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Kalinec-Craig, Crystal; Robles, Rose Ann – Mathematics Teacher: Learning and Teaching PK-12, 2020
The article describes how one fifth-grade teacher helped her students to exercise their Rights of the Learner (e.g., to be confused; to claim a mistake; to speak, listen, and be heard; and to write, do, and represent what makes sense) as they learned to graph and interpret non-linear data.
Descriptors: Elementary School Students, Grade 5, Elementary School Teachers, Classroom Techniques
Vondrová, Nada; Novotná, Jarmila; Havlícková, Radka – ZDM: The International Journal on Mathematics Education, 2019
Research has shown that word problem difficulty is influenced by various linguistic, numerical and general variables, but results in this area are inconsistent. This paper focuses on the question of how the order of numerical data, the context, the position of the unknown transformation, and the length of the statement in an additive word problem,…
Descriptors: Word Problems (Mathematics), Elementary School Students, Grade 4, Grade 5
Willingham, James C.; Strayer, Jeremy F.; Barlow, Angela T.; Lischka, Alyson E. – Mathematics Teaching in the Middle School, 2018
Middle-grades teachers and students can have different perspectives on the value of discussing students' mathematical mistakes, despite various classroom evidence that such discussions can help foster strong conceptual understanding. Some teachers consider student mistakes to be an opportunity to correct errors in individual student thinking.…
Descriptors: Mathematics Instruction, Misconceptions, Mathematical Concepts, Middle School Students
Tulis, Maria; Steuer, Gabriele; Dresel, Markus – Frontline Learning Research, 2016
Errors bear the potential to improve knowledge acquisition, provided that learners are able to deal with them in an adaptive and reflexive manner. However, learners experience a host of different--often impeding or maladaptive--emotional and motivational states in the face of academic errors. Research has made few attempts to develop a theory that…
Descriptors: Error Patterns, Metacognition, Learning Processes, Learning Motivation
Stacey, Kaye – Mathematics Education Research Group of Australasia, 2013
"Specific Mathematics Assessment that Reveal Thinking" (abbreviated as "smart tests") provide an on-line formative assessment of middle years students. They aim to put information from research on students' understanding directly into the hands of teachers, by providing quick automated diagnosis of learning for all students in…
Descriptors: Formative Evaluation, Mathematics Instruction, Middle School Students, Educational Research
Lim, Kien H. – Mathematics Teaching in the Middle School, 2014
Student errors are springboards for analyzing, reasoning, and justifying. The mathematics education community recognizes the value of student errors, noting that "mistakes are seen not as dead ends but rather as potential avenues for learning." To induce specific errors and help students learn, choose tasks that might produce mistakes.…
Descriptors: Secondary School Mathematics, Middle School Students, Error Patterns, Error Correction
D'Ambrosio, Beatriz S.; Kastberg, Signe E. – Teaching Children Mathematics, 2012
Asked to complete a decimal-ordering task, several preservice teachers were unable to arrange the values from smallest to largest. Even more surprising to the authors were the number who could solve this task correctly but could not justify their solution by representing each decimal in an area model using a decimal grid. Their preservice teachers…
Descriptors: Mathematics Instruction, Preservice Teachers, Error Patterns, Mathematical Concepts
Myers, Perla L.; Pelak, Colleen N. – Teaching Children Mathematics, 2012
As partners in a professional development project, the authors jumped at the opportunity to use a real-life problem to engage elementary and middle school teachers in a one-day exploration of the concept of area. "Length times width"--a common response to the question, "What is area?"--is a rote formulaic expression that applies only to certain…
Descriptors: Professional Development, Problem Solving, Misconceptions, Middle School Teachers
Cramer, Kathleen; Monson, Debra; Whitney, Stephanie; Leavitt, Seth; Wyberg, Terry – Mathematics Teaching in the Middle School, 2010
Fraction division is generally introduced in sixth or seventh grade with this rule: "Invert and multiply." The authors examined current commercial curricula and found that few textbooks use context as a way to build meaning for the division of fractions. When context is used, the connection between the invert-and-multiply rule and the context is…
Descriptors: Textbooks, Secondary School Mathematics, Arithmetic, Mathematics Instruction
Scheuermann, Amy; van Garderen, Delinda – Mathematics Teaching in the Middle School, 2008
Students are often told to use representations to solve mathematics problems, yet it may be a hindrance for many. This article contains an approach, the Graphic Representational Analysis Process, that teachers can use to analyze representations and focus future instruction. (Contains 7 figures.)
Descriptors: Error Patterns, Misconceptions, Mathematics Instruction, Graphs
Hawes, Kathy – Mathematics Teaching in the Middle School, 2007
This article describes activities that promote students' understanding of equation solving through analyzing and correcting student work. (Contains 5 figures.)
Descriptors: Error Analysis (Language), Equations (Mathematics), Problem Solving, Middle School Students