Tears of Joy: Canvas Analytics is ON

For years, instructors all over the world have been coached to begin making more “data-driven decisions” and for years, we just haven’t gotten easy access to our data. I won’t even begin to rant about just how difficult it has been to get usable data out of Blackboard or Datatel.  But on Thursday, that all changed.

Order of data randomly changed to protect student identities. Click on image to enlarge.

On Thursday, Instructure turned ON Canvas Analytics.  And now any instructor who’s been teaching out of Canvas can see ALL the data about their students and courses – not just from this point forwards, but from this point forwards AND backwards.  That is a HUGE leap forward in education.  In one hour, I have now seen more data about my students, their behaviors, and their interactions with the course I teach than I have from using Blackboard for 6 years.

This data is only going to get better and better as Instructure actually does listen to their clients and is constantly pushing for better and better features to help us do what we do best: help students to learn and be successful.

Here are the full images of screenshots of analytics from my Calculus course. I’ll keep adding snapshots as the semester progresses. Enjoy! Oh, and you might want to pull out your hanky first, because there are going to be tears of joy (if you use or are about to use Canvas) or tears of frustration (if you don’t).

Analytics is all about student success.  With data at our fingertips, we can be the best possible learning coaches.  We can perform better research about the Scholarship of Teaching and Learning. We can make better assessment decisions. We can make better pedagogical choices.  Welcome to the new era of learning.

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Giving up Calculation by Hand

This is scary stuff for math professors, but with the arrival of amazing programs like Wolfram Alpha, we’re going to have to start paying attention to the signs of change.  I talked to Conrad Wolfram (at Wolfram Alpha Homework Day) when he was still formulating what he wanted to say at this TED Talk.  I think it’s worth 18 minutes of your time to watch Teaching kids real math with computers.

Here’s an outline of the Conrad Wolfram’s argument (which I am paraphrasing/quoting here):

What’s the point of teaching people math?

  1. Technical jobs (critical to the development of our economies)
  2. Everyday living (e.g. figuring out mortgage, being skeptical of government statistics)
  3. Logical mind training / logical thinking (math is a great way to learn logic)

What IS math?

  1. Posing the right questions.
  2. Convert from real world to mathematical formulation
  3. Computation
  4. Convert from mathematical formulation BACK to real world

The problem? In math education, we’re spending about 80% of the time teaching students to do step 3 by hand.

Math is not equal to calculating, math is a much broader subject than calculating.  In fact, math has been liberated from calculating.

Should we have to “Get the basics first”?  Are the “basics” of driving a car learning how to service or design the car?  Are the “basics” of writing learning how to sharpen a quill?

People confuse the order of the invention of the tools with the order in which they should use them in teaching. Just because paper was invented before computers, it doesn’t necessarily mean you get more to the basics of the subject by using paper instead of a computer to teach mathematics.

What about this idea that “Computer dumb math down” … that somehow, if you use a computer, it’s all mindless button-pushing.  But if you do it by hand it’s all intellectual.  This one kind of annoys me, I must say.  Do we really believe that the math that most people are actually doing in school practically today is more than applying procedures to problems they don’t really understand for reasons they don’t get? … What’s worse … what they’re learning there isn’t even practically useful anymore.  It might have been 50 years ago, but it isn’t anymore.  When they’re out of education, they do it on a computer.

Understanding procedures and processes IS important. But there’s a fantastic way to do that in the modern world … it’s called programming.

We have a unique opportunity to make math both more practical and more conceptual simultaneously.

Personally, I’m all for it.  But how?  That’s the question.  How to shift and incredibly complex and interconnected system of education? How to train tens of thousands of teachers and faculty to teach a new curriculum that they themselves never learned?  Hmmm … it seems that we might need some help, maybe a new paradigm for education itself.  It’s coming.

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Measuring Teaching and Learning in Mathematics

This weekend at AMATYC I presented this Prezi presentation on How can we measure teaching and learning in math? My husband was kind enough to act as the videographer for the presentation, and so I can also share the video presentation with you today.

I think the video should add quite a bit of context to the presentation, so I hope you’ll take the time to watch it.  What I propose (at the end) is a research solution that would help all of the math instructors in the country (who want to) participate in one massive data collection and data mining project to determine what actually works to improve learning outcomes.

If you have any suggestions for where to go from here, I’d be happy to hear them.

