Implementing the Assessment Standards for School Mathematics: Teachers and Students Learning Together about Assessing Problem Solving

1997 ◽  
Vol 90 (6) ◽  
pp. 472-477
Author(s):  
Marge Petit ◽  
Judith S. Zawojewski
Keyword(s):  
Problem Solving ◽  
Mathematics Teachers ◽  
Teaching Methods ◽  
School Mathematics ◽  
Written Responses ◽  
Teacher Understanding ◽  
Reasonable Solution ◽  
Teachers And Students ◽  
Curriculum Instruction ◽  
Assessment Standards

Enhancing problem-solving capabilities for all students is a goal that can be reached only when curriculum, instruction, and assessment are aligned toward the same goals, along with student and teacher understanding of the expectations associated with reaching these goals (NCTM 1995). The assessment of problem solving in particular is a difficult aspect, even when teachers have developed adequate resources and teaching methods to facilitate problem-solving activities. Pertinent questions regarding problem-solving assessment include the following: How can students' work be evaluated fairly when many reasonable solution paths exist? How can teachers assess students' responses to open-ended questions in a way that yields documentation useful for preparing progress reports? How can teachers help students understand what is expected in their written responses?

scholarly journals The Effect of Problem Solving Course on Pre-Service Teachers’ Beliefs about Problem Solving in School Mathematics and Themselves as Problem Solvers

2018 ◽  
Vol 12 (2) ◽  
pp. 141-159
Author(s):  
Ljerka Jukić Matić
Keyword(s):  
Problem Solving ◽  
Mathematics Teachers ◽  
Teaching Practice ◽  
School Mathematics ◽  
Small Scale ◽  
Heuristic Strategies ◽  
Teachers Beliefs ◽  
Before And After ◽  
Problem Solvers ◽  
Positive Effect

Problem solving in schools begins with mathematics teachers. The degree to which mathematics teachers are prepared to teach for, about and through problem solving influences on their implementation of problem solving in school. We conducted a small scale study where we examined the effect of implementation of heuristic strategies and Polya’s steps in mathematics method course. We assessed pre-service teachers’ knowledge and attitudes about them as problem solvers before and after the course. Moreover we assessed their beliefs of problem solving in school mathematics. Those beliefs were assessed in two occasions: right after the course and after finished teaching practice. Although students’ knowledge on problem solving was improved, the results of students’ beliefs show that it is important that pre-service teachers, and consequently in-service teachers, are constantly reminded on the positive effect of constructivist and inquiry-based approach on teaching mathematics.

Investigating Problem-Solving Perseverance Using Lesson Study

2017 ◽  
Vol 111 (3) ◽  
pp. 207-212 ◽  
Author(s):  
Kristen N. Bieda ◽  
Craig Huhn
Keyword(s):  
High School ◽  
Problem Solving ◽  
Mathematics Teachers ◽  
Lesson Study ◽  
School Mathematics ◽  
High School Mathematics ◽  
High School Mathematics Teachers

Middle and high school mathematics teachers share what they learned about supporting students by conducting a series of three lesson studies.

Exploring Nonroutine Functions Algebraically and Graphically

2011 ◽  
Vol 104 (7) ◽  
pp. 508-513
Author(s):  
Christine P. Trinter ◽  
Joe Garofalo
Keyword(s):  
High School ◽  
Problem Solving ◽  
Mathematics Teachers ◽  
Multiple Representations ◽  
School Mathematics ◽  
High School Mathematics ◽  
Mathematics Tasks ◽  
Preservice Mathematics Teachers

Nonroutine function tasks are more challenging than most typical high school mathematics tasks. In our classes of precalculus students and preservice mathematics teachers, we have found that nonroutine tasks encourage our students to expand their thinking about functions and their approaches to problem solving. As a result, they gain greater appreciation for the power of multiple representations and a richer understanding of functions.

An Interesting Probability Problem

1982 ◽  
Vol 75 (9) ◽  
pp. 765-768
Author(s):  
Ernest Woodward ◽  
Jim R. Ridenhour
Keyword(s):  
Problem Solving ◽  
Mathematics Teachers ◽  
School Mathematics ◽  
Mathematics Textbook ◽  
Probability Problem

In An Agenda for Action: Recommendations for School Mathematics of the 1980s, NCTM (1980) recommends that “problem solving be the focus of school mathematics in the 1980s." Unfortunately, present day mathematics textbook problems can often be classified and categorized, and so they are not really problems at all but actually computational exercises. As a result, mathematics teachers need to be continually searching for interesting, challenging problems. Recently we found such a problem (Gardner 1961).

Fostering Mathematical Thinking through Multiple Solutions

2000 ◽  
Vol 5 (8) ◽  
pp. 534-539
Author(s):  
Jinfa Cai ◽  
Patricia Ann Kenney
Keyword(s):  
Problem Solving ◽  
Multiple Solutions ◽  
Mathematical Thinking ◽  
School Mathematics ◽  
Reform Movement ◽  
Mathematics Students ◽  
Mathematical Concepts ◽  
Teachers And Students

The reform movement in school mathematics advocates communication as a necessary component for learning, doing, and understanding mathematics (Elliott and Kenney 1996). Communication in mathematics means that one is able not only to use its vocabulary, notation, and structure to express ideas and relationships but also to think and reason mathematically. In fact, communication is considered the means by which teachers and students can share the processes of learning, doing, and understanding mathematics. Students should express their thinking and problem-solving processes in both written and oral formats. The clarity and completeness of students' communication can indicate how well they understand the related mathematical concepts.

scholarly journals Fases del razonamiento inductivo que presentan profesores de matemáticas al resolver un problema de generalización

