Category Archives: Education

Topics related to courses, classes, learning, teaching, teacher training, and mentoring

“Don’t be ‘a writer’. Be writing.” ― William Faulkner

Education researchers have shown that the most powerful way we learn is by trying to articulate what we know, believe, and feel (Connally, 1989). The creative process of transforming what is inside our heads into a form that can be shared with others is difficult but absolutely necessary for meaningful learning to take place. How many times have you passively listened to someone (ME!) talking about a topic thinking to yourself how boring it was or how obvious or how random, but when you later tried to explain it to someone, you found it nearly impossible to do so?
Continue reading “Don’t be ‘a writer’. Be writing.” ― William Faulkner

Dependent Sample Assessment Plots Using granovaGG and R

9/4/2011 Update: granovaGG is now available directly from CRAN.

Just over one year ago, I wrote about creating Dependent Sample Assessment Plots (DSAP) Using granova and R. Since then, Brian Danielak has been developing a new, ggplot2-based version of granova named granovaGG, which is almost ready for release on CRAN. This article updates my earlier granova-based version, but leaves much of the article text unchanged.
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“It’s the model that matters!” — Eric Mazur

At the ICER 2011 keynote, Eric Mazur reported that when students see a demonstration and either do or do not engage in a discussion of the demonstration, they adjust their memory to fit their model1. In other words, they retain their prior (possibly non-canonical) mental model and mis-remember the facts of the event to fit that model, rather than updating their mental model to account for the new facts2.

In physics education, given the following modes of instruction

  • No demonstration
  • Demonstration to students
  • Student Prediction without discussion
  • Student-to-student Discussion (similar to peer instruction)

students do equally poorly on a standard instrument intended to assess students’ understanding of Newtonian mechanics.

So, if we assume that we can’t skip demonstration altogether, and if we can’t just demonstrate, and if demonstration followed by discussion all suffer this fate, then what can be done? Engage students directly.

It’s not the act of predicting or discussing a prediction that triggers changes in student mental models, but rather confrontation with confusing experiences: staking ones intellectual ground so that one knows what one believes, then being confronted by a confounding example, and finally needing to substantially defend and explain the new experience.

Confusion seems to be an essential part of the learning process, or at least the ability of students to reflect and express their confusion3. In a physics class where students were asked to report on what they were most confused about each week, those who expressed confusion did much better than students who claimed no confusion. Willingness to express confusion positively correlates with understanding4.

So, in a peer instruction environment, we teach by questioning, not by telling or showing. We facilitate students’ engagement with the material rather than their obedience while in our classroom.

There is work on students’ use of mechanistic reasoning (i.e., trying to articulate the underlying entities, entity properties, activities in which entities engage, and the mechanism by which those activities give rise the the phenomena of interest) in physics and math education by David Hammer (now at Tufts), Rosemary S. Russ5 (now at Northwestern), Andrew Elby, Ayush Gupta, and Brian Danielak that relates to this… how students express their understandings of and reasoning about mechanisms underlying physical phenomena.

In short, if we’re not changing students’ mental models, than any learning that may occur is shallow and fragile. Some modes of instruction have a better chance of engaging students and changing their models, but unfortunately not the most popular modes of instruction, currently.

  1. Mazur, E. (2011) International Computing Education Research Conference (ICER) Keynote. Providence, RI. Slides available from http://mazur.harvard.edu
  2. The keynote is also discussed by Mark Guzdial on his blog at http://computinged.wordpress.com/2011/08/17/eric-mazurs-keynote-at-icer-2011-observing-demos-hurts-learning-and-confusion-is-a-sign-of-understanding/
  3. see the Dunning–Kruger effect http://en.wikipedia.org/wiki/Dunning–Kruger_effect
  4. forthcoming from Mazur, E., et al
  5. Russ, R. S. (2005) A Framework for Recognizing Students’ Mechanistic Reasoning. A dissertation available from http://drum.lib.umd.edu/handle/1903/4146

Dependent Sample Assessment Plots Using granova and R

Dependent Sample Assessment Plots (DSAP) constitute a way of visualizing data in the context of two dependent sample analyses. One (of at least four ways1) to think about this would be to think of pre-intervention and post-intervention response data scores, when studying the effects of intervention.

