Bachman, R. (2013). Shifts in attitudes: A qualitative exploration of student attitudes towards efforts of remediation. Research and Teaching in Developmental Education, 29(2), 14-29.

A summary of students’ attitudes and beliefs toward remediation and supplemental instruction. Bachman discusses students’ perceptions of themselves as math learners given that they are in such courses, and towards remediation in general via a series of interviews. Many common emotions and included fear, embarrassment, and distaste. Common attitudes included  feeling the efforts were a waste of time or an obstacle to their core coursework. Students also often feel remediation is either far too easy or far too difficult. Bachman also emphasizes the importance of the relationship between instructor and student in the minds of students, and the effect it can have on their mathematical affects.  This article is an important look into the beliefs, attitudes, and emotions of students who may find themselves taking or in need of co-requisite courses.

(cross-cutting)

Bonham, B. & Boylan, H. (2011). Developmental mathematics: Challenges, promising practices, and recent initiatives. Journal of Developmental Education, 34(3), 2-10.

An overview of  successful remedial instruction methods and techniques. The authors give a brief overview of the then-current state of remedial education, then give examples of successful and promising methods of remedial instruction. While I will not discuss them here, the article can give instructors ideas of the best practices to use in their remedial and co-requisite course delivery methods.

(cross-cutting)

Bressoud, D. (2015). Insights from the MAA national study of college calculus. The Mathematics Teacher, 109(3), 178-185. doi:10.5951/mathteacher.109.3.0178

An analysis of  many aspects of calculus education. Who takes calculus? What are their attitudes towards mathematics before and after taking calculus? Why do many students quit calculus? Bressoud also looks at demographic information and discusses the affects of students in calculus education. This article can give insight into common mindsets of students in calculus education, and the ways in which educators may help them succeed.

(calculus)

Hesser T. L. & Gregory, J. L. (2016). Instructional support sessions in chemistry: Alternative to remediation. Journal of Developmental Education, 39(3), 22-28.

Hesser and Gregory discuss a successful co-requisite model math course for chemistry students in which students received an extra 75 minutes of instruction per week focused on the math needed for the course. Students were also required to meet with TA’s or attend office hours. Students did not self-select, but rather were assigned to the course based on placement scores. The programme saw great success, but data may be skewed due to the support students having a higher overall attrition rate than students only taking the main course.

(cross-cutting)

Mireles, S., Acee, T. & Gerber, L. (2014). FOCUS: Sustainable mathematics successes. Journal of Developmental Education,38(1), 26-36.

The authors discuss a NCB co-requisite course for college algebra students tested of the course of three summer sessions and two semesters at Texas Tech. The course material was largely remedial mathematics, delivered in a “just in time” approach such that students received remedial instruction on topics before they would be built upon in the main course. The course was a one hour weekly course with additional tutoring requirements. Significant reductions in attrition from the main course were seen.

(college algebra/remedial)

Philipp, R.A. (2007). Mathematics teachers’ beliefs and affect. In Lester, F.K. Second Handbook of Research on Mathematics Teaching and Learning: A Project of the National Council of Teachers of Mathematics (1st ed., Vol. 2, pp.257-315). Information Age Publishing.

Used as a theoretical framework for the terms “affects”, “attitudes” “beliefs” and “emotions” in our study. Philipp defines these as follows:

• Affect - a disposition or tendency or an emotion or feeling attached to an idea or object. Affect consists of emotions, attitudes, and beliefs.

• Emotions - feelings or states of consciousness, distinguished from cognition. Emotions change more rapidly and are felt more intensely than attitudes and beliefs. Emotions may be positive (e.g., the feeling of "aha") or negative (e.g., the feeling of panic). Emotions are less cognitive than attitudes.

• Attitudes-manners of acting, feeling, or thinking that show one's disposition or opinion. Attitudes change more slowly than emotions, but they change more quickly than beliefs. Attitudes, like emotions, may involve positive or negative feelings, and they are felt with less intensity than emotions. Attitudes are more cognitive than emotion but less cognitive than beliefs.

• Beliefs-Psychologically held understandings, premises, or propositions about the world that are thought to be true. Beliefs are more cognitive, are felt less intensely, and are harder to change than attitudes. Beliefs might be thought of as lenses that affect one's view of some aspect of the world or as dispositions toward action. Beliefs, unlike knowledge, may be held with varying degrees of conviction and are not consensual. Beliefs are more cognitive than emotions and attitudes.

(cross-cutting)

Sadler, P. & Sonnert, G. (2018). The path to college calculus: The impact of high school mathematics coursework. Journal for Research in Mathematics Education, 49(3), 292-329.

A statistically dense article exploring the impact of  taking calculus in high school only to retake it in postsecondary education. Highlights an effective “spiral approach” wherein students are exposed to the same concept at increasing levels of difficulty over time, as opposed to the common hierarchical view of mathematics education. Also proves that markers such as high school Algebra 1 scores are effective predictors of performance in calculus even up to six years after completion of Algebra 1. Many ideas from this article could be applied to co-requisite education models in the classroom, and in identifying students who may benefit from taking a co-requisite class

(calculus)