Although policy documents promote teaching students multiple strategies for solving mathematics problems, some practitioners and researchers argue that struggling learners will be confused and overwhelmed by this instructional practice. In the current exploratory study, we explore how 6 struggling students viewed the practice of learning multiple strategies at the end of a yearlong algebra course that emphasized this practice. Interviews with these students indicated that they preferred instruction with multiple strategies to their regular instruction, often noting that it reduced their confusion. We discuss directions for future research that emerged from this work.
Kathleen Lynch and Jon R. Star
Alice J. Gill
The NCTM's Curriculum and Evaluation Standards (1989) supports the idea that problems can be solved in more than one correct way. This multiple-strategy approach contains the seeds of motivation, success, and mind stretching. The curriculum standards that focus on reasoning and communication skills are integral to delivering mathematics education that generates the cre ative, problem-solving, divergent thinker that the business community would like to employ.
Margaret R. Meyer
When teachers give a problem like “Find 3/4 of 60,” they can anticipate the ways in which students will respond. It is easy to tell whether the student knows how to do the problem and whether she or he got the right answer. The mistakes that students might make on this problem are also predictable. Other problems found in traditional middle school curricula might produce more variety in solution strategies, but usually few surprises greet the experienced teacher. Few judgments need to be made, because the strategy is either appropriate or not; and barring computational errors, the answer is either right or wrong. This familiarity with the mathematics, the problems, and potential student responses produces a desirable level of comfort for teachers, even for those who are sometimes uncertain about their own mathematical skill and understanding. It leaves them free to focus on preparing students for the next skill to be learned and assisting those students who need extra help to become proficient. What happens when the curriculum, some of the mathematics, the problems, and the solution strategies all seem new and unpredictable? What does this situation mean for the teacher and for the students?
Arthur T. Benjamin and Jennifer J. Quinn
We fully concur with Richard Askey's February 2004 “Delving Deeper” column. Discovering and proving identities containing Fibonacci numbers can be satisfying for students and teachers alike. His article touched on multiple strategies including induction, linear algebra, and a hefty dose of algebraic manipulation to derive many interesting identities. However, a single method can be employed to explain all of these identities more concretely, leading to deeper understanding and intuition. We are referring to the method of combinatorial proof.
Margaret Biggerstaff, Barb Halloran and Carolyn Serrano
Authentic assessment aligned with the curriculum is changing expectations of students' work in mathematics. The move away from one right answer to multiple solutions and multiple strategies in mathematics problem solving requires a way to increase students' awareness about expectations and increase their competence. Students need to know the criteria that will be used to measure their mathematics problem-solving work. Equitable mathematics instruction includes ensuring that all students understand the purposes, standards, and processes of assessment.
diagrams to make comparisons, such as drawing number lines to show who ran further if Emma ran 7/6 kilometers and Jordan ran 5/4 kilometers? Were you encouraged to generate multiple strategies for computation, for example, showing two ways to solve 4 × 27
Patrice P. Waller and Alison S. Marzocchi
multiple strategies ( Kalman 2004 ; Lim et al. 2015 ). Our favorite solution may not be the favorite solution of our students. “Let's take a look at this solution and see if we can make sense of it.” The mysterious “they” Sometimes we catch ourselves
Theresa J. Grant and Mariana Levin
nontrivial. An assumption that underlies the teaching practice we describe is that one begins with a task for which students can generate multiple strategies. We would argue (as have others, e.g., Hiebert et al. 1996 ) that this is not solely a
Kari N. Jurgenson and Ashley R. Delaney
while they learned about parts of two- and three-dimensional shapes. Students modeled shapes in the real world by combining them in drawings and actual structures. Engaging in the EDP encouraged students to try multiple strategies for solving a real
S. Asli Özgün-Koca, Jennifer M. Lewis, and Thomas Edwards
would use. Figure 4 Babysitting Problem Other teachers commented that they really liked the problem because of its context and the potential for the use of multiple strategies. Another teacher suggested a revision to this problem: “Caitlin is