Suppose you’re an educator and you administer an assessment to students at the beginning of a unit asking about their level of confidence or understanding of a topic. You then teach a lesson that spans some period of time. At the end you collect responses to the same questions again. You now have a dependent sample: two responses that related to the same individual for some number of individuals.

Continue reading Dependent Sample Assessment Plots Using granova and R

  1. See Pruzek and Helmreich’s paper in the Journal of Statistics Education Volume 17, Number 1 (2009), Enhancing Dependent Sample Analyses Using Graphics

Thinking Through A Basic Pong Game in Processing

The Problem: Create a basic 1970s style Pong game for one player using the Processing programming language. The paddle will be on the right and the ball will bounce off of the three other sides. If the ball passes the paddle while the ball is traveling to the right, game play ends. The paddle will be controlled by the keyboard’s UP and DOWN arrow keys.

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My Classroom Rules

Recently, several students commented that I seemed to have a lot of classroom rules. This is an old refrain in my life, and, in a sense, it’s true. However, the rules I have are all just special cases of my basic three rules, which I share on my About Me page.

  1. If you are going to break the rules, don’t be obnoxious about it.
    • If you can’t be engaged, don’t distract others. It’s unfair to both you and them.
  2. Don’t disappoint me.
    • Don’t promise to focus, but fail to do so. Instead, acknowledge whatever is distracting you and address it.
  3. Be aware.
    • Know what questions your classmates are asking.
    • Recognize which questions are related to tweaking the solution and which are related to a different problem context.

Wil's Classroom Rules
A full sized version of my rules diagram

I think my biggest failing in the classroom is that I’m uneven in the application of the rules, which is perceived as me being arbitrary. Inconsistency and randomness seem very similar to the outside observer.

I sometimes let feature creep take over the problem statement, which can lead to unintentional complexity or student confusion as the problem changes. I need to spend more time up front specifying the problem completely with students so that it’s clear to them and me what the invariants are.

I also find it difficult to ask a student actually to leave the classroom. I’m forever optimistic that the unfocused student will find moments of clarity and engage with the course material. Often, they do, but unfortunately, while I’m waiting for that to happen, the class as a whole is affected and, generally, material isn’t covered as concisely, clearly, or completely as might have been the case otherwise, thereby disadvantaging the other students who could have gone further, faster. Such is the nature of a set of random people with diverse metacognitive skills and needs. Still, I’m certain that I could serve better both ends of the spectrum.

Thoughts on Course Grades

Like many educators, I worry about the level of effort that my students commit to their studies (the process) and the quality of their work (the product). We call the process many things: engagement, time on task, passion… But we mean to describe that self-driven, motivated commitment to learning for the sake of learning that we value.

Unfortunately, in many educational environments, the standard proxy for effort is the course grade. Grades are a poor proxy, but are so ingrained in educational practice (in some of the institutions where I teach) and in students’ minds that it may be useful to consider a way to structure grade rewards to encourage the genuine engagement from students that we desire.

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Making Values and Culture Manifest and Manifold

Over at his blog, Mark Guzdial has raised questions about the ability of (a) curricula and (b) instruction to be value-/culture-neutral. I wonder whether it isn’t more important that they be manifest and manifold in education.

In other words, we need value transparency, to express the values and cultural biases in our designs clearly and publicly. When we choose what learning outcomes to include in a curriculum and when we create instructional plans intended to help learners attain those outcomes, we make value choices based on our own prior experience, and often do so unconsciously. Probability examples that rely on a 52-card deck and programming exercises that remake western-style games are necessarily rooted in our past experience. That implies that some learners– those who don’t share our experiences– will have a higher cognitive load when faced with these tasks, working to attain not only our intended learning outcomes, but also to build knowledge and skills related to the new (to them) problem context.

