Using a Pattern Table to Solve Contextualized Proportion Problems

2003 ◽  
Vol 8 (8) ◽  
pp. 432-439
Author(s):  
Janet M. Sharp ◽  
Barbara Adams
Keyword(s):  
Problem Solving ◽  
Sixth Grade ◽  
Grade Classroom

Students in a sixth-grade classroom we visited were celebrating a classmate's birthday and enjoying fun-sized bags of Peanut M&M's candies. We overheard them discussing their curiosity at the small number of blue M&M's each of them had received in their small bags. Because the students were occupied in an informal, party atmosphere, we were pleasantly surprised to hear one student, Rickea, comment on a related mathematical issue. She speculated that the teacher's class-sized bag would have relatively few blue M&M's, as well. What a wonderful teaching opportunity for ratios and proportions Rickea's casual comment posed! In this article, we describe (1) how we built a week-long, problem-based unit around Rickea's original proportion question and (2) the effectiveness of using problem solving to help Rickea and her classmates construct knowledge about ratio and proportional thinking.

Building on Students' Intuitive Strategies to Make Sense of Cross Multiplication

2003 ◽  
Vol 9 (3) ◽  
pp. 150-155
Author(s):  
Melissa D. Boston ◽  
Margaret S. Smith ◽  
Amy F. Hillen
Keyword(s):  
Problem Solving ◽  
Middle Grades ◽  
Sixth Grade ◽  
Grade Classroom

Middle-grades students' understanding of proportional relationships should be fostered through problem solving and reasoning (NCTM 2000). Toward this end, instruction in proportionality should expose students to a variety of strategies and allow students to gain experience modeling proportional situations (Langrall and Swafford 2000). Students should be given ample opportunities to develop intuitive strategies based on factor- of-change (“how many times as many”) relationships (Cramer and Post 1993). Research has shown that middle-grades students are more successful at method is appropriate to use” (NCTM 2000, p. 221). We begin our discussion by focusing on the events that unfold in Marie Hanson's sixth-grade classroom during a lesson on understanding ratios and proportions (Smith et al. forthcoming), and use this lesson as a context for considering how factor-of-change relationships might be used to assist students in understanding why cross multiplication works.

Links to Literature: Incredible Comparisons: Experiences with Data Collection

1998 ◽  
Vol 5 (1) ◽  
pp. 12-16
Author(s):  
Vicki L. Oleson
Keyword(s):  
Problem Solving ◽  
Data Collection ◽  
Mathematics Curriculum ◽  
Mathematics Classroom ◽  
Sixth Grade ◽  
School Year ◽  
Grade Classroom

The mathematics curriculum for a typical sixth-grade classroom easily provides ample content for an entire school year. It can be difficult to take the time needed to develop a mathematics concept through the use of literature. However, I found that by focusing on content. I was able to incorporate literature into one sixth-grade mathematics classroom. This activity presented an interesting springboard to problem solving, an opportunity to research famous mathematicians, and an excellent vehicle to enhance the understanding of mathematics concepts.

An Investigation of Sex-Bias in Classroom Teachers' Speech and Language Referrals

1980 ◽  
Vol 11 (3) ◽  
pp. 169-174 ◽  
Author(s):  
Ellen Marie Silverman ◽  
Katherine Van Opens
Keyword(s):  
School Districts ◽  
Voice Disorders ◽  
Communication Disorders ◽  
Sixth Grade ◽  
Sex Bias ◽  
Classroom Teachers ◽  
Communication Disorder ◽  
Primary Procedure ◽  
Teacher Referrals ◽  
Grade Classroom

Kindergarten through sixth grade classroom teachers in four school districts completed questionnaires designed to determine whether they would be more likely to refer a boy than a girl with an identical communication disorder. The teachers were found to be equally likely to refer a girl as a boy who presented a disorder of articulation, language, or voice, but they were more likely to refer a boy for speech-language remediation who presented the disorder of stuttering. The tendency for the teachers to allow the sex of a child to influence their likelihood of referral for stuttering remediation, to overlook a sizeable percentage of children with chronic voice disorders, and to be somewhat inaccurate generally in their referrals suggests that teacher referrals are best used as an adjunct to screening rather than as a primary procedure to locate children with communication disorders.

scholarly journals Motivational and Emotional Orientation, Engagement, and Achievement in Mathematics. A Case Study With One Sixth-Grade Classroom Working With an Electronic Textbook on Fractions

2021 ◽  
Vol 6 ◽  
Author(s):  
Frank Reinhold ◽  
Stefan Hoch ◽  
Anja Schiepe-Tiska ◽  
Anselm R. Strohmaier ◽  
Kristina Reiss
Keyword(s):  
Learning Outcomes ◽  
Prior Knowledge ◽  
Cognitive Learning ◽  
Sixth Grade ◽  
Emotional Engagement ◽  
Behavioral Engagement ◽  
Electronic Textbook ◽  
The Relationship ◽  
Grade Classroom

