Inverting the Remedial Mathematics Classroom with Alternative Assessment

Inverting the Remedial Mathematics Classroom with Alternative Assessment

Victor W. Brunsden (Pennsylvania State University-Altoona College, USA)
DOI: 10.4018/978-1-60566-667-9.ch012
OnDemand PDF Download:
$37.50

Abstract

The author present a case-study of a classroom technique that allows assessment and some remediation of several shortcomings of college student skills in mathematics, particularly problem solving. Students are required to write their own notes for class and hand them in at the end for credit. Instead of a traditional lecture format, the first part of class is used to do examples of problems, creating an opportunity to model problem solving strategies for the class. Students then are separated into groups to work on individualized homework sets delivered via WeBWorK and group projects. Although problem sets are individualized, the problem types are the same from student to student, and the groups work on problems from all students in the group. Several issues of implementation are identified. Also discussed are alternative implementations of parts of the strategy, and possible extensions of the strategy to other courses that aren’t based on problem-solving.
Chapter Preview
Top

Introduction

Like many instructors, I have wanted to find better ways to get my students to master the material. It is a common enough wish; students should gain an integrated understanding of the topics, develop the skills for applying the material and gain some ability to use mathematics outside the classroom. Ideally they might also see some of what is so fascinating about mathematics. Without insisting that all students become mathematicians they should master the material and get some idea of what the attraction of the subject might be.

It is frustrating that students have a hard time integrating and applying information from a lecture format class. Though they may appear to understand during class, their performance on quizzes, exams and assignments shows a general lack of root comprehension. While they might be able to mimic template problems from class, changing even small details can throw them completely. Integrating material from more than one topic is more problematic still.

Furthermore, many students seem to lack many fundamental skills, note taking and study skills being two of the most glaring deficiencies. Given this, the difficulties integrating and applying mathematics is no mystery. Add to that the passive nature of a traditional lecture course and it is evident that something needs to be changed for there to be any hope of remedying these lacks. Problems with passive learning are well documented; students have no responsibility for their own learning, nor are they actively involved in their own learning. In a traditional lecture format class it would appear (Silberman 1996) that students may recognize only about one word in three per minute (for an instructor speaking at roughly 150 words per minute).

Over and above this, there is the problem of skill acquisition in mathematics classes; there are certain habits of thought that students need to master and make habitual to effectively learn mathematics. This is similar to language acquisition. There seems to be no better way to do this than to practice, practice, and practice. In a typical mathematics course this is achieved by assigning homework. In a small school setting this becomes difficult to grade as there may not be any graders and the demands on faculty may be such that grading all student homework is impractical.

One approach to the problem of passive learning has been to develop active learning strategies (Silberman, 1996; Fujii, 1997) in which a major portion, if not the entire period is spent with students working on problem solving. As some have noted, this can lead to reduced coverage, a problem in courses that are part of a sequence or where the curriculum is not entirely at the instructor’s discretion. The approach adopted here follows that of Jones-Wilson (2005) in that a portion of the class is devoted to a combination mini-lecture and problem solving modeling session, with the remainder consisting of the students working in groups either on group assignments or on individual homework. It is this inversion of the standard lecture format, wherein notes are taken in class and problems worked on outside the class, which leads to the phrase “inverting the classroom”.

Assigning and grading homework is dealt with by utilizing the web-based assignment delivery and grading system “WeBWorK” (Gage, Pizer & Roth, 2002; Brunsden, 2005). This provides instant feedback to students as to the correctness of their efforts and relieves the instructor of grading each and every student’s assigned homework. Another advantage of WeBWorK is the capability for the instructor to arbitrarily allow many attempts by students at a given problem, where the number can range from a single attempt, to three or four attempts or even infinitely many (which is the default setting for most problems). Other advantages include a vibrant and helpful user community, a large and growing database of problems for various standard undergraduate mathematics courses together with the ability for instructors to add, debug or modify problems at will. In fact there is evidence that WeBWorK does in fact help students achieve mastery (Weibel & Hirsch, 2002).

It should be noted at the outset that all students would benefit from the methods outlined here, nor would the benefits be evenly distributed among those students who might benefit. A best case scenario was that this would help most of those students in the middle, and with care might broaden the middle.

Key Terms in this Chapter

Inverting the Classroom: Refers to an inversion of the standard lecture format wherein notes are taken in class and problems worked on outside the class; instead problems are worked on in the classroom.

WeBWorK: An Internet-based method for delivering homework problems to students over the Internet.

Active Learning Strategy: A major portion, if not the entire class period is spent with students working on problem solving.

