In Greer, Verschaffel & De Corte’s (2000) investigation into students’ and teachers’ beliefs about word problems, they deliberate the nature of mathematics traditionally, and how beliefs about word problems are shaped by classroom culture and broader contexts such as institutional beliefs and values and societal contexts.
Greer et al. (2000) critique the complacent nature of mathematics education, where few have questioned the role of word problems. One main purpose suggested by Greer et al. (2000) depicts word problems as a representation of application of mathematics to physical and social phenomena (p. 272). The second purpose is as vehicles for reasoning about mathematics structures, these scenarios are imaginable and not often realistic (p.272).
The authors emphasize mathematical modeling, which includes translation situations into mathematical relationships, manipulating relationships to give derivations, and interpretations of such derivations within the context give (p. 273).
Greer et al. (2000) explain that students’ beliefs of word problems are influenced from their perceptions and interpretations of socio-mathemaical norms. Normative practices such as how to behave in a mathematics classroom, that there must be a single, correct, and precise numerical answer are some examples. Many of these practices create harmful assumptions on mathematics problems, inhibiting critical attitudes and perpetuating passive attitudes towards pedagogy.
The authors ask students and teachers some questions that are “problematic”, where the application of judgement based on real-world knowledge and assumptions was required rather than the traditional artithemetical operations (p. 275). Additionally, Greer et al. (2000) enact an intervention study to determine the effects of non-normative mathematical practices to alter students’ perceptions of mathematics word problems. The underlying belief shared by students and teachers alike as that realistic considerations should not complicate the “real” mathematics (p. 278). That is, any conflicts between real-life understandings should be disregarded when dealing with mathematics word problems.
Stop #1
Quotation: Nevertheless, we are concerned about the apparent lack of sensitivity to the complexity of the mathematization of situations described in word problems amond the majority of the (future) teachers, and we recommend that more attention should be given to this fundamental topic in teacher training.
Explanation: While I agree with the concern about being more conscious of the assumptions we imply through our choices of mathematical word problems, I find the quote somewhat unfair. As a novice teacher, I face many tensions: maintaining a position at a new school, upholding institutional expectations, meeting the demands of stakeholders, and ensuring the overall success of our students. Greer et al. (2000) note that there has been little questioning of the significance and role of word problems. As pedagogy evolves to become more “realistic,” educators must critically examine the epistemology of word problems and their role in teaching. This brings to mind the fishbowl metaphor. For pre-service teachers, we often live in a fishbowl, consciously or not, shaped by pre-existing conceptions of what it means to implement the curriculum and our responsibilities regarding the “invisible curriculum.” Questioning the integrity of word problems—something I grew up accepting without question—feels daunting. This is why I agree that more attention should be given to these issues in teacher training.
Given my position as a novice teacher, the easiest path often seems to be accepting any given resources and working toward identifying problematic practices once I’ve secured my position. I wonder if this is why the more experienced teachers in Greer et al.'s (2000) study gave more “realistic” responses to the “problematic” questions. The statement about a “lack of sensitivity” disregards the broader power dynamics and the intersections of identity and context that influence teachers’ ability to “be sensitive.”
Question: How can educators navigate the power dynamics within the classroom while being more sensitive to the ways in which mathematization may unintentionally reinforce societal biases, and what strategies can be employed to ensure that mathematical practices are inclusive and reflective of diverse student experiences and identities?
Stop #2
Quotation: Teaches and students do not operate in isolation, and their beliefs are shaped by both the immediate and wider instructional environments in which they work.
Explanation: Greer et al. (2000) acknowledge that classroom culture and broader contexts influence the beliefs of both teachers and students. However, they also recognize that their research did not fully consider the impact of gender, race, and culture on these beliefs. They predict that cultural beliefs would strongly shape responses to word problems (p. 287). This is particularly interesting because their study, which focuses on teacher and student responses, should logically be influenced by the cultural beliefs, gender, and race of the participants. Yet, despite this, Greer et al. (2000) choose not to address these factors, potentially skewing their conclusions. By overlooking these crucial aspects, they seem to bypass the very complexities they acknowledge. It feels presumptuous to make definitive conclusions without considering the real influence of intersecting identities and the socio-political climate on participants' responses.
I understand that in 2000, intersectionality, critical race theory, and anti-racist pedagogy were just beginning to take root. As such, it is understandable that Greer et al. (2000) did not integrate these frameworks into their research. However, if we are to seriously consider the impact of instruction and assessment, it is imperative to evaluate the intersection of social inequities and aspects of identity.
Question: How might Greer et al. (2000) have approached their study differently if they had considered the intersection of gender, race, and culture in shaping responses to word problems, and what implications does this have for current research in education?
Do you think the conclusions of Greer et al. (2000) have changed if they had accounted for the intersectionality of gender, race, and culture in their study, how so, and what does this suggest about the importance of integrating these factors in educational research today?
Thank you Anna for the summary and reflections. Classroom power dynamics can be controlled by having students ask questions regarding word problems and reflect on real-world uses. Cross-cultural references and everyday life render mathematics more meaningful. It is important to examine if word problems have hidden assumptions and adjust them for fair for all the students. Teachers should be trained to identify and correct these issues and fix it. By creating a class where children feel that they matter and they can contribute by sharing, teachers make math participative and inclusive. Through this, they ensure that mathematics is not all about numbers, but it becomes the way through which they understand more about things surrounding them.
ReplyDeleteThe aspects such as gender, race, and culture defines the way teachers and learners understand and solve word problems. Ignoring them could have led to reduced conclusions that did not account for multi-faceted considerations. If such aspects were involved in the learning, the study could have illustrated the effect of cultural heritage on problem-solving approaches and communication in class. With this integration, more real, representative results are obtained to guide instructors on creating inclusive classrooms for all students.
Anna, well done for the work done; it's so thought-provoking of you. This issue of power dynamics is an important topic that must be considered. As a teacher, my strategy for handling power dynamics in the classroom is to create an inclusive and safe space where every student feels comfortable and is a co-stakeholder in the class. I won't allow any student to dominate the class teaching and learning activities as each student will take turns answering questions in the class. I will intentionally give pep talks in the class emphasizing the need for students to value and love one another and accommodate each other. I have to be very vigilant and create opportunities for students to work together. Lastly, I will use teaching styles that can cater to the types of learners in the classroom.
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