This longitudinal study evaluates the impact of a new Algebra 1 course at a High School for language-based learning-disabled (LD) students. The new course prioritized the teaching of relationship graphs and functions as an introduction to algebra. Across three studies, the dissertation documents and evaluates the progress made by LD high school…

This is a study about how graphs of functions of two-variables are taught. We are interested in particular in the techniques introduced to draw and analyze these graphs. This continues previous work dedicated to students' understanding of topics of two-variable functions in multivariable calculus courses. The model of the "moments of…

This paper seeks to show how self assessment facilitates student-centred learning (SCL) and fills a gap in the literature. Two groups of students were selected from a single class in a tertiary educational institution. The control group of 25 was selected randomly by the tossing of an unbiased coin (heads = control group). They were trained in the…

Data from a cough challenge study are displayed with dot charts to demonstrate the importance of graphs in understanding data, principles of graph construction and visual perception. The data are available for use in the classroom.

It is common for both algebra and calculus instructors to use power functions of various degrees as well as exponential functions to examine and compare rates of growth. This can be done on a chalkboard, with a graphing calculator, or with a spreadsheet. Instructors often are careful to connect the symbolic and graphical (and occasionally the…

Today, beginning algebra in the high school setting is associated more with remediation than pride. Students enroll by mandate and attend under duress. Class rosters in this "graveyard" course, as it is often referred to, include sophomores and juniors who are attempting the course for the second or third time. Even the ninth graders…

There are urgent calls for more studies examining the impact of Professional Development (PD) programs on teachers' instructional practices. In this study, we analyzed how grades 5-9 mathematics teachers used graphs to teach mathematics at the start and end of a PD program. This topic is relevant because while many studies have investigated…

This study evaluates the effects of an intervention aimed at improving representational flexibility in linear-function problems. Forty-nine students aged 13-16 participated in the study. A pretest-intervention-posttest design with an experimental and control group was used. At pretest, both groups solved a choice test, where they could freely…

As much as ever before, mathematics teachers are searching for ways to connect mathematics to real-life scenarios within STEM contexts. As students develop skill in proportional reasoning, they examine graphical representations of linear functions, learn to associate "slope" with "steepness" and rate of change, and develop…

A classroom discussion started after a student noticed three days of accumulated trash in the wastebasket and exclaimed, "Wow, look at the trash! If it keeps piling up like this, it will soon be everywhere!" His statement motivated the authors' class to research about the trash, or solid waste, we create and what can we do about it.…

The study aims to identify areas of difficulty in learning about volumes of solids of revolution (VSOR) at a Further Education and Training college in South Africa. Students' competency is evaluated along five skill factors which refer to knowledge skills required to succeed in performing tasks relating to applications of the definite integral, in…

This study reports from a pre-service teacher's online learning and assessment activity on determining variability of two graphical artefacts. Using a critical-analytical perspective to data, the present study indicates that the prospective teachers surveyed showed awareness of relevant subject specific operators and methods; however, these seem…

Ensuring science for all in the classroom requires that all students are afforded ways to grasp key science and engineering practices; however, we know that the practice of "obtaining, evaluating, and communicating information" can be a challenging task for children with high incidence disabilities (NGSS Lead States 2013, p. 15).…

Like many mathematics teachers, the authors often find that students who struggle with a difficult concept may be assisted by the use of a well-chosen graph or other visual representation. While one should not rely solely on such tools, they can suggest possible theorems which then might be proved with the proper rigor. Even when a picture…

Many social scientists have recently commented on the high levels of income inequality in the United States. Indeed, the last time income inequality was as great as it is today was 1928, the year before the stock market crash ushered in the Great Depression. In this article, the authors offer a historical look at income inequality and taxation in…