Melfried Olson

University of Hawaii at Manoa, College of Education, Curriculum Research & Development Group, Emeritus

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Problem Solvers: What Can You Measure?

Teaching Children Mathematics, 2000

<jats:p>The goal of the "Problem Solvers" department is to foster improved commun... more <jats:p>The goal of the "Problem Solvers" department is to foster improved communication among teachers by posing one problem each month for K–6 teachers to try with their students. Every teacher can become an author; pose the problem, reflect on your students' work, analyze the classroom dialogue, and submit the resulting insights to this department. Remember that even student misconceptions are interesting.</jats:p>

Problem Solvers: Coloring Tetras with Two Colors

Teaching Children Mathematics, 2001

<jats:p>The goal of the "Problem Solvers" department is to foster improved commun... more <jats:p>The goal of the "Problem Solvers" department is to foster improved communication among teachers by posing one problem each month for K–6 teachers to try with their students. Pose the problem, reflect on your students' work, analyze the classroom dialogue, and share your analyses with others by submitting the resulting insights to this department. Every teacher can help us all better understand children's capabilities and thinking about mathematics with their contributions to the journal.</jats:p>

Problem Solvers: Stair Skipping

Teaching Children Mathematics, 2000

<jats:p>The goal of the "Problem Solvers" department is to foster improved commun... more <jats:p>The goal of the "Problem Solvers" department is to foster improved communication among teachers by posing one problem each month for K–6 teachers to try with their students. Every teacher can become an author: pose the problem, reflect on your students' work, analyze the classroom dialogue, and submit the resulting insights to this department. Remember that even student misconceptions are interesting.</jats:p>

Math by the Month: It Could Be!… Well, Maybe?

Teaching Children Mathematics, 1996

These activities are designed to speak directly to students, giving them open-ended questions to ... more These activities are designed to speak directly to students, giving them open-ended questions to engage their intellect through their interests. Students may work on the activities individually, in pairs, or in small groups. No answers are given so that students will look to themselves as the mathematical authority, thereby developing the confidence and critical-thinking skills necessary to validate their work.

Children are mathematical problem solvers

This book emphasises the need for children to explore many experiences in problem solving in orde... more This book emphasises the need for children to explore many experiences in problem solving in order to apply and strengthen their mathematical abilities. It is composed of 29 problems from the "Problem Solvers" column in Teaching Children Mathematics, NCTM's journal for elementary school teachers. The situations offered are intended to engage students in interesting explorations in which they do challenging, interesting problem solving with significant mathematical content. The book also features solutions and children's work that were sent to the editors from children and teachers from around the country.

Take Time for Action: Students' Geometric Thinking about Rotations and Benchmark Angles

Mathematics Teaching in the Middle School, 2008

The Measurement Standard states that understanding angles and angle measurement is important in t... more The Measurement Standard states that understanding angles and angle measurement is important in the middle grades (NCTM 2000). To minimize misconceptions that the measure of an angle is determined by the length of its rays (Keiser 2000) or by its interior “space,” our curriculum research and development team decided to introduce angles and angle measurement using transformational geometry, specifically, the motion of rotation. Our class included ten fifth-grade students who had introductory experience with transformational geometry in the fourth grade. Our goals were for students to understand that 360 degrees measured a full rotation and to use this information to determine benchmark angles of 90 degrees, 180 degrees, and 270 degrees. To help achieve these goals, clockwise and counterclockwise movements were also emphasized. We hope the description of our students' developing understandings of angles and angle measurements will help you explore your students' thinking about...

Putting Essential Understanding of Ratios and Proportions into Practice in Grades 6-8

Take Time for Action: The Percent Predicament

Mathematics Teaching in the Middle School, Mar 1, 2010

Have you ever thought that a student grasped the ideas you were hoping they would learn only to f... more

Malthematical Preparation versus Career Aspirations: A Study of Wyoming's 1978 High School Seniors

This report provides a general description of the mathematical programs pursued by students in Wy... more This report provides a general description of the mathematical programs pursued by students in Wyoming's public schools, an evaluation of the adequacy of the high school mathematical preparation of college-bound students relative to the occupational aspirations cf those students, and a measure of the extent to which s'cudents are aware of the adequacy of that preparation. Each set of data was separated according to sex. Data indicate that many discreparcies exist between the vathematics program that students comrlete and what they actually should complete to insure successful entrerce into college programs. Furthermore, they demonstrate that females take fewer mathematics courses, and their poorer preparation severely limits their occuraticnal choices. Also included is an Afterword which suggests sources of information that might be useful in counterina the problems revealed in the study. (Author/MK)

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How teachers' beliefs about teaching and learning impact implementation of formative assessment in connected classrooms