Complete Chapter List

Search this Book:
Reset
Dedication
Editorial Advisory Board
Table of Contents
Preface
Christopher S. Schreiner
Acknowledgment
Christopher S. Schreiner
Chapter 1
Melissa A. Dyehouse, John Y. Baek, Richard A. Lesh
This chapter describes a model for evaluating complex organizations or systems. The design assessment model the authors propose is a response to... Sample PDF
Multi-Tier Design Assessment in the Development of Complex Organizational Systems
$37.50
Chapter 2
Hedva Lewittes
In this chapter critical thinking is assessed using two critical thinking learning outcomes that were required for the State University of New... Sample PDF
A Critical Thinking Rubric as the Basis of Assessment and Curriculum
$37.50
Chapter 3
Suzanne Pieper, Erika Edwards, Brandon Haist, Walter Nolan
The purpose of this chapter is to review literature over the past ten years regarding technology tools that are being used in higher education to... Sample PDF
A Survey of Effective Technologies to Assess Student Learning
$37.50
Chapter 4
John Baer, Sharon S. McKool
The Consensual Assessment Technique is a powerful tool used by creativity researchers in which panels of expert judges are asked to rate the... Sample PDF
Assessing Creativity Using the Consensual Assessment Technique
$37.50
Chapter 5
Christine Charyton, Zorana Ivcevic, Jonathan A. Plucker, James C. Kaufman
This chapter discusses creativity assessment as a means for evaluating skills required in higher education. Creativity is assessed in the context of... Sample PDF
Creativity Assessment in Higher Education
$37.50
Chapter 6
Asao B. Inoue
This chapter articulates writing assessment as a technology, theorized with three aspects (power, parts, and purpose), accounting for the ways in... Sample PDF
The Technology of Writing Assessment and Racial Validity
$37.50
Chapter 7
Sheila S. Thompson, Annemarie Vaccaro
The purpose of this chapter is to address epistemological and methodological approaches to assessing assessment. The authors’ intent is to show how... Sample PDF
Qualitative and Quantitative Methods as Complementary Assessment Tools
$37.50
Chapter 8
Teresa Flateby
The development of the Cognitive Level and Quality of Writing Assessment online system is described in this chapter. Beginning with needs identified... Sample PDF
Effects of Assessment Results on a Writing and Thinking Rubric
$37.50
Chapter 9
Barbara D’Angelo, Barry Maid
Outcomes-based assessment provides data for programs to demonstrate student learning as a result of their enrollment in the program and to assess... Sample PDF
Assessing Outcomes in a Technical Communication Capstone
$37.50
Chapter 10
Sonya Borton, Alanna Frost, Kate Warrington
As Jacqueline Jones Royster articulated at the 2006 Conference on College Composition and Communication, English departments are already assessing... Sample PDF
Assessing the Composition Program on Our Own Terms
$37.50
Chapter 11
Joan Aitken
This chapter uses a case study to exemplify one approach to assessment of three instructional delivery formats: (a) online, (b) distance, satellite... Sample PDF
A Case Study of Instructional Delivery Formats
$37.50
Chapter 12
Victor W. Brunsden
The author present a case-study of a classroom technique that allows assessment and some remediation of several shortcomings of college student... Sample PDF
Inverting the Remedial Mathematics Classroom with Alternative Assessment
$37.50
Chapter 13
David A. Eubanks
This chapter describes Coker College’s subjective performance assessment program to rate student thinking and communication skills. It uses a... Sample PDF
A Case Study of Authentic Assessment
$37.50
Chapter 14
P. Tokyo Kang, David Gugin
This chapter reports an outcomes assessment study conducted at the University of Guam. The assessment project was conducted during the 2006-07 and... Sample PDF
Outcomes Assessment in Japanese Language Instruction
$37.50
Chapter 15
Barika Barboza, Frances Singh
This chapter describes an outcomes assessment study completed in a basic composition course at a small urban open admissions community college. The... Sample PDF
Assessing the Effectiveness of a Basic Writing Course
$37.50
Chapter 16
Lorraine Gilpin, Yasar Bodur, Kathleen Crawford
Peer assessment holds tremendous potential to positively impact the development of preservice teachers. The purpose of this chapter is to describe... Sample PDF
Peer Assessment for Development of Preservice Teachers
$37.50
Chapter 17
Charlotte Brammer, Rhonda Parker
In 2002, Samford University began working on a long-term learning assessment plan designed to evaluate its undergraduates’ competencies in written... Sample PDF
Workshops and E-Portfolios as Transformational Assessment
$37.50
Chapter 18
Daniel F. Chambliss
This chapter describes how the trend favoring assessment initiatives of a system-wide scope such as program review and collegiate learning... Sample PDF
A Neglected Necessity in Liberal Arts Assessment: The Student as the Unit of Analysis
$37.50
Chapter 19
Deirdre Pettipiece, Timothy Ray, Justin Everett
Perhaps due to its applicability as a performance of skill sets in virtually all disciplines, writing as a mechanism for measuring student success... Sample PDF
Redefining Writing Reality Multi-Modal Writing and Assessment
$37.50
Chapter 20
Sean A. McKitrick
This chapter introduces methods that can be used to engage faculty in the assessment process, working within a shared governance structure in... Sample PDF
Engaging Faculty as a Strategic Choice in Assessment
$37.50
Chapter 21
Steven M. Culver, Ray VanDyke
There is much in the assessment literature about the necessity of developing a culture of assessment and mandates from accrediting bodies include... Sample PDF
Developing a Receptive and Faculty-Focused Environment for Assessment
$37.50
Chapter 22
John Wittman
This chapter argues that as primary stakeholders in writing program assessment, students and instructors need to be included proactively in... Sample PDF
New Collaborations for Writing Program Assessment
$37.50
Chapter 23
Mya Poe
The study of racial-ethnic group differences on educational tests has yielded a substantial body of research internationally in the last decade. In... Sample PDF
Reporting Race and Ethnicity in International Assessment
$37.50
Chapter 24
Joan Hawthorne, Tatyana Dumova, April Bradley, Daphne Pederson
In this chapter the authors describe a method developed to assess the outcome of a “cultural familiarity” general education goal. Challenges in... Sample PDF
Method Development for Assessing a Diversity Goal
$37.50
About the Contributors