Building Middle-Level Mathematics Teachers\u27 Capacities as Teachers and Leaders: The Math in the Middle Institute Partnership

This article describes professional development for middle-level mathematics teachers offered through the Math in the Middle Institute Partnership, a National Science Foundation-funded project to build teachers’ capacities to improve mathematics learning for all students. An overview of the project, including descriptions of its goals and curriculum are provided. Detailed descriptions of two mathematics courses and one pedagogy course are offered. The mathematics courses included here are the introductory course to the Math in the Middle Institute, as well as one of the final math courses of the Institute in which participants apply mathematical knowledge and processes to real-world problems. The pedagogy course features curriculum that enables teachers to acquire an understanding of the nature and purpose of action research, and launches teachers into planning and implementing systematic inquiry in their own mathematics classrooms around topics of their choosing. The varied abilities of teachers, as well as growth in teachers’ mathematical and pedagogical capacities, are represented by several samples of student work provided within the article. In addition, mathematical and pedagogical products of student work are also provided through the project’s URL links. Improving teacher quality is identified as a national need in mathematics education and one many universities and schools across the country are working in partnership to try to address. This article describes a professional development project aimed at improving mathematics teaching and learning in the middle grades. An overview of the project, along with a close look at several of its course offerings, are presented highlighting mathematical and pedagogical goals, challenges, and accomplishments

Coming Out of the Dungeon: Mathematics and Role-Playing Games

After hiding it for many years, I have a confession to make. Throughout middle school and high school my friends and I would gather almost every weekend, spending hours using numbers, probability, and optimization to build models that we could use to simulate almost anything. That’s right. My big secret is simple. I was a high school mathematical modeler. Of course, our weekend mathematical models didn’t bear any direct relationship to the models we explored in our mathematics and science classes. You would probably not even recognize our regular gatherings as mathematical exercises. If you looked into the room, you’d see a group of us gathered around a table, scribbling on sheets of paper, rolling dice, eating pizza, and talking about dragons, magical spells, and sword fighting. So while I claim we were engaged in mathematical modeling, I suspect that very few math classes built models like ours. After all, how many math teachers have constructed or had their students construct a mathematical representation of a dragon, a magical spell, or a swordfight? And yet, our role-playing games (RPGs) were very much mathematical models of reality — certainly not the reality of our everyday experience, but a reality nonetheless, one intended to simulate a particular kind of world. Most often for us this was the medieval, high-fantasy world of Dungeons & Dragons (D&D), but we also played games with science fiction or modern-day espionage settings. We learned a lot about math, mythology, medieval history, teamwork, storytelling, and imagination in the process. And, when existing games were inadequate vehicles for our imagination, we modified them or created new ones. In doing so, we learned even more about math. Now that I am a mathematics professor, I find myself reflecting on those days as a “fantasy modeler” and considering various questions. What is the relationship between my two interests of fantasy games and mathematics? Does having been a gamer make me a better mathematician or modeler? Does my mathematical experience make me a better gamer? These different aspects of my life may seem mostly unconnected; indeed, the “nerd” stereotype is associated with both activities, but despite public perception, the community of role-players includes many people who are not scientifically-minded. So we cannot say that role-players like math, or math-lovers role-play, because “that is simply what nerds do.” To get at the deeper question of how mathematics and role-playing are related, we first need to look at the processes of gaming, game designing, and modeling

Examining Middle School Students\u27 Methods Of Justification

Researching students’ thinking is imperative to improving the education system throughout the world. From extensive research, it is noted that students are unaccustomed and struggle with providing valid mathematical justifications (e.g. Inglis & Alcock 2012). The National Council of Teachers of Mathematics (NCTM, 2000) and Common Core State Standards of Mathematics (CCSSM, 2010) suggest that students should have several opportunities to construct mathematical arguments across all grade levels. To take a closer look at this educational phenomenon, we prompt fifth to eighth-grade students with nine mathematical tasks. Within our research, we focus on tasks based on number properties, algebraic thinking, and geometric thinking. Furthermore, our research examines students’ methods of justifications as well as the mathematical quality of the justifications. Overall, the research demonstrates that most students’ justifications are not mathematically complete. This research is of high value to educators, parents, school administrators, and students throughout the world as it provides a more beneficial method of student learning. Educational research is highly important as the future of the world lies within our classrooms today.https://ir.library.illinoisstate.edu/urs2021mat/1002/thumbnail.jp

Mathematical Literacy: A Case Study on Padang Students' Mathematical Ability

This study aims to analyze student mathematical literacy ability from the perspective of students' Mathematical Ability. This research is a descriptive study with a qualitative approach. The research subjects were three students of XI IPA 1 MAN 1 Padang with different mathematical abilities: low, medium, and high. Data were collected through documentation, tests, and interviews. The results of the analysis show that students with high abilities can solve routine problems, interpret problems and solve them with formulas, carry out procedures well, can deal with complex situations, use their reasoning in solving problems, can work effectively and interpret different representations and then relate them to the real world. Students with moderate abilities can solve routine problems, interpret problems and solve them with formulas, and carry out procedures properly. Meanwhile, students with low abilities are only able to solve routine questions. Based on these results, it is necessary to look for strategies in the mathematics learning process, which enable the improvement of students' mathematical literacy skills

Prediction and production of simple mathematical equations

An important issue in current psycholinguistics is the relationship between the production and comprehension systems. It has been argued that these systems are tightly linked, and that, in particular, listeners use the speech production system to predict upcoming content. We tested this view using a novel version of the visual world paradigm. Participants heard mathematical equations and looked at a clock face showing the numbers 1 to 12. On alternating trials they either heard a complete equation (3+8=11) or they heard the first part (3+8) and had to produce the solution (11, target hereafter) themselves. Participants were encouraged to look at the relevant numbers throughout the trial. On listening trials, the participants typically looked at the target before the onset of target name, and on speaking trials they typically looked at the target before naming it. However, the timing of the looks to the targets was slightly different, with participants looking earlier at the target when they had to speak themselves than when they listened. This suggests that predicting during listening and planning to speak are indeed very similar but not identical. The further methodological and theoretical consequences of the study will be discussed