Tuesday, January 30, 2018

Framing mistakes as a learning opportunity

In a mathematics class mistakes are really tricky. Many students have a very simple view of mistakes; they are bad and should be avoided. Unfortunately being human beings, we all make mistakes, even in a math class. Even me, at the front of the classroom, I will make mistakes. Hopefully we use these mistakes as learning opportunities, which we can only really do if we stop and reflect on what happened, and how to prevent it from happening again.

I made a mistake last week during one of my class's online quizzes, I made a very simple mistake in the setup of the question. Whenever this happens I am usually alerted by an industrious student, and fix the mistake.

During a previous class I shared a list of questions I had to answer when writing a student recommendation for an internship. One of the questions we discussed was "Does the student ask for help when needed?" In most situations it is preferable for someone to ask questions in order to know what they should do, than it is to have someone perform work they do not know how to complete. The time in detecting these errors, fixing them, and mediating any negative consequences is considerable, not counting money or other resources. No wonder an employer would want an intern (or employee) to ask questions when confused.

So this error cropped up in an online quiz, and we just talked about asking for help when needed. So I naturally asked "How many students will send me a message?", if they really listened to our discussion of this question they would ask for help when needed. Out of 29, 3 students sent me a message asking about this question. Ok, so they didn't hear me, not a big surprise. Whenever I talk about topics that are not math (study skills, organization, soft skills, group work, etc.) students usually tune out.

In class the next day I shared the story of the Mars Climate Orbiter. Long story short, a $350 million probe burned up in the Martian atmosphere because someone did not check the units of a calculation. This definitely go their attention, as it usually does; no one expects literal rocket scientists to make mistakes, let alone really simple ones. After talking about the orbiter I had a few questions for students:
  • Was this a preventable mistake?
  • Was this a significant mistake?
  • Do you think NASA learned from the mistake?
  • How many people here have made mistakes in their classwork during the last week?
  • How many people learned from those mistakes?
  • Are your mistakes preventable?
  • Are your mistakes significant?
  • Did any of your mistakes cost $350 million?
  • Do you have space in this class to make mistakes through unlimited attempts completing homework questions, Quiz corrections, and working with others in class?
We had some real-talk on making mistakes in math, and how they are part of learning the course material. By making it clear that I expect students to make mistakes ("Make them early and often.") and to learn from them I hope to lessen student fear of making mistakes, the stigma associated with them, and to reframe student's expectations of me. I regularly ask students to reflect on making study plans, if they were able to follow their initial study plan, what factors prevented them from following their plan, and what they are going to do in the future to prevent these factors from getting in the way. 

In the future I would like to do a few things with this theme of making mistakes:
  • A POGIL-like activity where students read through a description of the Mars Climate Orbiter, and come to some of these conclusions themselves.
  • Demonstrate the role reflection plays in learning from mistakes. 
  • Tie this into the growth mindset, a very natural place to discuss these issues. 
How do you address mistakes in your classroom? Do you do any specific activities with students to frame mistakes as learning opportunities?

Friday, December 29, 2017

Faculty Focus: Students' Self-Fulfilling Prophecies: Five Ways to Break the Cycle

The article Students' Self-Fulfilling Prophecies: Five Ways to Break the Cycle from Faculty Focus does a great job of identifying areas faculty can help students develop a positive self-image regarding their studies. In math classes I feel this issue is especially acute, given how many times students are unwilling to offer answers or solutions for fear of being labeled 'stupid' or worse.

I do a few of the suggestions in my current setup:

  1. Provide opportunities for metacognition. During the weekly binder checklists, and group quizzes, students have an opportunity to reflect on what they have learned and how. During nightly Check-Ins students are asked to think about the material from the day, and how well they know it. 
  2. Flip roles. In using the POGIL roles every student has a responsibility, and occasionally will become the manager of the group that day. In addition to "Creating leadership roles empower students who feel disenfranchised." it also provides structure to the group work, my main motivation for using them.  
  3. Create check-in points. My nightly Check-Ins are graded based on completion, and sometimes include the "muddiest point", "most important point", and "write a question to build understanding" questions. 
  4. Build in moments for dialogue. While my Check-Ins do have reflection questions, they don't specifically address negative self-image in the class. This is one question category I will try to incorporate into Check-Ins this term. Questions like "What if, after doing a bunch of homework and getting some questions right and some questions wrong, you start to feel discouraged? You start to feel like you just can't get this stuff, and that you're not 'smart'. What are you going to tell yourself to get out of this funk, and back on track?"
  5. Point it out. In my mini-lectures I do try to address process skills, and one of my usual 'spiels' is addressing anxiety and negative self-image. I try to relate to students explaining that I have anxiety about how each class will go, and that I use that anxiety to prepare for that class. I also make it clear that grades are a measure of understanding, not whether you are a good person or not. 
What do you do to disrupt a student's negative self-image, or their unhelpful self-fulfilling prophecies? 

