In “ASSESSING
UNDERSTANDING IN MATHEMATICS: STEPS TOWARDS AN
OPERATIVE
MODEL”, Romero and Mari use an interesting example of a multiplication algorithm to demonstrate the complexity of diagnosis and assessment of
understanding in mathematics for middle to high school students. By gathering explanations
and interviews on the students’ work, a “multi-faceted assessment strategy” is
proposed featuring the use of different tasks with an intention to obtain
indicators of students’ understanding of particular mathematics aspects.
The authors assert that “to achieve
this, it is important to make the learner feel involved in the situation, so it
is convenient for the situations to be specific, simple to understand, without
distracting elements and with controlled answers.” One challenge is always to get students “involved”
in the assessment procedure when the assessment is too general or too specific.
More studies need to be put into the dimensions and scope of such assessment.
The study provides three categories of assessment when
studying student’s use of algorithms and I find the Analytical category to be very innovative. According to the authors,
it includes situations that require a reflexive use of the
algorithm to lead to a solution rather than simply applying the knowledge. It requires
an intentional analysis of the “External structure” as explained in the example of “The
product of two consecutive natural numbers is 132. Find them.” This question is used as an analytical assessment of students' understanding of the algorithm, which goes beyond memorization from the original
procedure (it is more like a reversed or decomposed procedure that the student is required to reconstruct), and makes it possible
to identify analytical understating.
Question: Are there other ways to assess analytical understanding of math?
Question: Are there other ways to assess analytical understanding of math?
Thanks for sharing your thoughts. Although I found the gathering of explanations and interviews on the students’ work an interesting method to adopt, I found the article and the multi-faceted assessment strategy that the authors proposed a tad more theoretical and hence challenging to apply. I do note that the authors have indicated at the end of the article, about the need to verify the operativity of the model, and to develop systematic proposals to effectively include the current information obtained in regular curricular design, and understand that the purpose of the article could be limited to planting their idea for others to sow the seed thereafter.
ReplyDeleteNonetheless, perhaps greater elaboration on their ways of thinking that led to their proposal, with more applied examples, may help the reader's understanding. There seems to be some gap where readers are left to fill in the blanks ourselves. For example, in the distinction between exclusive and non-exclusive situations that was made towards the end of the article, the latter was defined as "situations which can be solved in different ways, one of which includes using the algorithm". The authors then suggest that "the student must first identify the situation as appropriate for being solved with the algorithm and then decide to use this method of calculation, instead of other alternatives of mathematical knowledge". As an educator, a question I had in response was, "How would one know when the question falls into which of the two situations? Are there any conditions or criteria that guide one to make that judgement?" It may have helped if the authors could have shared more on their thinking behind this categorisation, because the ability to make this judgement seems to assume a prior understanding of broad knowledge.
I think it's important to vary our assessment in mathematics. Students can present their understanding in quizzes/tests/assignments, but it's also nice to find ways to assess their understanding by encouraging them to explain notions to the class, describe their methods, ask them to demonstrate two ways to solve problems, find errors in other peoples' work and so on. As educators, we do this frequently in other subjects (such as languages, sciences etc.) Most educators (myself included) could likely challenge themselves to incorporate this into lessons and assessments more frequently.
ReplyDeleteI think it's important to vary our assessment in mathematics. Students can present their understanding in quizzes/tests/assignments, but it's also nice to find ways to assess their understanding by encouraging them to explain notions to the class, describe their methods, ask them to demonstrate two ways to solve problems, find errors in other peoples' work and so on. As educators, we do this frequently in other subjects (such as languages, sciences etc.) Most educators (myself included) could likely challenge themselves to incorporate this into lessons and assessments more frequently.
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