Grounded blends and mathematical gesture spaces: developing mathematical understandings via gestures

This paper examines how a person’s gesture space can become endowed with mathematical meaning associated with mathematical spaces and how the resulting mathematical gesture space can be used to communicate and interpret mathematical features of gestures. We use the theory of grounded blends to analyse a case study of two teachers who used gestures to construct a graphical anti-derivative while working on a professional development task in a calculus modelling activity. Results indicate that mathematical gesture spaces can encourage mathematical experimentation, lighten the cognitive load for students and can be limited by a person’s physical constraints.     

Partially correct constructs illuminate students’ inconsistent answers

We present a view of knowledge construction processes, focusing on partially correct constructs. Motivated by unexpected and seemingly inconsistent quantitative data based on the written reports of students working on an elementary probability task, we analyze in detail the knowledge construction processes of a representative student. We show how the nested epistemic actions model for abstraction in context facilitates following the emergence of a learner’s partially correct constructs (PaCCs). These PaCCs provide added insight into processes of knowledge construction. They are also used in order to analyze and explain students’ thinking in situations where some of the students’ answers were unexpected in light of their earlier answers or inconsistent with earlier answers. In particular, PaCCs are explanatory tools for correct answers based on (partially) faulty knowledge and for wrong answers based on largely correct knowledge.     

RESEARCH SECTION: Nurture groups: a large‐scale,controlled study of effects on development and academic attainment

Nurture groups have contributed to inclusive practices in primary schools in the UK for some time now and have frequently been the subject of articles in this journal. This large‐scale, controlled study of nurture groups across 32 schools in the City of Glasgow provides further evidence for their effectiveness in addressing the emotional development and behaviour problems of vulnerable children. In particular, Sue Reynolds, Principal Educational Psychologist, Maura Kearney, Senior Educational Psychologist, both working in Glasgow City Council Psychological Services, and Tommy MacKay, Professor at the University of Strathclyde and Director of Psychology Consultancy Services, suggest that is the first study to report quantitative gains in academic achievement when the progress of pupils in nurture groups is compared with that of matched children in mainstream classes. This highlights the importance of providing a nurturing context as a basis for promoting children's learning.     

Development of an Augmented Reality Game to Teach Abstract Concepts in Food Chemistry

One of the most pressing issues for many land grant institutions is the ever increasing cost to build and operate wet chemistry laboratories. A partial solution is to develop computer‐based teaching modules that take advantage of animation, web‐based or off‐campus learning experiences directed at engaging students’ creative experiences. We used the learning objectives of one of the most difficult topics in food chemistry, enzyme kinetics, to test this concept. Students are apprehensive of this subject and often criticize the staid instructional methods typically used in teaching this material. As a result, students do not acquire a useful background in this important subject. To rectify these issues, we developed an interactive augmented reality application to teach the basic concepts of enzyme kinetics in the context of an interactive search that took students to several locations on campus where they were able to gather raw materials and view videos that taught the basics of enzyme kinetics as applied to the production of high fructose corn syrup (HFCS). The students needed this background to prepare for a mock interview with an HFCS manufacturer. Students and instructors alike found the game to be preferable to sitting in a classroom listening to, or giving, a PowerPoint presentation. We feel that this use of gaming technology to teach difficult, abstract concepts may be a breakthrough in food science education and help alleviate the drain on administrative budgets from multiple wet labs.     

Predicting Mathematics Achievement of Eighth Grade Students in Germany: An Application of Parts of the Model of Educational Productivity to the TIMSS Data

Parts of the model of educational productivity provided by Walberg and colleagues (e.g., Walberg, 1981) were tested on the basis of the German TIMSS data. Due to its national extensions, the German study allows longitudinal analyses. Structural equation modelling was applied to the data at student level. Findings supported cum grano salis the model of educational productivity. The most powerful predictors were cognitive variables. Nevertheless, motivational determinants, leisure activities and students’ gender were also significant predictors of achievement. Mass media as well as home background, that is, the educational level of parents, their job prestige and their number of books at home, had no direct impact on learning.     

Why Johnny Can't Prove

The one sentence answer to the question in the title is that the ability to prove depends on forms of knowledge to which most students are rarely if ever exposed. The paper gives a more detailed analysis, drawing on research in mathematics education and classroom experiences.This revised version was published online in September 2005 with corrections to the Cover Date.     

Effectiveness of peer tutors vs. resource teachers

The purpose of this study was to determine whether mildly handicapped students working on a one-to-one basis with tutors would show a greater academic gain than students working in a small group with the resource teacher. By using a pretest-posttest control design it was found that after a three-month period, students who had tutors did show a more significant gain in reading (especially in the area of reading recognition). Teachers advised that no more than two tutors from one classroom be assigned to the tutor program, and teachers further felt that they could not supervise more than two tutorial pairs.