Friday, September 9, 2016

NEA Higher Education Advocate is actually pretty useful!

I am sure many of you get the National Education Association's little 'magazine' Higher Education Advocate. It is usually filled with either the higher education equivalent to fluff pieces on the local news, or legal/political issues that effect higher education. However, if you pull your September 2016 issue (Vol. 34, No. 4) out of the round filing cabinet, in the Thriving in Academe feature you will find an article by James M. Lang titled Small Teaching: Lessons for Faculty from the Science of Learning. Lessons for me? Based on actual science? Get out!

Really though, I feel like education today is similar to alchemy in its final stages; lore, superstition, and patterns that were not rigorously tested, and a new challenger approaches in the Enlightenment and the scientific method. Much of what I have read is based on educator's experience, and what has worked and not worked for them in the past. This is great and wonderful, and I eat it all up, but shouldn't there be an empirical way of looking at education informed by cognitive science? I know  cognition and epistemology are not everyone's cup of tea, but it seems that we have to get into it a bit to know which best practices are actually 'best'.

Lang breaks up his recommendations during four parts of the class session; right before class, opening class, the "long middle" of the class, and the ending of the class. He recommends instilling some kind of wonder or awe in the "right before class" section, which I can see working well in mathematics classes, if done correctly. Possibly a news-related result, or a classic fable like Xeno's Paradox, doubling rice grains on a chess board, etc. In the opening of the class he recommends asking students what they did in the previous class, in my mind activating prior knowledge, and building connections to that day's material. I do this in my daily Quizzes, but he seems to make it a bit more conversational. I like that, but unsure if I can squeeze it in my current setup.

During the middle of the class he recommends some notebook thing, I don't know, it didn't seem all that useful. What made an impact was his suggestion about the end of the class; a one-minute 'paper' answering one of the questions "What question remains in your mind after today's class?", and "What was the most important thing you learned today?" These reminded me of the 'Stickiest Point' question one of my tenure advisers suggested I use, and I have incorporated them into my post-class quizzes in our learning management system. The first question makes good use of a student's recall ability, points to areas an instructor could address next class, but is also broad enough that a student could ask how the ideas of that class connect to past or future classes. The second question also has students practice recall, but also asks them to summarize the content in their own words or possibly describe something new they learned about themselves.

Granted, all of the questions have a fatal flaw; a student could answer any of them with two to four words. In my post-class quizzes I award credit based on completion, and thus these students earn credit for poor answers. I do push that in these types of reflection questions you only get out what you put in; by taking the time to reflect on the question and your answer, you provide yourself another opportunity to think and learn about the material.

Coincidentally (or not) this article's title is also the title of his book, which will go on my long cobweb-collecting reading list.

What do you think? Did you read the article? Are you going to read his book? What are small things you are trying this term?

Thursday, September 8, 2016

Pre-Fall Term Psychic Exorcism: Statistics class ideas on a page

Past two weeks between summer term and the faculty work week has been spent packing (we bought a house!), cooking a lot of good food, watching Star Trek: TNG, and reading a variety of books and articles meant to 'help' my teaching. Not sure if they are helping right now, I just have a lot of ideas floating around in my head that I need to put somewhere, namely here.

  • I've been browsing Technology-Supported Mathematics Learning Environments 67th Yearbook (2005) and while focused on a K-12 audience, I have taken up a few ideas from it:
    • Teaching Strategies for Developing Judicious Technology Use by Ball and Stacey helped address my concerns of letting students run amok with calculators (mathematical totems I call them in class). They suggest, as is a common theme with many education best practices, that we have to model how to use technology tools. And not just their actual use, but whether to use them or not. I am hoping to incorporate some of the strategies below into my in-class activities, through question prompts, discussions, or demonstrations.

