Mathematics in the Real World

This paper reports on a class assignment written by preservice teachers on the use of mathematics in different professions. The professions included licensed practical nurse, auto mechanic, research and development product manager for industrial cleaning products, dental office assistant, snack bar employee at a beach club, beauty salon owner and operator, apple orchard and fruit stand owner, secretary at a university alumni hall, bus person at a restaurant, video store clerk, professional mover, convenience store assistant manager, pizza restaurant server, meteorologist, and land surveyor. (YDS

Crystal Shape Bingo: A Bingo Game for Teaching Recognition of Three-dimensional Crystal Shapes and Planar Geometric Shapes of Crystal Faces

This document describes a game that provides students with practice in recognizing three dimensional crystal shapes and planar geometric shapes of crystal faces. It contains information on the objective of the game, game preparation, and rules for playing. Play cards are included (four to a page)

EleFantastic Bingo: A Bingo Game for Teaching Science Concepts and Vocabulary Associated with Elephants

This game allows students to learn new science vocabulary and relevant facts about elephants. This bingo game is a valuable curriculum resource for any teacher who is teaching about elephants or other endangered animals. Directions for play, calling cards (six to a page), and play cards (four to a page), are included

Measurement Activities for Increasing Student Curiosity for Animal and Space Topics

These materials are intended for use by classroom teachers to generate student curiosity during an anticipatory set of a lesson or at the beginning exploration phase of a learning cycle lesson. Several different animal and solar system topics are presented

Wolf Bingo: A Bingo Game for Teaching Concepts and Vocabulary Associated with Wolves

This document describes a game that provides students with practice in learning vocabulary and concepts associated with wolves. Directions for play and play cards (four to a page) are included

Algebra Rules Object Boxes as an Authentic Assessment Task of Preservice Elementary Teacher Learning in a Mathematics Methods Course

The purpose of this study was to describe elementary preservice teachers’ difficulties with understanding algebraic generalizations that were set in an authentic context. Fifty-eight preservice teachers enrolled in an elementary mathematics methods course participated in the study. These students explored and practiced with authentic, hands-on materials called “object boxes,” then created sets of their own object box materials. Each algebra rules object box contained materials to illustrate and describe four different algebraic generalizations, or “rules.” The variables “n” and “z” were used in each of the generalizations. For each generalization, there was a set of objects attached to a piece of mat board that showed three cases of the generalization for different values of “n.” Two sets of cards accompanied these objects, giving word problems, defining variables, stating equations, and explaining the algebraic generalizations. Students matched word problems to the object sets, defined variables and checked their work, then wrote algebraic generalizations for the object sets and used the reverse sides of the equation cards to check their work. Projects were graded with a rubric. Students were then surveyed about their difficulties. Results of the analysis showed that students were able to make an assortment of authentic materials in a variety of contexts and enjoyed the creative aspects of the project, but found the algebraic content challenging. The most common mathematical difficulties were being able to define the variable, and identify the pattern. Examples of effective student materials are provided

Fifth Graders’ Creativity in Inventions with and without Creative Articulation Instruction

Industry and authors of 21st Century Skill Frameworks are calling for student proficiency in creativity, problem-solving, innovation, collaboration, and communication skills. This project involved 13 fifth grade gifted students in inventing products for a specified audience with a set of given materials, time limit, and topic constraints. The complex, challenging project supports Next Generation Science Engineering Process Standard 3-5-ETS1-2 and applies concepts of plant and animal adaptations. The study had a counterbalanced, repeated measures design in which student made an initial invention during the pretest, then participated in two trials with one in the control condition and the other in the experimental condition. The experimental condition involved creative articulation strategies of considering the audience for the invention, effective communication of the ways the product meets audience needs, and peer collaboration and feedback to improve the product ideas. Students found the invention process initially very challenging, especially generating unique ideas. No statistically significant differences were found in product creativity or student attitudes, which were very positive, between the two conditions of the experiment, likely because of the small sample size. Analysis of student advertisements revealed a statistically significant difference favoring the experimental condition with a medium effect size for including reasons the product meets audience needs in the advertisement. Examples of student-made products and teacher analysis of selected products provide ideas for coaching students into higher creative skill levels. Additionally, statistically significant gains in creativity skill occurred from the pretest to the invention of the product during the first trial and this was maintained into the second trial with large effect size. This study showed that multiple invention opportunities allowed students to develop their skills better than a single activity. The challenging, complex activities helped students achieve a state of flow as they worked during the experiment and helped students develop their creativity

Spotlight on Edward de Bono Thinking Skills and Twice-Exceptional Gifted Learners Applied to Mars Mysteries in NASA Photographs

This editorial provides background information concerning the lessons presented in the eight practical articles of this issue. All of these lessons address Mars Mysteries, anomalous features found in NASA photographs of the Martian surface. These unusual and thought-provoking features are explored by using Edward de Bono CoRT thinking skills to broaden perceptions enhancing critical and creative thinking. The lessons are intended to explore possibilities, but not to provide a definite final answer as to what the anomalies represent. These lessons were designed as enrichment lessons for gifted learners and support Renzulli’s Type I general exploratory experiences that expose students to a variety of issues not usually addressed by the school curriculum. These lessons also fit with Type II skill lessons because they focus on the de Bono thinking skills. Additionally, individual lessons are each designed to meet the needs of twice-exceptional gifted learners, containing lesson design features that assist gifted learners with specific disabilities or exceptionalities. Finally, each lesson includes a brief integrated arts project to synthesize the concepts discussed, expressing individual conclusions. Arts were integrated to foster engagement, increased level of attention, joy, and self-expression

