new (to me) things I will be doing is using a traditional textbook. Last year, I wrote my own notes for my classes, which was a great way to show students just what they needed, exactly when they needed it. I couldn’t be happier about how that went from my end. That isn’t to say that significant changes don’t still need to be made, but I really enjoyed the experience of making the course and materials purpose-built.

One of my meta-goals for the fall semester is to help my students become better readers of mathematical content, their traditional texts in particular. In this vein, I am trying to require the first exposure to new material to be through reading appropriate passages in the textbook. The way I am I am measuring/incentivizing this is different for each of my courses. In my trig classes, I have been writing short reading quizzes and reading guides to be completed a couple hours before class. An example of the kind of question I am using is:

“Write a sentence to explain what the mnemonic “All Students Take Calculus” helps describe.”

The final question on every reading quiz is:

“What question do you have after reading these sections?”

The reason I ask this last question is also the reason that I have these done a couple hours before class, namely that I will read and grade these quizzes right before class so that I can address some of the ideas that students did not understand from the reading. I am cautiously optimistic that this reading quiz idea will also supplement some the the student buy-in work that I am doing to combat the feeling that students are supposed to teach themselves. I’m hoping that I can convince and show students that with a little pre-class work and reading, I will be able to more appropriately introduce new ideas in class. I picked up these ideas and many more from a session on encouraging teaching innovation in early career faculty at Mathfest (run by David Failing and Susan Crook).

In my multivariable calculus class, we start each class meeting with student presentations on some of the problems we worked on previously. As the transition to the new material, I have been asking students to summarize in a couple of sentences what the big ideas are from the reading I assigned. Since this class is much smaller (11 students) and some of the students have had courses from me before, we are able to have a short low-pressure discussion of the concepts before we start working on new problems.

One thing that I have continually struggled with is writing problems that have the appropriate balance of conceptual versus computational versus discovery. The habit of writing exercises similar to what you would see in a textbook is so ingrained that I find myself writing doing just that unless have some explicit reminder of what the problem is really supposed to help the students see. That explicit goal, not just some implicit idea that I am modeling, has made the biggest difference in how much I am able to reframe the efforts that I am putting into my teaching.

Another slight change in my student buy-in plan has been in my explanation to students about why they have what seems to be three or four different kinds of work. For instance, I am using WebWork to allow students practice with computational problems, and I have been very conscious to remind students that the feedback they need on these kind of problems is best  given immediately by a system like WebWork. I am also quick to mention that this kind of work is best done after the conceptual work on these topics is completed. The best way to get good feedback on the conceptual work is to see how convincing your work is. I explain to my students that the best forum to get this kind of feedback is to have students present and discuss their work in class. In other words, the venue for the work should be selected based on what kind of feedback they need. I think convincing students about how important these ideas are will need to be something that happens with regular reminders through the semester.

We have had a few new writers on the blog and we will have a few more coming on board soon, so check back for more posts over the next few weeks. As always, I welcome your feedback and ideas in the comment section or by email at longne at sfasu dot edu.

Nick: Some IBL Things For My Summer Class

Nick Long is an Associate Professor at Stephen F. Austin State University

As great as most things have been with my transition to using IBL in my classes, I didn’t expect that future semesters of teaching the same course would be so intensive in preparing materials. With a traditional lecture, you can crank out a set of notes and apply minor tweaks when you use them in future semesters with relative ease. With my IBL materials, I have found I work almost as hard to edit and re-adapt my own materials in future semesters. This is how you get better materials that others can use, through a near constant flow of application and revision. My efforts this summer have been to add some problems in order for us to get more done. That may not sound right but when we prime our students to think more carefully and more deeply, then they can do more in less time. That’s the idea but as most of you know, the correct balance of problems is exceedingly difficult to produce. As many good resources as I got at the IBL Workshop last summer, I have been going over C. Von Renesse’s recent paper “A Path to Designing Inquiry Activities in Mathematics” which is to appear in PRIMUS soon. I have read and re-scanned this paper several times this summer as I have been asking myself “What is it I want my students to get out of these problems?” I have had my own share of productive failure this summer, which I have not hesitated to tell my students about, namely I had to abandon about 3 weeks of work writing materials for a 100-level trig class.When I thought about what I was writing, it turned out to be exercises that don’t really further understanding but rather just asked students to do something without really going anywhere. I hope to write more later about how I am trying to be more explicit with my own productive failures and why I think #pf is valuable to us as faculty.