2020 ◽  
Vol 14 (2) ◽  
pp. 118-140
Author(s):  
Landy Elena Sosa Moguel ◽  
Eddie Aparicio Landa ◽  
Guadalupe Cabañas-Sánchez
Keyword(s):  
Middle School ◽  
Mathematics Teachers ◽  
Inductive Reasoning ◽  
Middle School Mathematics ◽  
School Mathematics ◽  
Mathematical Structures ◽  
Written Responses ◽  
Generalization Problem

Se reportan seis fases del razonamiento inductivo que presentaron 19 profesores de matemáticas de secundaria al resolver un problema de generalización de un patrón cuadrático. Los datos se recolectaron mediante sus respuestas escritas y entrevistas. El análisis se realizó con base en el modelo de Cañadas y Castro (2007). Se encontró que, para generalizar de manera correcta, no basta con reconocer las regularidades en varios casos particulares, sino que se precisa de asociar esas regularidades con estructuras matemáticas que describan el patrón de manera general, y se detectaron dificultades en algunas fases que impidieron a los profesores llegar a generalizar.Inductive reasoning stages presented by mathematics teachers when solving a generalization problemThis investigation reports six inductive reasoning stages presented by nineteen middle school mathematics teachers when solving a generalization problem of a quadratic pattern. The data was collected through their written responses and interviews. The analysis was performed based on the model of Cañadas and Castro (2007). It was found that the correct generalization not only needed the recognition of regularities in some particular cases, but an accurate association between those regularities and the mathematical structures that describe the pattern in a general way. Furthermore, several difficulties that prevented the teachers from achieving a generalization were detected.Doi: 10.30827/pna.v14i2.9118

Some Interesting and Thought-Provoking Geometric Fallacies

2007 ◽  
Vol 101 (2) ◽  
pp. 114-119
Author(s):  
Alan Sultan
Keyword(s):  
High School ◽  
Problem Solving ◽  
Mathematics Teachers ◽  
School Mathematics ◽  
High School Mathematics ◽  
High School Mathematics Teachers

Some interesting geometric fallacies that were used in a problem-solving course for preservice high school mathematics teachers. Errors in logic and false assumptions lead to misleading conclusions. The authors demonstrate that incorrect sketches lead us to wrong conclusions. The use of Geometers Sketchpad is one strategy that will benefits students.

Implementing The Standards: Students' Microcomputer-Aided Exploration in Geometry

1990 ◽  
Vol 83 (8) ◽  
pp. 628-635
Author(s):  
Daniel Chazan
Keyword(s):  
High School ◽  
Problem Solving ◽  
Mathematical Structure ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Mathematics Standards ◽  
Mathematical Connections ◽  
Teachers And Students ◽  
K 12

Four important themes presented in the K–12 Curriculum and Evaluation Standards for School Mathematics (Standards) (NCTM 1989) are mathematics as problem solving, mathematics as communication, mathematics as reasoning, and mathematical connections. The high school component also stresses mathematical structure. Furthermore, the Standards calls for new roles for teachers and students and suggests that microcomputer technology can help support teachers and students in taking on these new roles.

Piano Tuners and Problem Solving

1989 ◽  
Vol 82 (4) ◽  
pp. 248-249
Author(s):  
Randolph A. Philipp
Keyword(s):  
Problem Solving ◽  
Mathematics Teachers ◽  
Mathematics Curriculum ◽  
School Mathematics ◽  
Central Focus

The draft of the NCTM Standards document states that problem solving should be the central focus of the mathematics curriculum (Commission on Standards for School Mathematics of the NCTM 1987). Now, more than ever, problem solving is being defined as a process. Akers (1984, 34) defined problem solving as “what you do when you don't know what to do,” and Schoenfeld (1988) wrote, “Indeed, ‘figuring it out’ is what mathematics is all about” (p. 8). Mathematics teachers, left with the task of determining how problemsolving skills should be taught, have the potential to play a key role in developing and sharing problems that interest students. I will share a certain type of problem that I think might be of some interest at the secondary and college levels.

scholarly journals Teachers’ and students’ beliefs in mathematics at State Senior High School 5 Semarang

2018 ◽  
Vol 5 (1) ◽  
pp. 64
Author(s):  
Muhtarom Muhtarom ◽  
Dwi Juniati ◽  
Tatag Yuli Eko Siswono ◽  
Ismi Rahmatika
Keyword(s):  
High School ◽  
Problem Solving ◽  
Mathematics Teachers ◽  
Natural Science ◽  
Senior High School ◽  
Beliefs About Mathematics ◽  
10Th Grade ◽  
Teachers And Students ◽  
Teacher's Beliefs ◽  
The Relationship

The aim of this research was to discover the relationship between teachers’ and students’ beliefs in mathematics. The sample consisted of two mathematics teachers, twenty eight students from 10th grade natural science 6 (X IPA 6) and twenty eight students from 10th grade natural science 10 (X IPA10) at state senior high school 5 Semarang. The data were collected from questionnaires and guided interviews on beliefs about mathematics. The research results showed that both of the mathematics teachers had platonist beliefs. It was found specifically that 4.76% of students in class X IPA 6 consistently had instrumentalist beliefs, 85.71% were consistent with their platonist beliefs, and 9.52% consistently had problem solving beliefs; while in class X IPA 10, 4.76% consistently showed instrumentalist beliefs, 80.95% were consistent with their platonist beliefs, and 14.29% consistently had problem solving beliefs. This indicates that there is a relationship between teachers’ and students’ beliefs, namely the tendency towards platonist beliefs; and also that the teacher’s beliefs influence the student’s beliefs.

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