Source: Journal of Mathematics Teacher Education, Volume 18, Issue 1, February 2015, p. 79-99.
(Reviewed by the Portal Team)
In this study, the researchers chose to explore the kinds of questions prospective teachers plan when utilizing literature in mathematics lessons to scaffold children’s understanding of the mathematics concepts presented through the text.
The study took place in an initial teaching certification program at a private university in the central United States.
The participants were fourteen elementary prospective teachers, who enrolled in one section of a junior-level field-based practicum course and were assigned to an elementary professional development school (PDS) for the experience.
All prospective teachers were required to incorporate children’s literature within the mathematics lessons they planned and presented during a field-based teaching experience.
They were expected to write questions on their mathematics lesson plans that they intended to ask students throughout the lesson.
Data were collected through observations; daily meetings with the prospective teachers to provide pedagogical instruction, support, and feedback relative to their teaching and assignments; and lessons plans prepared by the participants.
Results revealed that some of the prospective teachers possessed a limited recognition of or ability to incorporate questioning when planning lessons.
Furthermore, the results presented a need to analyze the planned questions based upon their dependency and utilization of said literature.
While some of the prospective teachers planned multiple questions at varied levels in a manner designed to forge and strengthen the relationship between the mathematics in the text and the mathematics in the students’ lives, others failed to plan even one text-dependent question within their lesson.
An examination of the content focus of questions revealed that a majority of the total planned questions were focused on mathematics.
However, the prospective teachers planned, wrote, and submitted questions that lacked clarity, were limited in mathematical connectivity, or included incorrect mathematical concepts.
An additional concern was the number of yes/no questions planned by the prospective teachers.
Yes/no questions represent a specific type of closed, convergent question that should be avoided because they can promote guessing and have low diagnostic power.
When yes/no questions are utilized, the teacher is unable to determine when or if a student response is a guess, a correct response with or without understanding, or an incorrect response with limited or no understanding.
The participants involved in the study planned approximately one out of every four questions in a manner that encouraged their elementary students to think mathematically, thereby allowing the prospective teachers to explore students’ thought processes during their construction of mathematical understanding.
Furthermore, data revealed that when utilizing the approach of literature integration in mathematics, the prospective teachers involved in the study went against the aforementioned trend. Also indicated within the presented data was that although closed convergent procedural questions did represent the highest number and the highest percentage of mathematics-focused questions, there was only a one question difference between this category and the closed convergent conceptually-based question category.
Based upon the results of this study, there are implications and recommendations for both classroom teachers and teacher educators alike to consider when making determinations relative to the mathematics classroom, course, and field experience. Although all the prospective teachers in this study were novices, they revealed a great deal of variance in their incorporation of questions within lessons integrating literature in mathematics.
The authors argue that when prospective teachers are involved in field-based experiences, it is important that teacher educators also consider the existence of possible external forces when developing, assessing, and evaluating assignments directly linked to those field experiences. When examining the written lesson plans for the types of questions prospective teachers were planning to pose when integrating literature within their mathematics lesson, it was surprising that prospective teachers planned a higher percentage of text-independent than text-dependent questions.
Additionally, some prospective teachers’ utilized didactic texts while others utilized narratives. In their initial attempt to apply the approach of literature integration in mathematics and to utilize questions designed to scaffold students’ understanding of the mathematics concepts presented through the text, the prospective teacher participants revealed that their attempts represented developing approximations of their abilities to both understand and to apply that understanding. Hence, teacher educators must recognize that prospective teachers’ attempts to implement instructional approaches are developing approximations, and without the provision of multiple opportunities and specific feedback, those approximations will never progress beyond the initial phase.
Furthermore, an examination of the numerous planned yes/no questions revealed that many of these questions could be easily modified so as to move the question from the closed convergent category to the open divergent category. Within all content pedagogy coursework, prospective teachers should be exposed to information related to the closed nature of yes/no questions, the inability of yes/no questions to assess student understanding, and the practice of revising yes/no questions to the creation of open divergent questions.
Additionally, prospective teachers at the elementary level must participate in mathematics content courses where their mathematics misconceptions and limited conceptions can be identified and addressed. Furthermore, within mathematics methods courses, prospective teachers must be introduced to the nature and impacts of mathematics misconceptions on student learning and understanding. They must then acquire the skills and abilities required in identifying and reconceptualizing those misconceptions.