Teaching Mathematical Reasoning In Secondary School Classrooms Mathematics Teacher Education

The lasting effects of teacher professional development (PD) are seldom examined. We investigated whether 44 teachers and their Grade 5 and 6 primary classes continued working with tasks for mathematical reasoning and employing a rubric after the PD finished. Questionnaires for students and teachers were administered before the intervention, at the end of the intervention, and 5 months later. The results of the longitudinal quantitative analyses with supplementary qualitative interpretations indicated that the mathematical reasoning features of the PD showed more sustainable effects than the use of the rubric. Explorative findings suggest that this outcome may be related to the teachers' pedagogical content knowledge.

Teaching Mathematical Reasoning in Secondary School Classrooms Mathematics Teacher Education

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Last week over 700 high school mathematics teachers and leaders participated in the first NCTM Interactive Institute: Infusing the Classroom with Reasoning and Sense Making. This three-day institute offered task groups, breakout workshops, discussion groups, featured speakers, and keynote presenters. The interest and commitment on the part of the attendees was truly inspiring as they developed plans to bring more emphasis on student reasoning to their classrooms and teaching practices. I tip my hat and salute all of those who attended for their hard work and professionalism during the institute. I am looking forward to hearing about their follow-up experiences as they implement reasoning and sense making in their classrooms this year, and share their efforts on the conference discussion blog set up on the NCTM website.

As educators respond to the political push for an emphasis on student reasoning, NCTM is developing resources for teachers to support the implementation of a focus on reasoning and sense making and to help sustain efforts to foster it over time. An online library of reasoning and sense-making tasks has been launched on the NCTM website so that teachers can access reasoning tasks along with supporting implementation materials. Several tasks have been posted (NCTM Standards) under the Focus on High School Mathematics: Reasoning and Sense Making link. A collection of video clips of secondary students engaged in reasoning in their classroom is also under development at NCTM. These clips are part of clusters of materials that will support teachers in their classrooms. The clusters will include examples of student work, clips of student reasoning, debriefing sessions of reasoning tasks with teachers, and implementation strategies for teachers and teacher leaders. Access to the video cluster work will be available on the NCTM website in the coming months.

Kristin Lesseig teaches elementary and secondary mathematics content and methods courses as well as foundational courses in education and educational research. Her research focuses on the design and implementation of professional learning experiences that support teachers (and future teachers) in their work to promote mathematical reasoning and sense-making in secondary mathematics classrooms.

Adding It Up explores how students in pre-K through 8th grade learn mathematics and recommends how teaching, curricula, and teacher education should change to improve mathematics learning during these critical years.

The committee discusses what is known from research about teaching for mathematics proficiency, focusing on the interactions between teachers and students around educational materials and how teachers develop proficiency in teaching mathematics.

The Secondary Teaching emphasis is designed for secondary school mathematics teachers interested in developing a deeper background in mathematics and pedagogy to enhance teaching and increase student learning.

This major is intended for teachers interested in mathematics for the elementary and middle grades (K-8) and for mathematics specialists and supervisors. Teacher licensure is a prerequisite for completing the program approval process for this major. Normally, candidates will have at least 2 years teaching experience.

Goal 1: Social Contexts of Mathematics Teaching and Learning - Well-prepared beginning teachers of mathematics realize that the social, historical, and institutional contexts of mathematics affect teaching and learning and know about and are committed to their critical roles as advocates for each and every student.

Goal 2: Knowledge of Students as Learners of Mathematics - Well-prepared beginning teachers of mathematics have foundational understandings of students' mathematical knowledge, skills, and dispositions. They also know how these understandings can contribute to effective teaching and are committed to expanding and deepening their knowledge of students as learners of mathematics.

Goal 3: Pedagogical Knowledge and Practices for Teaching Mathematics - Well-prepared beginning teachers of mathematics have foundations of pedagogical knowledge, effective and equitable mathematics teaching practices to support students' sense making, understanding, and reasoning. Additionally, well-prepared beginning teachers can develop effective assessment plans.

