There are two primary instructional approaches for mathematics classes, constructivist and explicit/direct (Miller & Hudson, 2007). Direct instruction is the traditional, teacher centered approach. The teacher explicitly teaches students the math content through lecture. The student’s role is to listen, take notes, and use the information later. The instruction has a prescribed direction that guides the students’ “acquisition, retention, and generalizations of new knowledge” (Przychodzin, Marchand-Martella, Martella, & Azim, 2004, p. 57). Direct instruction has been found to be effective for some students with learning disabilities (Miller & Hudson, 2007). The constructivist approach has an emphasis on inquiry-based problem solving. The constructivist approach is student-centered and encourages students to explore and discover math by capitalizing on the students’ interests (Audet, 2005). Inquiry is a National Council of Teachers of Mathematics (NCTM) standards-based approach, where the teachers are a “guide on the side” (White-Clark, et al., 2008). Inquiry-based learning allows students to have more freedom in the problems they solve, which is something the students want in middle and high school (Posamentier & Jaye, 2006). Both of these approaches support the learning of students but use different strategies to get there.
Teachers who use a combination of direct and constructivist instruction, and use research-based instructional strategies to support the instructional approaches, have the best chance of raising math understanding and achievement. If teachers use research-based instructional strategies that promote inquiry in their classrooms along with direct instruction, students will have a better understanding of math. In math, it is very easy to lecture to students. Therefore, I wanted to look at incorporating more constructivist instructional strategies in the classroom. The constructivist research-based strategies that I want to look at are: using real world problem solving, technology, visual aids and manipulatives, and collaborative learning.
Real-world problems that have a multicultural connection to the students have been found to be valuable for students in math classrooms. Using real-world applications in math helps students become more interested in the subject and fosters inspiration (Bellamy & Mativo, 2010; Posamentier, Hartman, & Kaiser, 1998). Real-world problem solving is a purposeful learning strategy which has been shown to increase the grades of poor students in an urban school in San Diego County (Kitchen, 2007). By using real-world problems, students will be able to see that math is in every part of their lives. Utilizing technology as a means of enhancing the curriculum is also effective for students. Since technology is one of the principles of the NCTM standards, teachers should use technology in the classrooms to meet this standard (McKinney, Chappell, Berry, & Hickman, 2009). Since our country relies heavily on technology and students are very technologically advanced, using different types of technology in the classroom gives students a tool they can use to explore math. Using calculators, computers, programs, and other assistive technologies to help students learn more about the subject makes learning more interesting for the students and motivates them to learn more. In conjunction with real world problem solving, technology has been shown to assist in strengthening the math skills of students with in juvenile correction schools (Maccini, Gagnon, Mulcahy, & Leon, 2006).
Visual aids and manipulatives allow students to visualize what they are learning and have been shown to help students learn math. Visual aids and manipulatives in math bring the content out of the text and into something the students can understand. They assist students in seeing the main subject instead of being confused by all of the other distractions in the text. Using manipulatives/visual aids allows students to see what the problem is about. Teachers can use graphic organizers and flow charts so that students can quickly understand and remember the material (Posamentier, et al., 1998). Although using in class takes time, it is worth the time to increase the understanding and interest of the students (White-Clark, et al., 2008). Manipulatives/visual aids let students work hands-on with the material and understand the information better.
Collaborative learning allows students to work together in many ways. Students can perform many different problems and activities in pairs, small groups, or large groups. When students work together, they have to verbalize their thoughts. Therefore, collaborative learning leads to greater understanding by more people (Posamentier & Jaye, 2006). Students who are in collaborative learning groups score higher on test than those who are did not learn the material by collaborative learning (Reid, 1997 as cited in Slavin, Lake, & Groff, 2009).
Including collaborative learning activities into class instruction varies the instruction for the students and keeps them interested in the content (Posamentier, et al., 1998; Posamentier & Jaye, 2006). Teachers can help improve student performance by choosing strategies that enable students to do their best for the given topic. Implementing these instructional strategies in an effective way can improve the student interest and understanding of math. Mathematics is an important subject in which student achievement has not been to levels it should be, based on standardized test scores. Math teachers need to help increase understanding of math by using researched-based strategies, which support constructivist learning, along with direct instruction. Using strategies, like using real world problem solving, technology, visual aids and manipulatives, and collaborative learning, have been shown help students build more understanding in math, along with the more traditional method of direct instruction.
Math is a complex subject, so using research-based instructional strategies could help students understand the complexities better when used with direct instruction. By testing research-based constructivist strategies such as real-world problem solving, technology, visual aids and manipulatives, and collaborative learning, along with direct instruction, I want to find out which instructional strategies enhance the learning environment and what are the pros and cons of each strategy. Since teachers tend to use direct instruction, which do not seem to be helping student performance in math, testing these strategies will give me new, non-traditional ways to teach the students for understanding. Also, this will give me strategies that students enjoy rather than boring teacher talk.
The questions I want to answer through my research of each instructional strategy are:
1. Do the students enjoy the research-based constructivist instructional strategies?
2. What are the advantages of the constructivist strategies?
3. What are the obstacles to the constructivist strategies? How difficult are they to implement?
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