I was struck by some of the points mentioned in Suurtamm (et al) article regarding large-scale assessment. The authors did well to illustrate how large-scale assessments, such as the EQAO Grade 9 mathematics assessment, may ironically conflict and contradict the tenants of reform-oriented curriculum they were originally designed to support.
Reform-oriented mathematics encourage learners to develop a deeper understanding of mathematics and promote “problem solving approaches to teaching mathematics” rather than memorizing procedural knowledge (p. 32). Using the content strands and the achievement chart (process) categories from Ontario’s Grade 9 math curriculum, the EQAO assessment divides each of the multiple choice items (questions) and short answer items into one content strand and one process category. The extended response tasks, on the other hand, are filtered (or “mapped”) into 1-2 content strands. These tasks, which are designed to promote and demonstrate critical thinking, are broken down into scaffolded questions in order to cover all process categories (knowledge, application, problem solving and communication). Once this is accomplished, all EQAO assessment items are then paired with the specific curriculum expectation(s) from the Ontario Ministry documents.
As the authors have pointed out, the structure for developing the Grade 9 EQAO assessment does not maintain the integrity of reform mathematics. By breaking down extended response tasks into smaller, scaffolded questions, the authors argue that the EQAO assessment “artificially isolates the processes” and once again, “problems are presented as a series of smaller steps”. Ironically, the EQAO assessment seems to value procedural knowledge and certain algorithms of problem solving. Also, the authors also note that assigning EQAO items with process categories can be extremely ambiguous and subjective as these categories are “neither easily separated, distinct, nor distinguishable” (p. 38). This lead to several inconsistencies and once again, EQAO assessment structures imply that these process components can be compartmentalized and segregated into mathematical tasks. Suurtamm et al. also attack the Grade 9 Ontario mathematics curriculum stating that it “gives no clear indication of the important ideas that should be focused on and hence assessed” (p. 41). Ultimately, a curriculum that perpetuates an “insufficient degree of specificity” leaves large-scale assessment incomplete.
After reading this article, I couldn’t help but wonder what exactly is so wrong about problem-solving tasks being broken up and scaffolded into smaller questions. Although reform-oriented mathematics education seeks to de-emphasize procedural knowledge, we certainly cannot dismiss it entirely. (After all, we’re still using “process” categories to measure and map assessment items that seek to shift attention away from procedural tasks – hmm). Considering elements of universal design, I think all students, regardless of mathematics ability, can benefit from scaffolded questions (like those found on the EQAO assessment) during problem solving tasks. Of course, many students may have different methods to solve a task and scaffolded questions may be somewhat limiting, but I don’t think this format would completely discourage a learner’s thought process. If we want to engage students into thinking in “multiple” ways and through different mediums, then perhaps we can consider these scaffolded questions as an example of “a way of thought”.
To add more complexity, I thought there was (dare I say it) a potential paradox with the arguments that the author(s) brought. Suurtamm et al. pointed out the lack of specificity with the curriculum but at the same time, they also value the broad and interconnected strands of mathematical problem solving and inquiry. If we are to ‘authentically’ promote the notion of interconnected-ness in mathematics, then can we have a curriculum that communicates a high degree of specificity in terms of individual expectations? A curriculum that is highly specified may also come across to many educators & stakeholders as being prescriptive and narrowing as well. Also, with the subjectivities that the authors pointed out in their article, I would also wonder who exactly gets to design and choose expectations for a focused curriculum? Again, I feel like we are walking in circles.
Hi Praboda,
ReplyDeleteYou made an interesting reference to a statement and so did Devika in her response to yours regarding the problematization of use of multi-step questions instead of the usage of open ended questions in the article by Suurtaam. I feel that the emphasis in the article is on oversimplification via the way of step wise approach to a particular problem and thereby, depriving students of critical thinking skills. On the other hand I agree with you both in the sense that scaffolding does ensure better student understanding in the initial process of concept attainment. However, the reason why majority of the teachers waiver from including open-ended problems in the beginning of teaching a new concept is not because it hinders understand but because of the difficulty associated in facilitating a class dealing with rich open-ended questions. I feel that open ended questions often leave students guessing and confused, forcing them to wonder about the problem and as teachers it is a difficult task for us to sit back and let them make their own associations and create their own understanding. I am sure an effective facilitator would be able to be a good guide by providing “leading questions” to ensure that students are not completely off-track- a good practice during preparation for EQAO tests. Thus, even though I agree with you as well as Devika with respect to scaffolding as the way to go for differentiating instruction and enhancing students’ procedural learning and understanding, I do agree with Suurtaam with that the over-emphasis on procedural learning can deprive students from being able to apply concepts in different scenarios and misunderstand the association of procedure and concept as being static rather variable and contextualized. With focus on math learning especially, students are majorly deprived from open ended questions that integrate several strands or units due to the emphasis on procedural learning. With reference to integration I do agree that our curriculum provides suggestions for combining various subject areas. I do however, see that being hindered through the administration of standardized tests which usually segment the subject areas and concepts. If the purpose solely becomes to teach to the test then the test would have to ensure integration as well as components of scaffolding as well as open-endedness to ensure student success.
Scaffolding to start, open-ended to end?
ReplyDelete"If we want to engage students into thinking in “multiple” ways and through different mediums, then perhaps we can consider these scaffolded questions as an example of “a way of thought”."
I agree with your comments about scaffolding and its benefits according to Universal Design. Scaffolding has definitely been promoted as a useful teaching tool and a good way for students to have a task "chunked" into manageable pieces, especially when they first start learning. I'm still having trouble getting my mind around students diving right into a math problem without any guidance whatsoever, which sometimes seems to be the recommendation of reform mathematics. I could imagine having the question about which bowlerama William and his friend should go to (given in the Suurtamm (2008) article on p.38) being scaffolded as much as it is shown to be at the beginning stages of learning how to problem solve. Perhaps the recommendation, then, is for this problem to be open-ended and holistically assessed because this test comes at the end of the grade 9 course.
Like Vivien said, I think a big problem with open-ended questions is that teachers sometimes have a hard time letting their students start something without first giving them a lot of guidance. However, I think that struggling with material is very useful, in math and in other fields. Sometimes, when teachers provide a lot of scaffolding, they are limiting students' opportunities to figure out how to start questions on their own. I think this is the problem that Suurtamm et al had with the step-by-step methods of the EQAO questions. The real trick, I guess, is knowing when a student needs to struggle with something and knowing when they really need that scaffolding.
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