Goal 4: Knowledge of Mathematics Well-prepared beginning teachers of mathematics possess robust knowledge of mathematical and statistical concepts that underlie what they encounter in teaching. They engage in appropriate mathematical and statistical practices and support their students in doing the same.

The mathematics degree program provides a wide variety of experiential learning opportunities including cooperative education programs, field trips, mathematical and statistics conferences, specialized courses, seminars, guest lecturers, and classroom speakers. Students also have access to networked computer laboratories equipped with mathematical software.

As a mathematics major at the University of Mount Union, you will take in-depth courses in calculus, statistics, differential equations and number theory. From the basics of algebra to econometrics, you will develop the ability to think critically and use mathematical reasoning in everyday life. As part of our mathematics major requirements and curriculum, you will solve problems, engage in research and benefit from opportunities to present your work, all while learning the skills necessary for success in a number of career fields.

Students may also pursue a teaching career by enrolling in our CAEP accredited Teacher Education Program for mathematics. As part of our program requirements and curriculum, students will spend time working in local secondary and middle school mathematics classes in order to gain hands-on experience in the field of mathematics teaching.

#260 Numeric, Algebraic, and Geometric Reasoning for Teaching and Learning. (4) A mathematics course for elementary and middle school teachers examining numbers, algebra, geometry, and measurement; featuring problem solving, applications, and concrete and visual representations. Prerequisite: WIU placement or MATH 128 (C or better) or equivalent.

#406 Problem Solving and the History of Mathematics. (3) Various problems, their solutions, related mathematical concepts, and their historical significance are analyzed through investigation of classic problems and their connection to middle school mathematics. Contributions by Archimedes, Descartes, Eratosthenes, Euler, Gauss, Pascal, Pythagoras, and others are studied. Open only to students majoring in an Elementary Education program. Prerequisite: MATH 123 or 128 or equivalent.

439 Teaching and Assessment in Secondary School Mathematics. (4) A study of teaching strategies and current trends in secondary mathematics education. Students will focus on curriculum, lesson-planning, and assessment, and will learn to effectively incorporate technology into the teaching and learning of mathematics. Open to Teacher Education majors only. Prerequisite: 2.50 GPA or higher in Mathematics; MATH 304, MATH 341, and co-registration in EIS 304; or permission of the department chair.

#409 Probability and Statistics for Middle School Teachers. (3) Probability laws, random variables, probability distributions, estimation and inference, sampling and data analysis, emphasis on concepts and connections of probability and statistical content to the challenges of teaching statistics for middle school teachers. Prerequisite: MATH 123 or 128, or equivalent.

This research is part of a three year project which focuses on the psychological effects of having issues with number sense processing in adolescents. Research suggests that this processing problem can affect their achievement in mathematics (Halberda 2008, Libertus 2011, Starr 2013), and can potentially therefore affect their psychological well-being. The research considers the perspectives of secondary age children with number sense difficulties and how these feelings compare with students who do not experience such problems. A struggle in the mathematics classroom brought about by processing difficulties may lead to far-reaching effects in many areas of life. Work on other learning disabilities such as dyslexia (e.g. Gunnel Ingesson, 2007) indicates this may be so. Q sort methodology was used to explore attitudes and aspirations of those highlighted to have number processing issues, those who have difficulties with mathematics but no processing issues and a group who were competent at mathematics. Students were identified initially by screening Key stage 3 students (n=375) at a school in the UK using a dyscalculia screener. The subsequent Q sorts were conducted on 36 students in total. Findings suggest that there are both optimistic and negative outlooks and attitudes from students who have mathematical difficulties, and that those who have problems processing mathematics are most likely to have a pessimistic viewpoint towards mathematics learning and their future. There are also effects from their mind-set and their perceived ability level as compared to their peers within their classes. However, it is also noteworthy that there were also negative attitudes expressed from mathematics competent students. This indicates that good ability is no guarantee of confidence and positivity towards mathematics. 2ff7e9595c