In this study, the researchers analyze portfolios submitted
by teacher candidates. They conclude that the lessons included many tasks involving
hands on activities or real world contexts and technology, multiperson
collaboration and hands-on material, but rarely required students to provide
explanations or demonstrate mathematical reasoning.
I wondered as I read this article how representative the
study would be. When I am in a job interview and asked to describe a lesson, I
generally describe a very hands-on activity such as building clinometers and
using them to measure heights as a way to make trigonometry meaningful. While I’m not misleading anyone, as I do run
this activity almost every year, it is the exception and not the rule in my
class, as I generally follow a fairly traditional lesson structure. Indeed, if
asked to provide a portfolio of my lessons, I would these ‘special’ lessons
which are not what the students in my classes experience most days. I would
suggest many other teachers might follow similar patterns.
The authors criticize that that tasks, while hopefully
engaging and meaningful, tend to have a ‘low frequency of high demand tasks’ in
exchange for a ‘higher incidence of innovative pedagogical features.’ This made
me think of two things: First, I often feel pressure to be ‘performing’ and ‘entertaining’
my classes, which I think does not need to be a teachers’ role. Secondly, particularly
with new curriculums coming into place, I hope math class remains challenging
as it is one of the last bastions of challenge (some) students have in schools.
Some of my students tell me they are used to getting near-perfect marks in most
other subjects simply for completing their work to an acceptable degree, with little
regard for quality. While I don’t mean
to torture students, I think part of what schools need to teach students is how
to work hard to achieve something that is difficult, and when we settle by
catering to a lowest common denominator, we may be robbing students of the
opportunity to have to work hard for something.
Finally, in their conclusion, the authors bring up the
concern of many studies including theirs focusing on classroom lessons and not
on assessment. For example, if teachers use methods of instruction that include
group work, hands on activities and technology, but their assessment focuses on
pencil and paper knowledge and problem solving, we are not being fair to
students. Indeed, lessons should prepare students for, and resemble,
assessment. Students get (rightfully) frustrated if they have done and
understood the coursework, yet are not able to be successful in assessments.
Question: How should policymakers determine appropriate
levels of difficulty for math classes?
Hi David, your notion of hoping math class remains challenging really strikes me and I believe this is one of the major reasons that I have decided to devote to my study. Not only students dismay any challenges and difficulties in schools, but policymakers disgrace hard-working to a visible extent. Some students have started to proudly claim they are not math person and it really annoys me.
ReplyDeleteToday, kids are not being asked to memorize their multiplication tables because simply memorizing the table won't help math thinking. It is questionable that simply stop doing the boring stuff will increase math thinking automatically. Alternative strategies and approaches are often introduced to make learning less intense and more interesting, instead of focusing on increasing the efficiency of learning.
Thanks David! I agree that the intent of pedagogies chosen should prioritise learners' understanding, and not only learners' interest or 'entertainment' (while being aware that the latter does have an impact on the former on some occasions, and perhaps vice versa too).
ReplyDeleteI am also with you on not robbing students of the opportunity to work hard for quality and excellence, within reasonable grounds. In another class, we were reading about this concept called "flow" (Csikszentmihalyi) and I liked how it was explained. Flow exists when the challenge of the task and the skill level is balanced/well-matched. Teachers can choose to vary the challenge of the task or level up the skills in order for students to be in a state of flow, which presumably is optimal for student engagement and learning. Too much challenge/difficulty with inadequate skill can lead to student anxiety, while too little challenge/difficulty matched with a high level of skill can lead to boredom, and there are varying degrees in between. Although it largely tends to come down to a balancing act, this may be something policy-makers or teachers may want to consider when deciding on appropriate levels of difficulty/challenge to meet students' unique and diverse needs.