    • Comparing Distributions and Growing Samples by Hand and with a Computer Tool by Bakker and Frederickson focused on middle school students and their conceptual development of data, samples, population, and measures of center. This passage in particular struck me:
      • We can compare this situation (focus on calculation of measures of center) to the proverbial tip of the iceberg. It is the substance beneath the surface that makes the iceberg float. In this metaphor, mean, median, and mode are the visible tip of the iceberg. What is beneath the visible surface is the knowledge and skills that students really need to understand and sensibly use these measures of center. 
      While it is necessary to be able to do the computations, it is much more critical for students to develop an understanding of when these measures are appropriate, and then apply and use these numbers in context. This reinforces the need for students to write these numbers in context, and base decisions on them. My in-class activities should always contain summary questions that ask students to write in words what their calculations are, and what they mean.

  • Student Engagement Techniques: A Handbook for College Faculty by Barkley offers a wide variety of ways to get students engaged with course material. One I found especially useful was the two-page section on "Try to rebuild the confidence of discouraged and disengaged students." Teaching statistics usually means teaching a student population that has some mathematical knowledge, but are not confident with that knowledge. Below is a list of strategies based on Motivating students to learn by Brophy (2004).

    I tried having students set goals in my summer Calculus course, asking them to describe what their study plan was for the weekend. I think this helped with planning, understanding consequences, and overall helped students understand responsibility. I will definitely incorporate these questions into post-quizzes for my statistics course.

    The entirety of Chapter 8: Tips and Strategies for Promoting Active Learning should be tattooed on my body somewhere. I know and apply a number of the strategies (Activate prior learning, clarify your role, limit and chunk information, etc.) but found the section on "Teach in ways that promote effective transfer." useful. I regularly refer to Bloom's Taxonomy in my classes, but the below table really hit home that your strategies and methods for developing those cognitive tasks should be different for each level of understanding.
So in summary, for my Fall Statistics course I will:
  • Include judicious technology use questions throughout in-class activities. 
  • Have questions that ask students to interpret their calculations, and make decisions based on them. 
  • In announcements and post-quizzes write comments or questions that have students think about what they have accomplished, set realistic goals, go to different support services, and to reflect on their own cognitive processes. 
  • During the start of the course, and during exam review sessions, share the Learning Strategies table and have students determine what a question is asking, at what level, and possibly how they should study for such a question. 
Glad I got those ideas out, and can now refer back to them after the term to keep me accountable. What ideas are floating around in your head for the upcoming term? Any exciting projects, new ways of doing things, assignments, assessments? Feel free to share below. 

Wednesday, July 27, 2016

Starting the Guided Pathways conversation at my insitution

I applied to and was accepted to the Clark College Summer Guided Pathways Institute. It is a four day workshop that looks to start the conversation on Guided Pathways (GP) at the college. There have been a number of readings that have discussed the data supporting the use of GPs, different models used, and how Choice Architecture can be applied to helping undergraduates choose majors and/or programs.

Overall I have been really impressed with the thoughtful and smart people in the institute. The conversations have always been positive, constructive, and shared different perspectives I would not have normally encountered in my day-to-day. The readings have been helpful to see what other institutions are doing, and we've begun to think about what parts of these programs we want to try.

Below is a version of a discussion forum post I made to the course site. Feel free to add your thoughts, or comments below.

I finished Implementing Guided Pathways at Miami Dade College: A Case Study and had a few thoughts.
  1. The recommendation "Integrate academic programs and student support services." seemed on-point for our campus. The few times I have reached out to support services the results have always been positive, and we achieved more than I could as an individual instructor. I get the sense that faculty occasionally feel like the world is on our shoulders, when we can (and should) share the load with student support service staff. In most cases they may be better trained and equipped to help in certain situations and with specific student populations. I would love to see a way to integrate these two pillars of the college through Canvas, CTC Link, or some other medium.
  2. The recommendation "Increase student engagement through communities of interest." is very appealing, and would strengthen a number of goals in the Academic Plan. These communities could be students from the same meta-major, and supported through a 'wrap-around' class. As the terms progress students could be exposed to other classes they may want to take, student clubs they may find interesting, student government positions that are open, career services for their industry, and the talks and seminars we regularly put on. (The STEM Seminar Series is awesome btw.) I could also envision these communities of interest organized around specific themes, or the big intractable problems of the day. A Global Warming Group could contain students from biology, government, engineering, and a variety of other meta-majors to talk about the causes, 'controversy', solutions, market applications, and the other facets of this problem.
  3. The "Getting Faculty Buy-In at the Front End" issue, in my view, is one of the thornier questions of this entire endeavor. What does the arc of developing these pathways look like when some faculty don't even recognize the problem?
  4. "Because of the initial positive results from the restructured intake process and the added revenue generated by the improved retention, the college's leadership approved the hiring of 25 new full-time advisors." (emphasis mine) This was not something I thought very much about until reading this article; increased retention rates would help provide for the funding of the continued development of pathways. It may also increase our ability to try new initiatives within pathways as they develop over time.
  5. "Overall, the largest threat to institutional redesign at MDC was organizational inertia. Communicating frequently about progress, building consensus, and creating a sense of urgency were vital to creating a sense of shared ownership and to generating momentum for change across the college." Once we leave this institute, what group/committee/mechanism will there be to communicate progress on developing pathways? How are expectations for progress going to be set? Can the 2016 Fall Term Faculty Workdays be structured in a way to move this forward?