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Student Conceptions of Mathematics

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Do you ever get the feeling that you’re not making any real progress with your students?  Sure, they pass tests and progress through the courses (well, most of them), but have you ever just had the uneasy feeling that they really don’t get what math is all about?  Suppose you were to ask your students the following question:

Think about the math that you’ve done so far.  What do you think mathematics is?

What do you think they would tell you?

Well, in 1994, a research group from Australia did ask 300 first-year university students this question (Crawford, Gordon, Nicholas, and Prosser).  They identified patterns in the responses, and classified all 300 responses into categories of conceptions in order to explore the relationships between (a) conceptions of mathematics, (b) approaches to learning mathematics, and (c) achievement.

If you want all the gory details about the study, you’ll have to track down the journal article, but let me attempt to summarize their findings.

Students’ conceptions of mathematics fell into one of five categories (Crawford et al., 1994, p. 335):

  1. Math is numbers, rules, and formulas.
  2. Math is numbers, rules, and formulas which can be applied to solve problems.
  3. Math is a complex logical system; a way of thinking.
  4. Math is a complex logical system which can be used to solve complex problems.
  5. Math is a complex logical system which can be used to solve complex problems and provides new insights used for understanding the world.

The first two categories represent a student view of mathematics that is termed “fragmented” while the last three categories present a more “cohesive” view of mathematics.  Note that the terms fragmented and cohesive are well-used throughout the international body research.  The categories above, as you may have noticed, form a hierarchical list, with each one building on the one above it.

Here’s where this study gets (even more) interesting.  The researchers also asked students about how they studied (changing the language slightly here to “americanize it” a bit):

Think about some math you understood really well. How did you go about studying that?  (It may help you to compare how you studied this with something you feel you didn’t fully understand.) How do you usually go about learning math?

Again, the researchers went through a meticulous process of categorization and came up with five categories (Crawford et al., 1994, p. 337):

  1. Learning by rote memorization, with an intention to reproduce knowledge and procedures.
  2. Learning by doing lots of examples, with an intention to reproduce knowledge and procedures.
  3. Learning by doing lots of examples with an intention of gaining a relational understanding of the theory and concepts.
  4. Learning by doing difficult problems, with an intention of gaining a relational understanding of the entire theory, and seeing its relationship with existing knowledge.
  5. Learning with the intention of gaining a relational understanding of the theory and looking for situations where the theory will apply.

Again, these five categories were grouped, this time according to intention, into two general categories: reproduction and understanding.  In the first two approaches to learning math, students simply try to reproduce the math using rote memorization and by doing lots of examples.  In the last three categories, students do try to understand the math, by doing examples, by doing difficult problems, and by applying theory.  Other researchers in this community have seen similar results on both general surveys of student learning and on subject-specific surveys and have termed this to be surface approach and deep approach to learning (see Marton, 1988).

Still reading?  Good.  Remember my first question? Do you ever get the feeling that you’re not making any real progress with your students? Let’s answer that now.

Here’s how the conceptions of math and the approaches to learning math correlated in this study (Crawford et al., p. 341):

conceptions_of_math

Did you catch that?  Look at how strongly conception and approach correlates.  It’s probably what you’ve always suspected, deep down inside, … but there’s the cold, hard, proof.

Of course, all this is not so meaningful unless there’s a correlation with achievement.  At the end of their first year, the students’ final exam scores were compared to the conceptions and approaches to mathematics (again, for technical details, get the article). The researchers made two statistically significant findings:

  1. Students with a cohesive conception of math tended to achieve at a higher level (p < .05).
  2. Students with a deep approach to learning math tended to achieve at a higher level (p < .01).

Okay, so where does this leave us?  Well, we don’t have causation, only correlation (at least, that’s all we have from the 1994 study).  However, Crawford, Gordon, Nicholas, and Prosser were nice enough to use their research to develop a survey inventory that we can use to measure students’ conceptions of mathematics (1998).  The 19-item inventory (5-point Likert scales) has been thoroughly tested for validity and reliability, and can be found in their 1998 paper, University mathematics students’ conceptions of Mathematics (p. 91).

Suppose you want to try something innovative in your math class, but you don’t know how to tell if it works.  You could, at the very least, try to measure a positive change on your students’ conceptions of math (there are other ways to measure the approach to learning, but this is already a long blog post and you’ll have to either wait for another week, or view my presentation How can we measure teaching and learning in math?).

measure_tlm

To give the Conceptions of Mathematics Questionnaire (CMQ) would take approximately 10 minutes of class time (you should ask for permission from Michael Prosser before you launch into any potentially publishable research).  This would give a baseline of whether students’ conceptions are fragmented or cohesive.   If you were to give the survey again, at the end of the semester, you would be able to see if there is any significant gain in cohesive conceptions (or loss of fragmented conceptions).