Preservice Elementary Teachers Use Drawings and Make Sets of Materials to Explain Multiplication and Division by Fractions

Background: Multiplication and division by fractions are among the most troublesome concepts in the elementary mathematics curriculum. Recent studies have shown that preservice elementary teachers in the United States do not have deep understandings of these concepts. Effective ways to improve preservice teachers\u27 conceptual understanding of these concepts need to be identified. Citation: Rule, A. C., & Hallagan, J., editors. (2006). Preservice elementary teachers use drawings and make sets of materials to explain multiplication and division by fractions. A research study presented at the 2nd Annual Preparing Mathematicians to Educate Teachers (PMET) Conference at Oswego, New York, June 6, 2006. Conclusions: The two activities increased student understandings of multiplication and division by fractions. Although students improved through the activities, many students\u27 understandings were still incomplete. More than two focused activities are needed to ensure deeper understanding of concepts. Preservice teachers need concrete experiences with these concepts in their mathematics classes as well as in mathematics education coursework. 2 Control or Comparison Group: Both the control group and the experimental group consisted of preservice teachers from several sections of the same instructor\u27s undergraduate mathematics methods courses and were matched on pretest scores. Both groups completed the homework assignment in which they used drawings to illustrate multiplication and division by fractions. The instructor did not present lessons on these concepts to the classes until after the posttest had been completed so that the effects of these activities would not be confounded. The experimental group completed the additional activity of making hands-on materials to model these concepts. The study examined the increase in preservice teachers\u27 conceptual understanding of multiplication and division by fractions through the two activities. Data Collection and Analysis: Both control and experimental groups were assessed with identical pretest/ posttest instruments constructed by the investigators to determine both procedural knowledge of solving equations involving multiplication and division by fractions and conceptual knowledge of writing equations for story problems and using drawings to illustrate concepts. Posttest scores, student work on the assessments, drawing assignment, and hands-on materials were examined along with student comments on a survey that asked what subjects learned from participating in the intervention activity. Findings: The two activities improved preservice teachers\u27 understandings of these concepts as revealed by the change in scores from pretest to posttest (50.8% on pretest to 67.5% and 71.4%). Those who completed both assignments scored somewhat higher (71.4% compared to 67.5%) than those who only completed the drawing assignment, but this difference was not statistically significant. Preservice teachers reported that their understandings of these concepts improved through the activities. Intervention: Both control group and experimental group participated in composing story problems with drawings to illustrate multiplication and division by fractions. The experimental group completed the additional activity of making hands-on materials with accompanying story problems to model multiplication and division by fractions. Purpose: The purpose of the study was threefold: 1) to investigate the effectiveness of two activities in helping preservice teachers develop deeper understandings of multiplication and division by fractions; 2) to identify typical errors preservice teachers make and identify difficulties they encounter while learning these concepts; and 3) to provide examples of drawings and hands-on materials that effectively model multiplication and division by fractions for others to use in learning and teaching. Research Design: The study was a pretest - intervention - posttest design with control and experimental groups. Because lower-performing students tended to volunteer for the extra-credit activity (the intervention for the experimental group), blindly matched groups were formed on pretest scores. Setting: Preservice teachers from three mathematics methods classes of college students majoring in elementary education at a mid-sized college in central New York State during the spring semester of 2006. Study Sample: Forty-two white preservice elementary teachers enrolled in a mathematics methods course. The experimental group consisted of 18 females and 3 males; the control group consisted of 16 females and 5 males

Making Cereal Box Dioramas of Native American Historic Homes and Culture

Hands-on projects such as creating a three-dimensional diorama are among the most memorable of positive elementary school experiences, yet they are generally uncommon because these complex projects are daunting to undertake. Therefore, it is important to prepare preservice teachers with the skills to lead children in creating these types of projects. This document is a compilation of preservice teacher work completed during a social studies methods class that assists instructors in teaching students to create unique dioramas. After the preservice teachers had constructed dioramas and assisted elementary students in making their own, they reflected on previous social studies projects from their childhoods and considered the learning outcomes of the current project. Eighty preservice teachers enrolled in a social studies methods course participated in the study. These college students created their own Native American dioramas along with images for furnishing and finishing dioramas of the Native American group on which they focused. The five Native American groups explored through dioramas include the Iroquois of the northeastern United States, the Seminole of the Southeast, the Lakota of the Central Plains, Hopi (and Navajo) of the American Southwest and the Haida of the Northwest Coast. This document provides photoillustrated examples and steps of how to create an intricate diorama from a cereal box, recycled copy paper, white craft glue, paints, images, and common craft items. The cereal box base is cut to open like a book and a model of a Native American home made of recycled cardboard is affixed over a cut-out hole in the cover so that the box opens to reveal the interior of the home. All surfaces are covered with a layer of torn recycled copy paper that is securely glued, coated with white gesso base paint, and then decorated with acrylic craft paints. In the facing inside enclosure, a ceremony scene is displayed. The back of the cereal box features crafts of the Native American group, while the other cereal box exterior sides show foods, clothing, and other cultural Reflection data indicate that preservice teachers recognized the large amount of time and patience necessary to complete a quality diorama and the valuable amount of in-depth learning that results, including a deeper respect for Native American people and greater confidence in teaching these concepts. Therefore, we recommend diorama projects in teaching about diverse cultures (2 tables, 5 figures, 2 photo-illustrated appendices)