Middle School Teachers’ Use of Mathematics to Make Sense of Student Solutions to Proportional Reasoning Problems

Mathematics teacher education aims to improve teachers’ use of mathematical knowledge to support teaching and learning, an aspect of pedagogical content knowledge (PCK). In this study, we interviewed teachers to understand how they used mathematics to make sense of student solutions to proportional reasoning problems. The larger purpose was to find accurate ways of categorizing teachers’ ability to do this vital aspect of teaching and thereby to inform assessment, teacher education, and professional development. We conjectured that teachers’ PCK for proportional reasoning could be reliably described in terms of attention to quantitative meanings in story problem contexts and in terms of understanding naïve forms of proportional reasoning. Instead, our findings reveal that individual teachers used a variety of means to make sense of (1) cognitively similar student solutions to different tasks and (2) mathematically related steps of a student solution within a single task. These findings illustrate the complexity of PCK for the topic of proportional reasoning and suggest the limits of what can be inferred about teacher knowledge from teachers’ evaluations of student solutions. We discuss implications for teacher education and assessment.     

Narrating Characters: The Making of a School Bully

Jake was a popular sixth-grader at a local public school. He had plenty of friends and admirers, made good grades, and had adequate social skills. Jake was also a bully. Over the course of that sixth grade year Jake recruited a couple of friends, and then a much larger groups of peers, to target a classmate: Matthew. The school was quick to respond, but despite clear training, strong reprimand, and relentless surveillance the bullying of Matthew only stopped when he finally transferred to a new school. The next year Jake picked a new target: Trent. To date bullying research has largely employed empirical methodologies, including qualitative and quantitative approaches. This paper offers a fresh perspective, employing a missing philosophical lens toward the instantiation of bullying on the school campus. How might a bully – or a group of bullying participants – be narrated in such a way that he or she chooses violence or domination as a means through which to secure status? More specifically, what forces bear upon the experience of bullying, what cultures might its dominance mirror, and from where is its meaning derived? In considering these questions I employ the voices of two disparate philosophers; John Dewey and Michel Foucault.     

Early word decoding ability as a longitudinal predictor of academic performance

This study, using a longitudinal design with a Swedish cohort of young readers, investigates if children’s early word decoding ability in second grade can predict later academic performance. In an effort to estimate the unique effect of early word decoding (grade 2) with academic performance (grade 9), gender and non-verbal cognitive ability were controlled for in hierarchical regression models. Results show that even after accounting for these factors, word decoding successfully predicted subject marks as well as attendance in advanced courses and language classes. The authors conclude that children’s early ability to decode words could be an important factor for predicting performance in school and, thus, stress the importance for schools to investigate children’s early word decoding ability.     

The effects of explicit timing on middle‐school students’ writing production across 5‐ and 15‐min sessions

Enhancing rates of accurate, active, academic responding can enhance learning. Both temporal manipulations (i.e., reducing time to work on assignments) and providing multiple distributed temporal cues (MDTC), sometimes referred to as explicit timing, have been shown to enhance rates of accurate mathematics responding. The current study was designed to evaluate the effects of session length (i.e., 5 vs. 15 min to write) and temporal cues (i.e., a single initial temporal cue vs. MDTC) on seventh‐ and eighth‐grade students writing assignment rates and writing accuracy. Results showed that the 5 min writing sessions did result in significantly greater rates of accurate responding than the 15 min sessions; however, explicit timing did not significantly alter writing rates or accuracy. These findings suggest that educators can enhance rates of accurate writing by reducing writing session lengths. Discussion focuses on applied implications of providing briefer writing sessions and future research investigating the interaction between multiple temporal cues and assignments.     

Resources In Review

Abstract

The RFF Reader in Environmental Science and Resource Management , edited by Wallace E. Oates. Washington, DC: Resources for the Future. 1999. Paperback. $22.95. ISBN 0-915707-96-9.

Science through Multiple Intelligences: Patterns that Inspire Inquiry , by Robert Barkman. Tucson, AZ: Zephyr Press, Inc. 1999. Paperback. 165 pages. $39.00. ISBN 1-56976-096-9.

Earth Report 2000: Revisiting the True State of the Planet , edited by Ronald Bailey. New York: McGraw-Hill. 2000. Paperback. 362 pages. $19.95. ISBN 0-07-134260-5.

Hard Green: Saving the Environment from the Environmentalists (A Conservative Manifesto) , by Peter Huber. New York: Basic Books. 1999. Hardcover. $25.00. ISBN 0-468-03112-9.

