Category: Pedagogy

Expectations of Math

Jonathan Wai wonders, “Why Is It Socially Acceptable To Be Bad At Math?” After all, it’s not socially acceptable to be illiterate.

The cultural norm that it’s okay to be bad at math has deleterious effects on student motivation. I’ve seen it myself. One parent of an excellent, hard-working student confessed that it was probably her talking about how bad she was at math that helped her kid feel like they didn’t need to work that hard at the subject; especially since the student didn’t think that they were going to use the math anyway.

Some think that the solution is to use a more integrated curriculum and teach, “a math curriculum that focused on real-life problems,”:

Imagine replacing the sequence of algebra, geometry and calculus with a sequence of finance, data and basic engineering. In the finance course, students would learn the exponential function, use formulas in spreadsheets and study the budgets of people, companies and governments. In the data course, students would gather their own data sets and learn how, in fields as diverse as sports and medicine, larger samples give better estimates of averages. In the basic engineering course, students would learn the workings of engines, sound waves, TV signals and computers. Science and math were originally discovered together, and they are best learned together now.

— Garfunkel and Mumford, 2011: How to Fix Our Math Education in the New York Times
— ↬ The Dish ↬ Finding the Next Einstein

Which seems like a good idea — more of an apprenticeship-style approach to math — but there still needs to be some space for the wonderful elegance of some of the apparently more abstract math. More real world applications could certainly be incorporated into the current curriculum, but it would be short-changing our students if we just left math for problem solving and did not delve a little into the principles behind the mathematical techniques they’re using in a more general way.

Daniel Pink on Motivation

Take home message: As soon as someone’s paid enough that money is no longer an issue, paying them more (or giving bonuses) can even have a negative effect on their performance on anything that requires higher level thought.

Which suggests that if we take grades out of the equation kids will learn more?

Audio from Daniel Pink’s TED talk on motivation.

↬ Mrs. D.

Learning Differences that Matter

Cedar Riener and Daniel Willingham expand on the argument (previously discussed here and here) that learning styles do not exist. They do not, however, deny that different people learn differently and this needs to be taken into account in teaching.

Real differences that affect learning:

  • Different talents: “[W]hether we call it talent, ability, or intelligence, people vary in their capacity to learn different areas of content.” (ᔥ Riener and Willingham, 2012). Some of this is probably genetic, while some of it is probably due of nuture., which leads to:
  • Different interests: Students with an interest in a subject are more motivated to learn and will learn it faster.
  • Different background knowledge: Student retain more then they are able to fit new knowledge into an existing mental scaffolding.
  • Learning disabilities: There are neurological differences that result in things like dyslexia that have a strong influence on how some students learn.

Riener and Willingham argue that while students do have preferences for ways they learn (visual vs. auditory vs. kinesthetic etc.) these have no real effect students’ learning. Information should be presented in ways that are appropriate to the content:

If I were to tell you “I want to teach you something. Would you rather learn it by seeing a slideshow, reading it as text, hearing it as a podcast, or enacting it in a series of movements,” do you think you could answer without first asking what you were to learn—a dance, a piece of music, or an equation? While it may seem like a silly example, the claim of the learning styles approach is that one could make such a choice and improve one’s learning through that choice, independent of content.

We all agree that some kids show more interest in math, some start their education more interested in poetry, and others are more interested in dodgeball. The proof that the learning-styles theorist must find is that for some sort of content—whether it be math, poetry, or dodgeball—changing the mode of presentation to match the learning styles helps people learn. That evidence has simply not been found.

— ᔥ Riener and Willingham, 2012: The Myth of Learning Styles in Change, The Magazine of Higher Learning.

Finally, they assert that, “it is a waste of time to assess learning styles rather than, for instance, background knowledge.”

Still, even with learning styles taken out of the equation, it seems to me that presenting information in multiple modes remains beneficial. It forces the teacher to approach the subject matter from different perspectives, and presents students with multiple opportunities to encounter information in a way that would fit into their existing knowledge scaffolding. However, it is useful to recognize that we don’t have to force ourselves too fit content into incongruent learning styles (although that in itself might be a useful mental exercise for the teacher, or a good way for students to demonstrate that they can apply their knowledge into other domains).

