Exploring Patterns in Nonroutine Problems

1997 ◽  
Vol 2 (4) ◽  
pp. 262-269
Author(s):  
Frances R. Curcio ◽  
Barbara Nimerofsky ◽  
Rossana Perez ◽  
Shirel Yaloz
Keyword(s):  
Middle School ◽  
Middle School Students ◽  
Algebraic Thinking ◽  
School Students ◽  
The Past ◽  
Instructional Activities ◽  
Essential Components ◽  
Heterogeneously Grouped ◽  
Nonroutine Problems

For the past several years, we have been examining ways to introduce notions of algebra to our heterogeneously grouped middle school students. Through our experiences of designing instructional activities that integrate nonroutine, nontraditional problems. we found a meaningful way to involve students in exploring and formalizing patterns, conjecturing about the patterns they identify, verbalizing relationships between and among elements in patterns, and eventually generalizing and symbolizing the relationships—all essential components of algebraic thinking (Silver, in press).

The Arcs of Archaeology

1996 ◽  
Vol 1 (9) ◽  
pp. 688-693
Author(s):  
Bonnie S. Spence
Keyword(s):  
Middle School ◽  
Middle School Students ◽  
Real World ◽  
School Students ◽  
The Real ◽  
The Past ◽  
Hands On ◽  
New Ideas

For the past several years, i have sought out opportunities outside mathematics for personal enrichment and enjoyment. These experiences have caused me to become more aware of the connections between mathematics and other areas. As a result, I have begun developing lessons to show my students how mathematics is used in the real world. One summer I joined another teacher and twelve middle school students and decided to brave the eighteen-hour drive from Oklahoma to the Crow Canyon Archaeological Center in Co1tez, Colorado. The mathematical lesson discussed in this article emerged from one week of learning about the Anasazi culture and experiencing hands-on archaeology. Throughout the years, this lesson has been revised and expanded as both students and experience have given me new ideas.

Listening to Middle School Students' Algebraic Thinking

2000 ◽  
Vol 6 (3) ◽  
pp. 156-161
Author(s):  
John P. Smith ◽  
Elizabeth A. Phillips
Keyword(s):  
Middle School ◽  
Middle School Students ◽  
Mathematics Curriculum ◽  
Algebraic Thinking ◽  
School Students ◽  
The Core ◽  
K 12

NO PART OF THE K–12 MATHEMATICS curriculum is more fluid and controversial than introductory algebra. Content and assessment issues lie at the core of this debate: What algebra skills and understandings are important? What kind of evidence suggests that students possess these skills? Neither question can be answered in simple terms; in fact, no single “right” answer may exist for either one.

Take Time for Action: Perimeter or Area? Which Measure Is It?

1999 ◽  
Vol 5 (1) ◽  
pp. 20-23
Author(s):  
Michaele F. Chappell ◽  
Denisse R. Thompson
Keyword(s):  
Middle School ◽  
Middle School Students ◽  
Conceptual Understanding ◽  
Physical Environment ◽  
Mathematics Curriculum ◽  
School Students ◽  
The Past ◽  
Fundamental Understanding ◽  
K 12

During the past twenty years, documents have recommended that the mathematics curriculum include measurement for all grades, K–12 (NCTM 1980, 1989). Indeed, students interact daily with measurement in their physical environment, for example, by finding the distance from home to school, their height and weight, and wall space for posters. Adolescents bring to the classroom varied conceptions of measurement, which may be in the form of basic applications or general formulas. All too often, a fundamental understanding of these ideas is sacrificed while students learn general formulas. This situation is particularly true for attributes of perimeter and area. To what extent do middle school students possess a conceptual understanding of these measurement concepts?

Students Perspectives Of Bullying In Schools

2012 ◽  
Vol 5 (2) ◽  
pp. 117 ◽  
Author(s):  
Bonni Gourneau
Keyword(s):  
Middle School ◽  
Middle School Students ◽  
Review Literature ◽  
School Students ◽  
The Past ◽  
The Future ◽  
Short Messages ◽  
Bullying In Schools

Bullying has proven to be a major problem in our society, one that can no longer be ignored. Unfortunately, every day children of various ages leave schools feeling scared, sad, anxious, and embarrassed, which greatly interferes with their ability to learn and to enjoy their childhood. This paper will review literature on bullying as well as the typical characteristics of the bully, the bullied, and the bystander. This paper will also describe a 2011 bullying survey and program that was presented to 500 middle school students by the author. In the Anti-Bullying Presentation, students were given short messages that could easily be remembered in the future when confronted with bullying situations. For example the scars that bullying leaves are like tattoos, everyone comes to school with a bag of chips; some bags are full and some only have crumbs left, everyone can make a decision on what kind of person they want to be in life, or what shirt they want to wear in life, etc. The term pro-respect was also emphasized with the students. If bullying is ever going to be a thing of the past, parents, students, and teachers must collaborate to overcome this epidemic of a lack of empathy for others feelings amongst todays youth.