Song of the Meadowlark , by James Eggert. Berkeley, CA: Ten Speed Press. 1999. Paperback. 145 pages. $12.95. ISBN 1-58008-034-0.

The Greening of Planet Earth: The Effects of Carbon Dioxide on the Biosphere , Greening Earth Society, 4301 Wilson Blvd., Suite 805, Arlington, VA 22203-4193; tel. 703-907-6168; fax 703-907-6161; info@greeningearthsociety.org. 1992. Color. 27 min 50 s. $15.00.

The Greening of Planet Earth Continues: The Promise for the 21st Century & Beyond , Greening Earth Society. 1998. Color. 27 min 30 s. $15.00 (or both for $25.00).

Nature's Nation: An Environmental History of the United States , by John Opie. New York: Harcourt Brace and Company. 1998. Paperback. 515 pages. ISBN 0-15-500219-8.

Visions of Paradise: Glimpses of Our Landscape's Legacy , by John Warfield Simpson. Berkeley: University of California Press. 1999. Clothbound. 387 pages. $35.00. ISBN 0-520-21364-5.

Beyond the Land Ethic: More Essays in Environmental Philosophy , by J. Baird Callicott. Albany: State University of New York Press. 1999. Paperback. 427 pp. $24.95. ISBN 0-7914-4084-2.

The Morning After Earth Day , by Mary Graham. Washington, DC: Brookings Institution Press. 1999. Hardcover, 153 pages. ISBN 0-8157-3236-8.

Natural Resource Management and Institutional Change , by Diana Carney and John Farrington. New York: Routledge. 1998. Hardback. 120 pages. $60.00. ISBN 0-415-18604-8.

Green Ink: An Introduction to Environmental Journalism , by Michael Frome. Salt Lake City: University of Utah Press. 1998. Paperback. 204 pages. $19.95. ISBN 0-87480-582-1.     

Media Effectiveness in a Malaysian Park System

Abstract

The effectiveness of three media formats (guides, booklets, and signs) were compared for use on a nature trail at Kinabalu Park, Malaysia. Based on a multiple-choice, cognitive test taken by 1,194 visitors, the guide treatment scores were significantly higher than the other media treatments. There was no difference between booklet and sign treatments, and all the media treatments scored higher than the control group (F _3,1190 = 173.76, α = .05). A second experiment compared only booklet and sign media. There was still no difference in effectiveness (Paired t test, t = 0.22, df = 566, p □ .05). The first language and educational backgrounds of visitors influenced media effectiveness. However, age, sex, residence, interest level, prior knowledge, and prior park visitation did not influence the relatively great effectiveness of the guide treatment. Other factors, such as cost, time, and numbers served, may justify use of media formats other than guides.     

Effects of a prenatal care intervention for adolescent mothers on birth weight, repeat pregnancy, and educational outcomes at one year postpartum

About one-third of adolescent mothers receive inadequate prenatal care, and babies born to young mothers are more likely to be of low birth weight. The objective of this study is to evaluate a peer-centered prenatal care program for adolescent mothers. Pregnant adolescents were randomly assigned to an experimental or control group in a mastery modeling peer-support intervention designed to improve long- and short-term perinatal outcomes. A sample of 282 urban pregnant adolescents (94% African American, 4% Caucasian, 2% other) participated in the study. Participants were recruited from five clinics located mainly in Detroit, Michigan. Participants in the experimental group received care in a small group setting and learned to perform critical measurements with a peer partner during prenatal visits. Participants in the control group received individual prenatal care in the same clinics. Outcome measures included birth weight, years of schooling completed at one year postpartum, planned and unplanned pregnancy at one year postpartum, and employment and school attendance at one year postpartum. Mothers in the experimental group had a lower rate of low birth weight (6.6% vs. 12.5%, p=0.08). The rate of unplanned pregnancy was also lower for adolescents in the experimental group (13.4% vs. 15.9%), although this difference was not statistically significant. Adolescents who participated in the intervention were more likely to have continued their education during the pregnancy and the postpartum year. The mastery modeling, peer-centered, prenatal care program produced some positive pregnancy outcomes for adolescent mothers.     

Reciprocal (and Reductionist?) Newswork

This paper builds upon previous research that examines participatory forms of “reciprocal journalism” and “public communication” led by high school and college students in Miami, Florida, USA, in the fall of 2014. In this study, the students’ assessment of local and national media coverage is used to reveal greater details inherent in examining participatory methods of newswork. Collectively, students said that media coverage emphasis on local and national public officials instead of residents and community members who experience sea-level rise first-hand, combined with a lack of scientific explanation of and solutions for sea-level rise reduced the event's potential to build reciprocal relationships with younger audiences.