↬The Dish

Legitimacy Must be Earned, For Teachers and Even for Parents

My students always have the right to expect a reasonable answer from me to their questions. Even the hard ones that don’t have to do with the subject at hand: things like, “why do I have to learn this, I’m not going to be an engineer?” It’s part of authoritative (not authoritarian) teaching. Students have a right to wonder why they’re doing what they’re doing. It keeps me on my toes; considering if there’s a good reason for doing what we’re doing. It helps them to see how to make a rational argument — and sets, by implication, a high bar for the quality of their arguments. I also figure that if I’m respectful to them, and share my reasoning, they’re more likely to go with my decisions voluntarily, even if they don’t particularly like them.

And it seems that same approach also applies to parenting. A study (Trinkner et al., 2012) finds that adolescents respect and defer to their parents only to the extent that they see their parents as being fair, considerate and respectful of them. When kids believe that their parents’ decisions are legitimate, they are more likely to obey them. Conversely,

… authoritarian parenting was negatively associated with parental legitimacy.

— (Trinkner et al., 2012): Don’t trust anyone over 30: Parental legitimacy as a mediator between parenting style and changes in delinquent behavior over time, in Journal of Adolescence.

The way to earn legitimacy is by being authoritative not authoritarian (as described by Baumrind’s parenting styles).

… authoritative parents are warm and responsive, providing their children with affection and support in their explorations and pursuit of interests. These parents have high maturity demands (e.g., expectations for achievement) for their children but foster these [through] communication, induction (i.e., explanations of their behavior), and encouragement of independence. For example, when socializing their children (e.g., to do well in school), these parents might provide their children with a rationale for their actions and priorities (e.g., “it will allow you to succeed as an adult.”). Authoritative parents score high on measures of warmth and responsiveness and high on measures of control and maturity demands…

— Spera, 2005, A Review of the Relationship Among Parenting Practices, Parenting Styles, and Adolescent School Achievement in Educational Psychology Review.

It also turns out that authoritarian, “because I told you to” parents were most likely to have delinquent, disobedient kids.

Enhancing Creativity Just by Doing Things a Little Bit Differently

When my verbal students complain about having to do diagrams (or vice versa) I try to explain that it’s useful for them to see, and be able to learn from, different points of view. There also a body of research showing that breaking familiar routines enhances creativity.

Actively doing something different, just by changing your routine for example (milk first then cereal instead of the other way around), seems to improve people’s cognitive flexibility (see: Ritter et al., 2011), but you have to do it yourself.

… being exposed to simple unconventional events, such as preparing breakfast in the “wrong” order, increased cognitive flexibility. Furthermore, these effects were found only when people actively participated in the unconventional activities. Just seeing someone else perform the activities was not enough (my emphasis).

— Damian, R., 2012: Why Would Doing Something Unconventionally Make Us More Creative? in Science + Religion Today.

These findings also suggest that greater diversity also promotes creativity — periods of greater immigration have been followed by increases in innovation.

Challenge vs. skill, showing "flow" region. (Image and caption by Wikipedia User:Oliverbeatson).

It also suggest one reason why a little challenge is essential for motivating students to get into the flow zone for learning. People learn more, and become more engaged, when they’re challenged, have to struggle a little, and think differently, while figuring things out for themselves.

An interesting interview with Csikszentmihalyi is here.

Master and Apprentice

Handmade Portraits: The Sword Maker from Etsy on Vimeo.

This video, contains some fascinating reflections from, Korehira Watanabe, one of the few remaining traditional sword makers in Japan.

Particularly intriguing is Watanabe’s somewhat counter-intuitive need to keep exploring new challenges in swordmaking, so that he might keep the ancient traditions alive. He’s also very interested in instilling the same type of drive in his disciple, with the hope that his disciple will someday surpass him.

I personally find this to be a quite appropriate perspective for a teacher.