Using Mission US

2010 ◽  
pp. 255-273 ◽  
Author(s):  
Karen Schrier ◽  
James Diamond ◽  
David Langendoen
Keyword(s):  
Middle School ◽  
Middle School Students ◽  
Real World ◽  
Thinking Skills ◽  
School Students ◽  
Classroom Implementation ◽  
Historical Empathy ◽  
The Past ◽  
Ethical Thinking ◽  
Design Challenges

In this chapter, the authors describe Mission US: For Crown or Colony?, a history game for middle school students that they collaboratively designed, developed and tested. The authors argue that empathy is an important component of ethical thinking, and that history games, if well designed, can support the practice of empathy. The authors analyze how they designed Mission US to encourage the development of historical empathy and ethical thinking skills. Moreover, the authors also relate their design challenges, and the ethics of representing the past in games. They conclude with real world results from classroom implementation of the game, and design recommendations for creating games for historical empathy.

Do You Understand Your Algorithms?

2006 ◽  
Vol 12 (1) ◽  
pp. 42-47
Author(s):  
Jamar Pickreign ◽  
Robert Rogers
Keyword(s):  
High School ◽  
Middle School ◽  
Middle School Students ◽  
School Districts ◽  
Middle School Teachers ◽  
Algebraic Thinking ◽  
Computational Algorithms ◽  
Successful Completion ◽  
School Teachers ◽  
School Students

Because an increasing number OF school districts requires the successful completion of an algebra course to graduate from high school, many middle school teachers are beginning to focus more attention on introducing algebraic thinking to their students (NCTM 2003). Consequently, it becomes important to consider ways to ensure that these experiences are meaningful and connected to arithmetical experiences from the earlier grades. We believe that presenting middle school students with activities that involve exploring computational algorithms—how and why they work—can contribute to the development and promotion of algebraic thinking.

scholarly journals How Visual Word Decoding and Context-driven Auditory Semantic Integration Contribute to Reading: A Test of Additive vs. Multiplicative Models

2021 ◽  
Author(s):  
Yu Li ◽  
Hongbing Xing ◽  
Linjun Zhang ◽  
Hua Shu ◽  
Yang Zhang
Keyword(s):  
Middle School ◽  
Reading Comprehension ◽  
Middle School Students ◽  
Chinese Character ◽  
Additive Model ◽  
Semantic Integration ◽  
Future Research ◽  
School Students ◽  
Speech In Noise ◽  
Essential Components

Theories of reading comprehension emphasize decoding and listening comprehension as two essential components. The current study aimed to investigate how Chinese character decoding and context-driven auditory semantic integration contribute to reading comprehension in Chinese middle school students. Seventy-five middle school students were tested. Context-driven auditory semantic integration was assessed with speech-in-noise tests in which the fundamental frequency (F0) contours of spoken sentences were either kept natural or acoustically flattened with the latter requiring a higher degree of contextual information. Statistical modelling with hierarchical regression was conducted to examine the contributions of Chinese character decoding and context-driven auditory semantic integration to reading comprehension. Performance on Chinese character decoding and auditory semantic integration scores with the flattened (but not natural) F0 sentences significantly predicted reading comprehension. Furthermore, the contributions of these two factors to reading comprehension were better fitted with an additive model instead of a multiplicative model. These findings indicate that reading comprehension in middle schoolers is associated with not only character decoding but also the listening ability to make better use of the sentential context for semantic integration in a severely degraded speech-in-noise condition. The results add to our better understanding of the multi-faceted reading comprehension in children. Future research could further address the age-dependent development and maturation of reading skills by examining and controlling other important cognitive variables, and apply neuroimaging techniques such as functional magmatic resonance imaging to reveal the neural substrates for the contribution of auditory semantic integration and the observed additive model to reading comprehension.

Sign in / Sign up

Export Citation Format

Share Document