Interactive and adaptive scaffolds implemented in electronic mathematics textbooks bear high potential for supporting students individually in learning mathematics. In this paper, we argue that emotional and behavioral engagement may account for the effectiveness of such digital curriculum resources. Following the general model for determinants and course of motivated action, we investigated the relationship between students’ domain-specific motivational and emotional orientations (person)—while working with an electronic textbook on fractions (situation), their emotional and behavioral engagement while learning (action), and their achievement after tuition (outcome). We conducted a case-study with N = 27 students from one sixth-grade classroom, asking about the relationship between students’ motivational and emotional orientations and their emotional and behavioral engagement, and whether emotional and behavioral engagement are unique predictors of students’ cognitive learning outcomes while working with an e-textbook. For that, we designed a four-week-intervention on fractions using an e-textbook on iPads. Utilizing self-reports and process data referring to students’ interactions with the e-textbook we aimed to describe if and how students make use of the offered learning opportunities. Despite being taught in the same classroom, results indicated large variance in students’ motivational and emotional orientations before the intervention, as well as in their emotional and behavioral engagement during the intervention. We found substantial correlations between motivational and emotional orientations (i.e., anxiety, self-concept, and enjoyment) and emotional engagement (i.e., intrinsic motivation, competence and autonomy support, situational interest, and perceived demand)—with positive orientations being associated with positive emotional engagement, as expected. Although the correlations between orientations and behavioral engagement (i.e., task, exercise, and hint count, problem solving time, and feedback time) also showed the expected directions, effect sizes were smaller than for emotional engagement. Generalized linear mixed models revealed that emotional engagement predicted cognitive learning outcomes uniquely, while for behavioral engagement the interaction with prior knowledge was a significant predictor. Taken together, they accounted for a variance change of 44% in addition to prior knowledge. We conclude that when designing digital learning environments, promoting engagement—in particular in students who share less-promizing prerequisites—should be considered a key feature.

Use of Apple iPads in K-6 Math and Science Classrooms

2013 ◽  
pp. 177-192
Author(s):  
Tara Bennett ◽  
Florence Martin
Keyword(s):  
Instructional Strategies ◽  
Science Classroom ◽  
Sixth Grade ◽  
Comfort Level ◽  
Magnet School ◽  
Middle Grade ◽  
Addition And Subtraction ◽  
Grade Classroom ◽  
Interest In Technology

In this chapter, the authors review how iPads were used in a middle grade math classroom of a technology magnet school. The school has received two mobile iPad carts in addition to the three they have. Ms. Martin, a science teacher at this middle school, has received one of the mobile iPad carts due to her interest in technology integration. Ms. Martin is considered to be an early adopter of technology at her school, and she has been using iPads for more than a year in her sixth grade classroom. Ms. Bennett, who recently received 25 iPads, paid a visit to Ms. Martin’s classroom to learn how to integrate iPads in her science classroom. This case study describes Ms. Bennett’s visit to Ms. Martin’s classroom on the day when the students were studying how to solve inequalities by using addition and subtraction. Ms. Bennett’s goal for the visit was to identify the different ways Ms. Martin was using iPads with her students, and monitor the comfort level of her students with the iPads. She documents what she learns from the visit, and discusses it with Ms. Martin; she also meets with Mr. Pallapu, the technology facilitator at school. Ms. Martin shares some tips and techniques that she can use in her classroom, and also some benefits and challenges of using the iPad. Mr. Pallapu provides her with a list of recommended apps and instructional strategies for using iPads in the classroom.

Assessing Self-regulation Development through Sharing Feedback in Online Mathematical Problem Solving Discussion

2010 ◽  
pp. 232-247 ◽  
Author(s):  
Bracha Kramarski
Keyword(s):  
Problem Solving ◽  
Mathematical Reasoning ◽  
Mathematical Problem ◽  
Self Regulation ◽  
Sixth Grade ◽  
Mathematical Problem Solving ◽  
Social Feedback ◽  
Self Regulated Learning ◽  
Metacognitive Teaching ◽  
Online Feedback

This study examined the relative efficacies of two different metacognitive teaching methods – problem solving (M_PS) and sharing knowledge (M_SK). Seventy-two Israeli sixth-grade students engaged in online mathematical problem solving and were each supported using one of the two aforementioned methods. M_PS students used a problem-solving and feedback process based on the IMPROVE model (Kramarski & Mevarech, 2003). In contrast, M_SK participants were instructed to reflect and provide feedback on the solution without an explicit model. This study evaluated each method‘s impact on the students’ mathematical online problem solving. It also examined self-regulated learning (SRL) processes by assessing students‘ online feedback using a rubric scheme. Findings indicated that M_PS students outperformed the M_SK students in algebraic knowledge and mathematical reasoning, as well as on various measures of sharing cognitive and metacognitive feedback. The M_SK students outperformed the M_PS students on measures of sharing motivational and social feedback.

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