Enhance Mathematics Learning Research Articles

Scaffolding practices that enhance mathematics learning

It is over 25 years since Wood, Bruner and Ross (1976, Journal of Child Psychology and Psychiatry, 17, 89–100) introduced the idea of ‘scaffolding’ to represent the way children’s learning can be supported. Despite problems, this metaphor has enduring attraction in the way it emphasises the intent to support a sound foundation with increasing independence for the learner as understanding becomes more secure. It has resonance with the widely accepted notion in teaching of construction and the constructivist paradigm for learning. The discussion that follows will characterise some teaching approaches that can be identified as scaffolding, revisiting some of the original classifications, and identifying further scaffolding strategies with particular reference to mathematics learning. Examples will be given from studies relating to geometry learning with four to 6 year olds and to arithmetic learning with older pupils.

Improving Mathematics Teaching and Learning Experiences for Hard of Hearing Students With Wireless Technology-Enhanced Classrooms

Hard of hearing students usually face more difficulties at school than other students. A classroom environment with wireless technology was implemented to explore whether wireless technology could enhance mathematics learning and teaching activities for a hearing teacher and her 7 hard of hearing students in a Taiwan junior high school. Experiments showed that the highly interactive communication through the wireless network increased student participation in learning activities. Students demonstrated more responses to the teacher and fewer distraction behaviors. Fewer mistakes were made in in-class course work because Tablet PCs provided students scaffolds. Students stated that the environment with wireless technology was desirable and said that they hoped to continue using the environment to learn mathematics.

The Constant Feature: Spanning K–12 Mathematics

When I reflect on my many years of teaching mathematics, one of the most enjoyable and fruitful ideas for calculator use came from an article that appeared more than twenty-five years ago (Judd 1976). It gave suggestions for using the constant feature of a simple calculator to enhance mathematics learning. I have used Judd's idea successfully in many classrooms at grades levels ranging from kindergarten through twelfth grade. This article revisits the constant feature for four-function calculators and extends it for use with graphing calculators and computer algebra systems (CASs) for a broad range of topics.

A third way of teaching mathematics to engineers

In recognition of the need to enhance mathematics learning, particularly for under achievers, to reflect the changing pattern of student intake to undergraduate degree courses in engineering, this paper describes a proposed alternative approach, designated the third way, of teaching the mathematics component of such courses. Attributes of the third way, together with characteristics of the existing first and second ways, are discussed. Meta-level knowledge structures and learning actions of students are described and connections between these and learning mathematics are outlined.

Implementing the Assessment Standards for School Mathematics: Enhancing Mathematics Learning with Open-Ended Questions

This composite vignette about Louise Mason is based on a series of classroom observations of five secondary mathematics teachers working to bring some new methods, including the use of open-ended questions, into their assessment practice (Hancock 1994). Although the teachers recognized that opening up the possibilities for responses to questions “really makes the students think,” they encountered difficulties when bringing such questions into their daily practice. As expressed by Ms. Mason, a common concern among the teachers was that using open-ended questions increased the amount of time required for assessment. My consideration of the teachers' dilemma led to some thoughts about the relationship between learning and new forms of assessment that may be helpful to teachers dealing with similar difficulties.

Reply to Fudin's comments on Hudesman, Page, and Rautianen's experiment on the use of subliminal psychodynamic activation to enhance mathematics learning.

Fudin in 1993 raises a number of methodological concerns that he believes limit the generalizability of the 1992 results obtained by Hudesman, Page, and Rautianen. We believe that the conclusions presented are appropriate to the procedures and results.

Research into Practice: Enhancing Mathematics Learning through Imagery

Mathematics is often seen as a subject in which rules are followed and symbols manipulated to achieve “correct” answers. Fortunately, this characterization of mathematics is changing, in large part because of NCTM's initiatives. As we move into the decade of reform in school mathematics, we should explore all options for enhancing mathematics learning. This article considers the role of visual imagery in doing mathematics.

Mathematics achievement, language and cognitive development: Classroom practices in Papua New Guinea

A case study was conducted of mathematics instruction at five sites in Papua New Guinea. Trial instructional materials were developed, teachers received inservice training and implementation was carefully monitored for a six-week period. English and mathematics achievement instruments and eight measures of cognitive development were administered to a sample of 201 students in grades two, four and six. Mathematics and language achievement varied significantly among the five sites. Students at all grade levels exhibited poor application of problem solving skills while showing computation, measurement and mathematical language abilities superior to results previously reported. English reading and measures of conservation and classification competence were highly correlated with mathematics achievement. Correlations between memory measures and mathematics achievement decreased from grade two to grade six while correlations between measures of language and cognitive development and mathematics achievement tended to increase. The results indicated that the non-consumable student textbooks ameliorated to some extent the problems associated with non-native language instruction for the students involved in the study. It was concluded that locally developed textbooks with an appropriate language load would enhance mathematics learning, particularly in remote-rural areas where current teaching conditions and lack of materials interact with poor English skills to create an imbalance in achievement.