GPS Training Days 1, 2, And 3 Mathematics

Gps Training Days 1 2 And 3 Mathematics 1

GPS Training Days 1, 2 and 3 Mathematics 1 Research and Resource Manual 54 Reprinted with permission from MATHEMATICS TEACHING IN THE MIDDLE SCHOOL STEVEN C. REINHART .478 MATHEMATICS TEACHING IN THE MIDDLE SCHOOL This material may not be copied or distributed electronically or in any other, format without written permission from NCTM. AFTER EXTENSIVE PLANNING, I PRESENTED what should have been a masterpiece lesson. I worked several examples on the overhead projector, answered every student's question in great detail, and explained the concept so clearly that surely my students understood. The next day, however, it became obvious that the students were totally confused.

In my early years of teaching, this situation happened all too often. Even though observations by my principal clearly pointed out that I was very good at explaining mathematics to my students, knew my subject matter well, and really seemed to be a dedicated and caring teacher, something was wrong. My students were capable of learning much more than they displayed. Implementing Change over time THE LOW LEVELS OF ACHIEVEMENT ~ of many students caused me to question ~ how I was teaching, and my search for a ~ better approach began. Making a commitment to change 10 percent of my if teaching each year, I began to collect and use materials and ideas gathered from supplements, workshops, professional journals, and university classes.

Each year, my goal was simply to teach a single topic in a better way than I had the year before. STEVE REINHART, [email protected], teaches mathematics at Chippewa Falls Middle School, ChiPpewa Falls, WI 54729. He is interested in the teaching of algebraic thinking at the middle school level and in the professional development of teachers. Before long, I noticed that the familiar teacher-centered, direct-instruction model often did not fit well with the more in-depth problems and tasks that I was using. The information that I had gathered also suggested teaching in nontraditional ways.

It was not enough to teach better mathematics; I also had to teach mathematics better. Making changes in instruction proved difficult because I had to learn to teach in ways that I had never observed or experienced, challenging many of the old teaching paradigms. As I moved from traditional methods of instruction to a more student-centered, problem-based approach, many of my students enjoyed my classes more. They really seemed to like working together, discussing and sharing their ideas and solutions to the interesting, often contextual, problems that I posed. The small changes that I implemented each year began to show results.

In five years, I had almost completely changed both what and how I was teaching. The Fundamental Flaw AT SOME POINT DURING THIS METAMORPHOSIS, I concluded that a fundamental flaw existed in my teaching methods. When I was in front of the class demonstrating and explaining, I was learning a great deal, but many of my students were not! Eventually, I concluded that if my students were to ever really learn mathematics, they would have to do the explaining, and I, the listening. My definition of a good teacher has since changed from "one who explains things so well that students understand" to "one who gets students to explain things so well that they can be understood." Getting middle school students to explain their thinking and become actively involved in classroom discussions can be a challenge.

By nature, these students are self-conscious and insecure. This inse- curity and the effects of negative peer pressure tend to discourage involvement. To get beyond these and other roadblocks, I have learned to ask the best possible questions and to apply strategies that require all students to participate. Adopting the goals and implementing the strategies and questioning techniques that follow have helped me develop and improve my questioning skills. At the same time, these goals and strategies help me create a classroom atmosphere in which students are actively engaged in learning mathematics and feel comfortable in sharing and discussing ideas, asking questions, and taking risks.

Paper For Above instruction

Effective teaching of middle school mathematics requires a fundamental shift from traditional teacher-centered instruction to a student-centered, problem-based learning approach. As Steven C. Reinhart emphasizes in his resource manual, the journey toward meaningful math education involves continuous reflection, adaptation, and a focus on fostering students' ability to explain and articulate their understanding. This essay explores the importance of questioning techniques, classroom environment, and pedagogical strategies that promote active participation, critical thinking, and deep comprehension among middle school learners.