Friday, February 19, 2016

Lots of little changes to classes this week.

I've been making little tweaks to my classes based on student performance and responses. All of these actions are being taken on qualitative data, not quantitative data, which isn't a bad thing, but something I want to move away from. I would like to develop some metrics over spring break to put into place next term that would help me make these decisions based on data. Percentage of available homework in the online system (WAMAP) that is complete, number of zero quizzes, and other metrics would help in making data-driven decisions.

My tweaks this week:

  • In Calculus I students were to complete the homework on the related rates section on Tuesday. Most did not. This was not completely surprising, the topic is a physical application, and the setup of each question can take a while. Additionally this homework took quite a bit more time than others, so even if they budgeted for it, they may not have budgeted appropriately. I gave them an additional six days, to Monday at 11:59 PM, the day of our next exam. 
  • Also in Calculus I we are currently talking about graphing functions, using information about the first derivative and second derivative. This is a difficult section because it includes conceptual knowledge about these derivatives, and quite a bit of computation. For today's quiz in the morning class I divided students into two groups. One group would work on graphing one function, the other group, another function. For the first five minutes students were to work on it themselves. Next five minutes students were to work with a partner. Last five minutes students were to working with all the students who had the same function. Each group would have one person present the question. After trying it out, only one group presented, and I finished the other question. To let them using the quiz as a study aide, I allowed them to take it home, but to get credit they would have to email me a hand-drawn graph of the function I presented. 
  • In College Algebra I did not have a pre-made quiz to start the day so I had students take out a sheet of paper, write one of the questions we have been talking about, give it to another student, and have them solve the question. Overall it was a fun activity, albeit a little broccoli covered in cheese. At the end I talked about how I like them making these questions, 
What change in course structure, grading, or presentation did you make on the fly that worked well? That didn't work so well? Feel free to share below. 

Tuesday, February 16, 2016

Same course, different terms, completely different classes.

Last term I taught MATH151 Calculus I in the morning daily, and it felt so RIGHT. The pacing of the class, my in-class examples, questions from students, the schedule, the end of week activities that have students explore different topics, everything felt like the best it could ever be. This term for whatever reason things are not going so well. I'm teaching two sections of the class and both feel wildly different.

The morning class seems tired, not really 'there', and swings between general bewilderment and complete boredom at what we're doing. Test scores are low, and there are still (WEEK 7!) students who haven't registered for the online homework system. I've even started moving back to lecturing two days a week since participation through the in-class examples has been low. There are a number of students who think of mathematics in very linear terms which limits their ability to solve application questions, but at the same time their work is unorganized. Other students are unprepared to complete most of the algebra in the course, whom I fear are not going to pass for this reason. In this class I feel like a task master.

The afternoon class is energetic, but has a habit of going off the rails at the slightest provocation. I have to do a lot of sheep-dogging (making sure the group is together) as we go through each question. In-class examples are better received with this class, and they work well in groups, but questions that require a long, sustained method are difficult. Numeric outcomes for this class are generally positive, but I wonder if they are getting the conceptual understanding down. In this class I feel like a positive guide to the discipline.

I hope this doesn't come across as complaining about my students, it just seems that a class reflects both the instructor and students, as it is a culture both groups are building together. I'm coming to recognize that each class has to be different because it contains different people in it. I may have 'empirical' ('imperial'?) methods and assessments, but if they don't somehow reflect the students in the course am I being as effective as I could be?