I have added a couple new writing assignments to my courses this summer as well. Specifically, I am opening the semester by having students write their math autobiographies. While not all of the students took this assignment very seriously, I got a lot of wonderful responses from students which showed both a wide range of experiences and somehow that ~80% of my students thought they were below average. One thing I am trying to figure out how to do is share some of these wonderful ideas with the class, but I’m not sure how to do this while respecting the anonymity of the students. The other new writing assignment I have added was shamelessly borrowed from Francis Su’s article in the June/July issue of the MAA Focus. His assignment is stated as:

One of the luxuries of the internet era is that you can look up the answer to almost any problem you  want- as long as it’s been solved. Yet when you are learning a subject it can be counterproductive. In this class, I have emphasized the importance of struggling in mathematics: that it’s normal and part of the process of learning, and that when you are stuck, you should just “try something.” Describe an instance, so far in this course, where struggling and trying something was valuable to you. 

I really like this assignment as an end of semester reflection that I hope will reinforce a lot of the non-mathematics things that our class has worked on this semester. I’m sure I will get to talk about the responses in the future.

As for the particulars of this summer’s course, I have a great mix of students. One superstar student can’t believe how well doing problems explains all the things she has ever done in math without someone telling her stuff. She even brought her 12 year old son to class when he didn’t have other summer activities and he was able to do a surprising amount of the work in the class because he saw how much math should make sense.There are a bunch of other students who are starting to understand that when something doesn’t make sense, you need to start working: In other words, don’t just say something on your homework and move on… think about what precisely you are stuck on and work to have it make sense. I’m at the point in the semester where they have normalized just about everything they are expected to do with homework, presentations, and respectful behavior. I barely need to be there but to be an administrator (and ask them a lot of questions to see how well they believe their own work). Two areas that I am particularly happy with the progress of this class is how they work and speak to each other effectively and respectfully as well as their persistence in problem solving. They have really been struggling with algebra and simplifying some of our work on conic sections but most students have not gotten over discouraged by the amount of effort they are putting into their work.

As always, I welcome your feedback and ideas in the comment section or by email at longne at sfasu dot edu.

 

Nick: How Things Went This Semester

Linear Algebra: In previous semesters, students who put forth a good and legitimate effort were not just able to pass the course, but make great progress in how they were working. I had three students who were really trying to do well, and while they made progress, they did not pass the class. I am trying to figure out what more I could have done, but I think there was too significant of a gap in their ability to get work done in timely manner. After I let students know that I want them to come talk to me about how they did in the class (individual feedback other than their grade), I had a lot of students recognize how far they came in terms of problem solving and understanding the importance of sense making. I think I will keep sending out that email at the end of the semester because it really reinforces the idea that this is about more than a grad

Geometry: This semester has been a struggle for many different reasons. I feel like I need to find a better way to get students going at the beginning of the semester. As part of this I am going to be evaluating how I do Buy-in in my 100 level classes. I will probably be bothering some of you about ideas.

In reexamining the activities I used this semester, I found that I was just covering topics with some of the problems in my notes. But this, I mean that I talked about a topic just to talk about it, rather than building towards something. Stan’s post about ways to get students to learn what your really care about is something that I am trying to take to heart as I rewrite a good bit of my materials this summer.

Another difficulty I had was that I was not able to build persistence in my students this semester. The final stretch of problems includes many that can not be done (even by the best students) in 15 minutes. Students were able to do these in small groups but it took a long time. Even after congratulating them, they just saw it as a bunch of algebra they did rather than they had a great new tool to solve the next set of problems.

Differential Equations: About half the class was able to make great progress in understanding the whys of the class but I don’t feel like I made much of a difference in the students who were either ill prepared or unmotivated. This was a difficult class to teach because I only had about 50% attendance in many class meetings. Since I did not have time to prepare much active learning for this class, I would usually introduce a new topic and then start students working on problems. I would usually try to pull things back together after most students were able to finish the first few problems. This really seemed to work well since homework scores and exam scores significantly improved over the course of the semester.

I will also be preparing to teach a freshman level trigonometry course and a multi-variable calculus course in the fall. I have decided to use a traditional text for each and to supplement with my own problems and projects. I am hoping that this will mitigate some of the complaints that I need to do more example problems for students in the future.

And finally, I will be heading to Mathfest this summer (my first one), so come out and see my talks in sessions on building a problem solving culture and teaching tips for early career faculty.

Nick: Old Habits Die Hard

Anyone who has children knows that telling them once is not enough, even if you explain things to them and answer all of the many times they ask “Why?”. In fact, you often find yourself saying things you would never have thought any person anywhere would have to say. I’m talking about things like “Toes do not go in your drinks” and “You need to keep your pants on at the grocery store”. This works as a great analogue for how lecturing about a topic for a few minutes will not really foster a transformative experience. A lot has been written about how to help students break their old habits, but what I want to talk about for a little bit is how we as faculty often need to break some of our old habits. Sometimes we need to be told the same thing many times before it really sinks in.