So, I have permission (I met Michael Prosser this summer when he was at a conference in the U.S.), and I’m going to use this in all my classes starting next week.  I figure that when I start to see major differences on those pre and post-semester CMQ inventories, that I’m doing something right.  If I’m not seeing any gain in cohesive understanding of mathematics, then I’m going to keep changing my instructional practices until I do.

Papers that you will want to find (and read!):

Crawford, K., Gordon, S., Nicholas, J., & Prosser, M. (1994). Conceptions of Mathematics and how it is learned: The perspectives of students entering University. Learning and Instruction, 4, 331-345.

Crawford, K., Gordon, S., Nicholas, J., & Prosser, M. (1998, March). University mathematics students’ conceptions of Mathematics. Studies in Higher Education, 23, 87-94.

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The Cohort Effect: Coming of Age in Academia

The non-italicized portions below are excerpted from portions of my dissertation-in-progress.  Just so we’re clear, the quoted material in this post is strictly copyrighted (not licensed under the CC for the rest of the blog).

There is little doubt that self-experience influences beliefs (Nespor, 1987 and Goodman, 1988 as cited by Pajares, 1992). Instructors’ self-experience regarding educational practice comes first from their own experiences as a student (e.g. how they experienced instruction from a students persepective), and second, from their experiences as a practitioner in the classroom (e.g. the outcomes they observed as a result of their instruction). Early experiences tend to form beliefs that are highly resistant to change (Pajares, 1992). These beliefs are so strong that people will go out of their way to avoid confronting contrary evidence or engage in discussion that might harm these beliefs (Pajares, 1992). Instructors may present particularly resilient educational beliefs they spent years experiencing the system of education and likely, and most had positive identification with education to be motivated to pursue a career in it (Pajares, 1992; Ginsburg and Newman, 1985).

There is some natural resistance to change as a result of the human aging process, but there is also evidence that the greatest resistance to change in academia seems to come from cohort effects (Lawrence & Blackburn, 1985). In the cohort effect, new propositions may be in conflict with the longstanding core beliefs of an individual, which formed during the time that they came of age in academia. Faculty careers are best explained by the cohort model – that is, “…professors who complete their graduate work and achieve tenure during the same historical era are enculturated with a particular set of values that remain constant over time” (Lawrence & Blackburn, 1985, p. 137). Further evidence of this can be found in the 2004-2005 HERI Faculty Survey, which found that there were considerable differences in the use of student-centered instruction versus teacher centered instruction across the different faculty career stages (see figure below). Early-career faculty were more likely to use a variety of student-centered instructional practices (i.e. group projects, student presentations, reflective writing) and advanced-career faculty were more likely to use extensive lecturing (Lindholm et al., 2005).

cohort-effect-heri

Recognizing that an instructor is most likely to change during the time they “come of age” in academia, many faculty development programs target brand-new faculty.  What follows are descriptions of two of the math-specific programs that are aimed at new faculty.

Project NeXT and Project ACCCESS are professional development programs, sponsored by MAA and AMATYC respectively, that focus on brand-new college math faculty. Project NeXT (New Experiences in Teaching) is for new or recent Ph.D.s and provides training on, among other things, improving the teaching and learning of mathematics (LaRose, 2009). Project ACCCESS (Advancing Community College Careers: Education, Scholarship, Service) is a mentoring and professional development initiative that was conceived originally as a version of Project NeXT for community college faculty. ACCCESS is now wholly administered by AMATYC, and its mission is “to provide experiences that will help new faculty become more effective teachers and active members of the broader mathematical community.” (Project ACCCESS website, 2009).

So, let’s be clear here.  I don’t think we use the cohort effect as an argument to give up on mid- and advanced-career faculty.  But given the cohort effect, it may be necessary to give experienced faculty an intense and lengthy experience that causes them to “come of age” again in academia.  For example, many participants in our week-long Math & Technology workshop have told us that they had forgotten what it was truly like to be in the student role.  After a week of being confronted with lots of new technology and experiencing learning in new (and much more active) ways, these faculty tell us they have fresh perspective on teaching and learning.  Will that translate into more student-centered instructional practices?  I have no idea.  But I’d like to see AMATYC and MAA create a professional development program for a cohort of experienced faculty every year, using the model already established for Project NeXT and ACCCESS.

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