In this article, Boaler tells the story of a school in an underprivileged
area which has a forward thinking math department. The students demonstrate
strong increases in achievement and strong results on independently developed
forms of assessment, but still perform poorly on Standardized assessments.
Boaler outlines the damage that is done to students’ self esteem as they work
hard to achieve and feel like they have learned and understand, yet are still
told they are ‘below average’ on these high stakes assessments. If I had to
criticize the article, it would be that Boaler does not adequately describe the
practices the math department undertakes in order to increase students’
mathematical understanding. She non-specifically states that they observe each
other’s classes, meet regularly, and take part in professional development
opportunities, but I would have been interested in more specifics about their
teaching practices.
A stop for me in the article occurred when Boaler that students
might perform poorly on standardized assessments as they are set in contexts
that are confusing to linguistic-minority and low-income students. She gives an
example of the following question:
A cable crew had 120 feet of cable left on a 1,000 foot spool
after wiring 4 identical new homes. If the spool was full before the homes were
wired, which equation could be used to find the length of cable (x) used in
each home?
F. 4x + 120 = 1000
G. 4x - 120 = 1000
H. 4x = 1000
J. 4x - 1 000 = 120
This brought to mind the only high stakes provincial testing
we still have in BC – the Math 10 Provincial exam. All Grade 10 students write
a provincial math exam, but they are divided into one of two groups based on course
they are enrolled in – the Foundations/Pre-Calculus (FPC) class exam focuses
more on algebraic skills, and the exam reflects this. Alternately, the
Apprenticeship/Workplace (AW) exam, which usually attracts students who are
more challenged in math, features mostly extremely ‘wordy’ problems similar to
the one above. In my experience, students in the FPC course generally score
close to their term marks, but the majority of students fail the AW exam. I
believe the intention of the writers of the exam is that the math will make
more sense to students if it is put into context, but there is a disconnect and
students find reading the long problems challenging, and often don’t know how
to apply the math to the problem, even if they understand the mathematical concept.
Question: How can we put math concepts into meaningful concepts without overwhelming students with language and concepts they might not be familiar with (like spools and cable in the question above)
Thanks for sharing, David! I was also curious to know more about how the teachers had helped enhance students' mathematical understanding; and how different the school-designed tests were from the standardised tests, beyond the broad differences that were outlined. There may be good learning here!
ReplyDeleteA stop for me in this article was the usage of real life contexts, which educators are so often encouraged to use in teaching so as to enhance student understanding of mathematical concepts as they make links with prior knowledge that they may be able to relate to or make meaning from. However, the distinction of using it as a pedagogy, as opposed to part of an assessment is made stark for me here, particularly if the assessment comes in the form of standardised examinations administered to a culturally and socially heterogeneous and diverse student population, possibly leading to inequalities/biases.
This forced me to stop and think again about what competencies mathematics educators are trying to assess - for example, (i) whether the demonstration of the understanding of mathematical principles and procedures is key; or (ii) whether the application of appropriate mathematics competencies and their accurate execution when placed in authentic real life situations is key. The purpose of the assessment would undoubtedly have an integral role to play in determining the positioning, language, complexity (specificity of details) of the questions assessed. And once again, there is also the question of the appropriate mode of questioning - we see here how the options made available in multiple choice questions may limit the thinking and approach to solutions, as the answer options may be presented in a form that espouses a few selected ways of solving the problem that may attain in the shortest possible time (essential for examinations) the form of the answer displayed by the options provided.
There's great beauty and power to math, as we have witnessed in our last few sessions. I’m grateful for the opportunity but at the same time, I regret that its beauty and power are rarely apparent in school classrooms, at least in the early years when a student is most likely to get hooked. And David, I totally agree with you that making sense of math to students rather than handing out marks in multiple-choice exams is a great privilege and responsibility of teachers as well. With more ELL students coming to BC, we can anticipate more problems linked to language incompetency (“spool” would be a good example). Many lessons in existing curricula are designed for native speakers (but not all) and do not support ELL.
ReplyDelete