The particular instance that brought these ideas to my mind was when a few trusted colleagues started chuckling as I was lamenting how many times each semester I have to give students a pep-talk and remind them about the reasons we are doing things differently than they are accustomed to. The reason they were laughing is that they had to give me the same kind of pep-talk about this time in the semester several times in the past year. One of them had already talked to me about this challenge this semester. The meta-ness of needing a reminder about why it’s reasonable and necessary to give students reminders struck me as something to write about.

Of course this is not the only time that I have found old habits of teaching hard to break. One of the biggest changes, but happened quite slowly over the course of the past decade for me, is the realization that we need to be explicit to our students in what we are trying to do. For some people, this means writing out all the algebra steps in a problem, but lately, I have found that it means that modeling behavior is not enough. I will go a step further and say that modeling the behavior that I want in students is impossible. I can’t model a transformative experience because that is a ridiculous thing to try to do in hour long chunks a couple times a week. I can’t model how to dissect my thoughts internally. I usually couch this discussion to students by the following analogy: “I can’t teach you how to be clever. I can be clever in front of you, and I can show you how I incorporate other people’s ideas to seem even more clever. But I just don’t know how to teach you to be clever.” Expecting others to pick up what is going on will not reliably work. It will work for some, but it will not reliably work.

One of the best things that my incorporation of inquiry based methods has done for me is the normalization of thinking deeply about what I am doing in the classroom. Meaningful change for me does not come in the form of radical changes. I am far too much a creature of habit. I am incredibly jealous of my wife and son because they have made significant changes, in which they did not later regress, by acting quickly. I know that the most effective way for me to change something is to incorporate the evolution I want into my habits and routines. The preparation needed to use inquiry based methods has incorporated this deep thinking of why I do particular actions into my daily/weekly routine.

When talking to students about the importance of effective communication, I often ask
“How great or useful is an idea if you are the only one who understands it?” As someone who loves to travel and give math talks, I understand the importance of tailoring your argument to your audience. I often ask myself how convincing an argument am I making to my students? Too often I rest on the old belief that students should listen to my ideas on the importance of modifying their perspective or attitude because my name is on the syllabus or because I am at the front of the room. Right now, I feel like I  am persuasive to my junior levels students, and not just because I’m the professor. One of my greatest struggles right now is finding a convincing argument for my freshmen students that would be just as persuasive if I wasn’t the person who puts their final grades into the computer.

As always, I welcome your feedback and ideas in the comment section or by email at longne at sfasu dot edu.

Nick: Trying for Earlier Ah-ha Moments

A few years ago, my wife bought me a yoga mat and a membership at an awesome studio in town. While I had done some yoga-ish things before, I had never really had a yoga practice. After doing a foundations course, I regularly attended different classes at different levels. One of the things I enjoyed about yoga was how different it was from almost any other athletic activity. In other words, the difficulty was the draw. About six months later, I was in a more advanced class. I had done the poses many times and heard the instructions about how to move into the positions just as many. I don’t remember what I was working on in particular but I finally heard what my instructor was saying about the movements. It was a revelatory moment; I finally understood the poses and motions were more than just lift your leg and extend your arm type things. I also understood that those other little modifications weren’t always apparent to someone watching from across the room. They were very personal modifications. I know I had an excellent teacher when after I started to try to find those personal adjustments, she gave me even more comments during class. I’m pretty sure she saw things she wanted me to change for those six months (and sometimes she did comment), but I wasn’t ready for those small but personal changes yet.

Those revelatory moments are impossible to predict but monumental in their effect. One of the big things I am trying for this semester is get more of those moments as early as possible for my students. This spring I have three different courses: a freshman level analytic geometry class, a junior level linear algebra, and a section of junior level differential equations.

Since I have done the geometry class and linear algebra several times before, I am making relatively minor changes to both classes. The biggest changes I am trying to make in my geometry class is a shift in the early problems. I am spending a couple of weeks doing some problems that I would expect students to know before coming into this course. Since many of the students know how to find the answers (and thus have an early success), I get to use this time to acclimate students to focusing on the whys of the problem. One of the important algebra skills in the course is taking the algebraic expression you are given and making it fit a very specific form (think of skills like completing the square). Students rarely have an idea of why they do the algebra they do. In fact, they are usually told by a teacher that the algebra will make the problem easier, but they don’t often see it that way. Students have had about a dozen Ah-ha moments already with the following two problems:

Question 14.

a) For what values of A and q will the expression 3x+2 be of the form A(x+q)?
b) For what values of A and q will the expression 3+2x be of the form A(x􀀀-q)?
Question 15.

a) Expand (x􀀀-a)2.
b) What value should ♦ be so that x􀀀2 -4x+ ♦ is of the form (x􀀀-a)2?
What is a for your expression?
c) What about for x􀀀2 +9x+ ♦?
d) Or 2x􀀀2 -2/3 x+ ♦?
e) For what value of ♦ will 2x􀀀2 -2/3 x+ ♦ be of the form B(x􀀀-a)2?