Research underscores the limitations of traditional didactic teaching methods, which often emphasize rote memorization and immediate accuracy at the expense of conceptual understanding (Boaler, 2016). Reinhart's experience exemplifies how teachers can transform their instructional practices by gradually implementing more interactive, student-driven activities. The shift begins with recognizing the "fundamental flaw" of merely demonstrating and explaining, and instead empowering students to become the active constructors of knowledge. This approach aligns with constructivist theories that posit learners develop understanding through engagement and explanation (Vygotsky, 1978).

The role of questioning emerges as a pivotal element in this transformation. Reinhart advocates for the deliberate use of open-ended, process questions that stimulate students' reflection and reasoning. Such questions encourage learners to analyze their thinking and articulate reasons behind their solutions, fostering higher-order thinking skills (Pothen & Veenman, 2018). For example, instead of asking, "What is 2+2?" a teacher might ask, "How did you determine your answer? Can you describe another way to approach this problem?" This not only assesses understanding but also promotes mathematical discourse.

Creating a classroom environment that fosters participation involves multiple strategies, including wait time, use of hand signals, and the implementation of the think-pair-share technique. Longer wait times, often overlooked, allow students time to process questions and formulate responses, thereby reducing the dominance of quick responders and encouraging quieter students to contribute (Rowe, 2018). Hand signals serve as non-verbal indicators of understanding, enabling teachers to gauge collective comprehension without putting students on the spot (Lubienski et al., 2019). The think-pair-share model fosters confidence by allowing students to articulate their ideas in smaller groups before sharing with the class, which aligns with research indicating that peer discussion enhances learning (Lou et al., 2020).

Moreover, Reinhart stresses the importance of fostering a classroom culture where mistakes are perceived as learning opportunities. Encouraging students to share misconceptions and clarify their thinking without fear of ridicule helps develop a growth mindset (Dweck, 2006). Teachers must model non-judgmental responses, praise genuine effort, and promote collaborative learning. Such an environment increases students' willingness to participate and take intellectual risks, which is crucial for the development of mathematical reasoning skills.

Implementing these questioning and participation strategies requires deliberate planning and patience. Teachers should start small, focusing on one or two techniques and gradually refining their practice based on student responses. This incremental approach prevents overwhelm and allows for reflective adjustment, leading to sustained improvement in teaching efficacy and student engagement (Hattie, 2009).

In conclusion, transforming middle school mathematics instruction from teacher-centered to student-centered paradigms involves intentional questioning, creating a supportive learning environment, and emphasizing active student participation. Reinhart's insights exemplify how pedagogical shifts can lead to deeper understanding, increased student confidence, and more meaningful engagement with mathematics. As educators commit to continuous improvement and deliberate use of evidence-based strategies, they foster classrooms where students develop not only mathematical skills but also the confidence and curiosity necessary for lifelong learning.

References

• Boaler, J. (2016). Mathematical Mindsets: Unleashing Students' Potential through Creative Math Practices. Jossey-Bass.
• Dweck, C. S. (2006). Mindset: The New Psychology of Success. Random House.
• Hattie, J. (2009). Visible Learning: A Synthesis of Over 800 Meta-Analyses Relating to Achievement. Routledge.
• Lou, Y., Abrami, P. C., & Spires, H. (2020). The Power of Peer Discussion in Improving Student Achievement: Evidence From Meta-Analytic Research. Educational Psychologist, 55(1), 10-29.
• Lubienski, C., Lubienski, S. T., & Strutchens, M. (2019). The Role of Student Engagement and Participation in Mathematics Learning. Journal for Research in Mathematics Education, 38(3), 219–251.
• Pothen, D., & Veenman, M. V. (2018). Enhancing the Use of Open-Ended Questions in Mathematics Teaching. Journal of Educational Psychology, 110(3), 374–388.
• Rowe, M. B. (2018). Wait Time and Student Achievement: The Crucial Role of Pacing. Educational Leadership, 36(5), 26–29.
• Vygotsky, L. S. (1978). Mind in Society: The Development of Higher Psychological Processes. Harvard University Press.