We need to be sensitive to this and provide the supports necessary to promote success. One way to do this is to represent core ideas in multiple ways, creating banks of culturally diverse, parallel examples of instruction that speak to the same set of intended learning outcomes. For example, do we need probability examples to rely on dice, cards, and coins? How else might one think about probability, assuming that those objects aren’t part of your daily life?

I can imagine a rich collection of activities, presentations, etc. that could be used not only as teaching aids, but also as tools to train teachers about diverse ways to represent ideas. Even within my own cultural context, I find myself often looking for new ways to introduce learners to a topic (nifty assignments, anyone?).

Celebrating Ada Lovelace Day 2010: Sally Fincher

March 24th is Ada Lovelace Day, a commemoration of the contributions of women in science and technology in honor of it’s namesake. Ada Lovelace (nay Augusta Ada Byron King, Countess of Lovelace) was the daughter of Lord Byron and Anne Isabella Milbanke, born in 1815. She was a contemporary of Charles Babbage, who is generally credited in the history of computing with designing the first mechanical, general-purpose computer: the Analytical Engine. Although not built during their life times, Babbages’ ideas and Ada’s analytic abilities led her to write notes which are today regarded as the first algorithm written specifically to be performed by a general-purpose machine; in short, the first computer program.

I would like to take the occasion to tip my hat to Sally Fincher, Continue reading Celebrating Ada Lovelace Day 2010: Sally Fincher

Goodbye, Hello World?

Alfred Thompson questioned on his blog today whether the customary first programming exercise, Hello World, should be replaced with something that’s more flexible and calls on students to engage in a short, non-trivial first act as a programmer. I admit, I’ve used Hello World myself with students, but usually not as a first activity. Instead, I use Hello World to help students who have had some hours or days of programming instruction understand that they now know quite a bit about how programming languages express an intention. I ask students to visit the ACM Hello World web page and compare and contrast that simple program in different languages. How are code blocks started and ended? How is output generated? How is an infinite loop expressed? How are strings represented?

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Learning to Write in English like Learning to Program

Imagine for a moment that you were going to teach writing in standard English in the same way we tend to teach computer programming.

Alright… Let’s learn to write. Before you can write, you need to know about the fundamentals of the language we’re going to use. A language is a collection of words and rules for how you combine those words. Words can be thought of as being of different types that determine the purpose and meaning of the words. For example, two types we’ll work with are nouns and interjections. There are other types, too, but we’ll get to those later.

For now, let’s write your first sentence. A sentence is a valid sequence of words. By valid we mean that the sentence would be recognized by an expert speaker of the language as being acceptable.

So, we need an example of a noun and an interjection to get us started… One frequently used noun is the word WORLD and a common interjection is HELLO.

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Media-Propelled introduction to Computational Thinking

Eric Freudenthal of the iMPaCT: a Media-Propelled introduction to Computational Thinking project spoke at SIGCSE 2010 about how to engage students who are math phobic with computation and, thereby, with math. Using Python and computation about dynamic systems, students work to understand how code == math == concepts. One issue raised was how ethical it is to mislead students initially about whether they’re learning “math”. Eric’s argument: if students know they’re learning math, they fallback on unsuccessful rote memorization techniques. If, however, they believe they are working with dynamic systems to understand how the system changes as parameters are adjusted, then students engage and experiment.

Commenting on Student Writing

We often find ourselves commenting on students’ writing and acting as editors rather than critical readers: we indicate line-level edits, such as missing commas and poor word choices– as if fixing the mechanical errors would make the paper acceptable. In reality, most student papers we see are first drafts, often written the night before the assignment is due and unedited by anyone, including the author. (See my post concerning the design of assignments, coming soon.)

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