I don’t really know why we have had so many Ah-ha moments with what seems to me to basic problems, but I’m thrilled to have them.

In my linear algebra class, I am using my own set of problems that have worked out pretty well for students the last couple of semesters. One difference that I think will make this semester interesting is that I only have 1 student in the class who has seen this material. In previous semesters, there were at least three students repeating this course. I’m not sure how this will effect the level of work the students present but I’m interested to see how this is different than previous iterations.

I last taught our junior level differential equations course three years ago and only found out that I would be teaching this class the Friday before classes began. I have to thank everyone who sent me information about active learning activities in an ODE class. I am using a great traditional text (Blanchard, Devaney, and Hall) but I didn’t feel like I had time to prepare much in the way of activities. As of now I am introducing new topics and having students work on problems as a class or in small groups. I’m hoping that I will incentivize reading before class enough that we can work up to a minimal discussion lead by me followed by students working in class with homework presentations at the start of the next class.

As always, I welcome your feedback and ideas in the comment section or by email at longne at sfasu dot edu.

 

Nick: How Things Went This Semester

We often ask our students to perform some reflective exercises as part of the process of changing their mindset about mathematics and more generally about education. I think it is just as valuable to do such exercises as part of a culture of growth and improvement in teaching. I have been using this blog as one of my outlets for these reflective exercises and I think it has been a very valuable experience. I hope to have a few more people write on this blog even if just for a single post as part of discussing the reflective part of teaching. I am also thankful for the people who have responded  and the productive discussions that have ensued.

I wanted to finish off my posts on the fall semester with a few things that went well, a few things that I can improve on, and what is perhaps a crazy idea that I am considering for the spring.

With no further ado, one of the things that went well in all of my classes was that students were challenged in their mathematical ability as well as other areas that will be vital to their future success, like persistence in problem solving and ability to work on problems that are not mechanical calculations or problems that have no immediate path to a solution. Additionally, some students had enough “Ah-ha!” moments to realize that math should make sense to them and that math was not just some tricks given to them by someone at the front of the room.

About three quarters of the way through the semester, my linear algebra class was discussing some homework that had been presented when a student asked, “Do all linear algebra classes talk about all of this stuff?” Another student quickly offered the response that they had taken this course with another professor and “while the other class talked about more topics, this class is more… profound.” I did not have a stoic response to these comments, in fact one student asked why I “was smiling like that”. After several other students agreed with that statement about this course being more profound, I replied that I was very happy to hear that students had what I think is a wonderful response to what can be a very difficult learning experience.

One of the biggest things I will look to improve on is getting a better set of opening problems to mitigate the frustration students have when they are not simply shown how to do examples. As I wrote about earlier, I think the problems (and probably the students) get better as the semester goes on and in reviewing my questions, I expected to much of the students. It was not that they were not capable of doing what I asked but that the mechanisms for getting unstuck were not fully in place, so students did not always respond well to adversity.

One of the things I am looking to improve is to have earlier reflective exercises in order for them to embrace the growth mindset and help them make more lasting changes. I have seriously reworked some of the opening material in my classes to backup these earlier reflective exercises.

Something else that I have talked about and is really guiding my approach to classes in the spring is that I can talk in the classroom.  In fact I should talk, but I should not be the dominate voice in the room . Further what is done and said in class should be guided by students. Toward this end, I am trying to make sure that I have brief demonstrations or 5 minutes of introducing new material for each class meeting. I have been building a lot of things on Desmos since that makes dynamic presentations easy. An example that built for hyperbolas is here.

While students will identify that they need to do more than get the answer, making the changes to sense-making as the primary response to math is a long process. It is my job to get them as far in that process as I can in one semester. Sometimes I can help and sometimes I can’t.

I will end this post with a crazy idea that I have been thinking about especially for my 100-level geometry course. What if I gave student’s the answers to the problems? Not solutions including process but just something like x=2 and y=4. I’m not sure if this would properly alleviate any of their anxiety about getting the answer and allow them to focus on process. Has anyone ever just given answers willingly to students in order to change the conversation?

As always, I welcome your feedback and ideas in the comment section or by email at longne at sfasu dot edu.