ABSTRACT We report on research conducted with six seventh-grade mathematics teachers who particip... more ABSTRACT We report on research conducted with six seventh-grade mathematics teachers who participated in a two-year professional development research study on implementing formative assessment in networked classrooms. While the full study used a variety of both quantitative and qualitative data sources, this report focuses on data from the semi-structured interviews conducted at the end of the project. We describe three of the categories that emerged from the coding (Strauss &amp; Corbin, 1998) and relate these to teachers&#39; use of the technology. There are few studies that examine teacher learning and practice for more than a year, especially looking at the impact of technology-focused professional development (Mouza, 2009). In this paper, the impact of two years of professional development on teachers&#39; implementation of formative assessment in a connected classroom is analyzed through the lens of the interactive relationship between practices and beliefs. Analysis is based on case study data collected from six of 30 teachers who participated in Project FANC 1 , a research study of implementing formative assessment in a networked classroom using the TI-Navigator System 2 and graphing calculators. The goal of the research in Project FANC was to investigate the use of formative assessment in a networked classroom as it affects middle grades student learning of algebra concepts. In particular, Project FANC studied the effects of one-half of the 30 teachers using formative assessment with the TI-Navigator System for two years and compared them to the effects of the other half using formative assessment with the TI-Navigator System for one year after receiving professional development in formative assessment the first year. Detailed descriptions of the two different models of professional development can be found in Olson et al. (2010). In How People Learn (NRC, 1999), classroom networks were suggested as one of the most promising technology-based education innovations for transforming the classroom environment. Wiliam&#39;s (2007) description of a pedagogy of contingency, in which the essence of formative assessment is instruction contingent on what students have learned, can be accomplished through the use of technology that has potential to overcome the major hurdle to utilizing formative classroom assessment: the collection, management and analysis of data. While feedback loops in the regular classroom are very slow, classroom networked technology has the capability to provide rapid cycles of feedback to improve ongoing activity in real time (Roschelle, Penuel, &amp; Abrahamson, 2004). Using the TI-Navigator System, what students know and can do is easily assessed and anonymously displayed. Students can enter and send their responses to the teacher computer and teachers can easily send questions, and receive, organize, and display students&#39; answers, so that the interaction between the teacher and students and among students is greatly facilitated. Four functions of TI-Navigator System particularly helpful for formative assessment implementation are: (a) Quick Poll—allowing teachers to immediately collect and display all students&#39; responses to a question; (b) Screen Capture—allowing teachers to monitor individual students&#39; progress at anytime; (c) Learn Check—allowing teachers to administer quick and frequent formative assessments and

The Impact of Measurement Models in the Development of Rational Number Concepts

ABSTRACT

Life with an Exciting Nine-Year-Old

The Arithmetic Teacher, Dec 1, 1982

I share the same concern as Moser (1982) who, in his article “Dear Kathy&amp;#39;s Teacher,” ... more I share the same concern as Moser (1982) who, in his article “Dear Kathy&amp;#39;s Teacher,” indicated he was as concerned about the whys in mathematics as about the hows. My daughter does well in the mechanics of mathematics; she feels that is what must be important because that is what the teacher demands. After years of being accused of being crazy by this child who, through reluctant patience, has managed to put up with my attempts to encourage her to become “friendly with numbers” rather than to do just computation, I received an unexpected reward.

Brief Reports: Mathematical Preparation Versus Career Aspirations: Sex-Related Differences Among College-Bound Wyoming High School Seniors

Journal for Research in Mathematics Education, Nov 1, 1981

Students from a broad range of fields of study at the University of Wyoming have commented that t... more Students from a broad range of fields of study at the University of Wyoming have commented that the mathematics courses required for completion of their college programs were posing serious obstacles. When questioned, the students report that they terminated their study of precollege mathematics as early as possible on the assumption(s) that no mathematics was required for the fields they wished to enter and/or that college mathematics courses were available wherein they could correct any mathematical shortcomings. For many students, both assumptions proved erroneous.

Investigations into Mathematics Teachers’ Propositional Logic Capabilities

Responses to the Coloring Tetras with Two Colors Problem

Teaching children mathematics, 2002

Responses to the Tiles and Sides Problem

Teaching children mathematics, Dec 1, 2001

Activities for the Young Adolescent

School Science and Mathematics, Apr 1, 1982

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Fraction Concepts and the Conservation of Area: Ideas for Consideration

School Science and Mathematics, Mar 1, 1988

Students are asked to imagine that the two squares are pastures with identical amounts of grass i... more Students are asked to imagine that the two squares are pastures with identical amounts of grass in them. Four identical wooden cubes are placed in each pasture and identified as barns.. .. Students are told that a cow has been placed in each of the pastures.Ĥ ow many times have you heard teachers engaged in a discussion related to the problems they have helping students understand fractional concepts? This seems to be a problem area in the curriculum of many schools and at many grade levels. Research currently under way at the Science and Mathematics Teaching Center at the University of Wyoming and the Mathematics Education Resource Office at Western Illinois University indicates that there may be basic developmental prerequisites that many students have not yet acquired before they are introduced to fractions. Unfortunately, these prerequisites may still not have been acquired at the time students are expected to perform

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The Apple Box Problem

School Science and Mathematics, Feb 1, 1988

. imagine that we have taken the apples out of the box and then someone sat on it giving it a new... more . imagine that we have taken the apples out of the box and then someone sat on it giving it a new shape.. /) For several years we have been interested in how children at all levels learn mathematics, especially how they conceptualize topics they have been "taught." Stepans and Olson refer to the need to teach students more than symbol manipulation.1 The data reported here serve to substantiate that claim. Specifically this article addresses the understanding of a concept, volume, which is "taught" to students in grades 7-12.

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Can Drill Lead to Concept Development?

School Science and Mathematics, May 6, 1979

Drill exercises: can they be used to introduce concepts, be meaningful, lead to discovery and inc... more Drill exercises: can they be used to introduce concepts, be meaningful, lead to discovery and incorporate problem solving techniques? These thoughts are often neglected as we usually relegate drill to a lesser level of importance. However, I feel that some concepts can be introduced from exercises that ostentatiously have their origins in drill exercises, that initially appear to have no connection to the concept involved. Proposed solutions, of course, vary with the individual instructor and are often dictated by his philosophical concerns. Consider Example 1 and Example 2 which initially resemble drill exercises involving addition of whole numbers.

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