Curriculum Research Group

The Math You Need, When You Need It: Online Modules That Remediate Mathematical Skills in Introductory Geoscience Courses By Jennifer M. Wenner, Helen E. Burn, and Eric M. Baer

Pilot studies of an NSF-funded project called The Math You Need When You Need It (TMYN; http://serc.carleton. edu/mathyouneed) reveal that online, asynchronous learning modules are effective at remediating students’ quantitative skills in introductory geoscience in both community college and university settings. TMYN uses a just-in-time and necessity approach to mathematical learning, with online modular tutorials assigned prior to students encountering a quantitative concept in a geoscience context. Preand posttest scores show that TMYN modules used in conjunction with a geoscience course successfully increase student’s quantitative skills. Survey responses indicate that students perceive the modules as helpful. Variation in student completion rates across the pilots illustrates challenges to effective implementation of online learning modules and suggests that instructional methods and students’ perceptions (and instructor reinforcement) of task value and expectancy of success may influence student interaction with TMYN and, thus, effective mathematics remediation. Class size and focus, concepts covered, and grading stakes seem to have a negligible influence on student completion and success rates, illustrating TMYN’s flexibility in a variety of instructional settings. The modular, asynchronous, and online approach of TMYN represents a promising solution to the challenge of teaching quantitative material that is contextually framed in a science context. 16

Journal of College Science Teaching

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ncreasingly, students arrive in college underprepared to use mathematics in introductory science courses. Estimates of the percentage of entering students needing remediation in mathematics vary. Self-report data suggest 15%–22% of first-year students entering postsecondary institutions in 2008 registered for a remedial math course (Planty et al. 2008). Similarly, a study of a single community college found that 65% of first-time students took a remedial mathematics course and roughly half passed (Fike and Fike 2008). High demand for remedial mathematics courses is disturbing given evidence that success in mathematics shapes interest in STEM disciplines, particularly in young women, and leads students to choose math and science majors (Betz

The Math You Need, When You Need It and Hackett 1983; Nora and Rendon 1990; Sadler and Tai 2007; Starobin and Laanan 2005). If STEM disciplines are to increase the number of well-qualified majors with significant quantitative skills, collegiate departments must explore ways to “level the playing field” by addressing incoming students’ diversity in mathematical skills and preparation. Many universities address students’ diverse quantitative skills by attaching mathematics prerequisites to introductory science courses. However, this solution may be ineffective given the wide range of mathematics skills used throughout the sciences—from arithmetic and geometry to trigonometry—and the challenges students face in transferring mathematical knowledge across academic domains (Bransford, Brown, and Cocking 1999). Furthermore, attaching prerequisites causes students to incur additional costs and may present a barrier to enrollment in introductory science courses. Students’ diverse and often weak quantitative skills have been a concern of geoscientists for decades (Macdonald, Srogi, and Stracher 2000; Manduca et al. 2008; Wenner et al. 2009). Because of declining enrollments in the 1970s and 1980s, quantitative content was stripped from introductory geoscience textbooks in favor of more qualitative and descriptive treatment (Shea 1990). Although the outcome—public perception of geoscience as descriptive—resulted in increased enrollments, removing quantitative content from introductory classrooms poorly serves future geoscience majors by masking the reality that geoscience is data rich and quantitative (Manduca et al. 2008). The resulting dearth of high-quality, quantitative content has recently led to a concerted effort by geoscience faculty to reintroduce numeracy into geoscience courses and to provide quantitative exercises and teaching methods that are steeped in best practices (e.g., http://serc.carleton.

edu/quantskills/; Wenner et al. 2009). To provide student support for quantitative learning, we recently piloted an NSF-funded project called The Math You Need, When You Need It (TMYN)—online, studentcentered resources designed to remediate introductory geosciences students’ differential mathematical skills (NSF# DUE-0633402, -0633755, -0920583 and -0920800; Wenner, Baer, and Burn 2008). Results of piloting TMYN suggest that online modules are one solution to the challenge of teaching to students with differential mathematics skills and can be effective in a variety of settings. This paper presents pilot results and discusses challenges to effective implementation of online learning modules, including factors that influence student engagement in online, modular support.

TMYN design and conceptual framework The idea for TMYN modules originated as a joint project between Highline Community College (HCC) mathematics and geoscience faculty to support students with insufficient quantitative skills in a Physical Geology class. Because no individual mathematics course comprehensively covered the mathematical skills needed, faculty compiled a one-credit course that ran concurrently with the geoscience course. When a significant increase in performance and retention resulted (Baer et al. 2002; Baer et al. 2005; Baer, Wenner, and Burn 2008), an online version of this course was created in an effort to serve more students. However, because the impact on retention and mastery was not clearly replicated with the online version, we undertook TMYN as a redesign effort aimed at developing more effective online materials to teach quantitative concepts in a wide variety of introductory geoscience contexts. Successfully engaging students in online, out-of-class mathematics

modules can be difficult. Today’s students are increasingly utilitarian and tend to value assignments by the extent to which they are relevant to their future careers or will impact their grade (Astin 1998; Brint 2002; Cox 2009). At the same time, students often associate mathematics with anxiety and failure, which can negatively influence engagement (Barkley 2010; Wigfield and Eccles 2002). Without intentionally addressing incentives such as grading stakes and the alignment and timing of online modules, student engagement may be low (Vonderwell and Zachariah 2005). Alternatively, the modules may be used as a means of cramming, leading only to surface learning (Phillips, Baudains, and Van Keulen 2002). TMYN is a set of modular online student resources that review remedial mathematical concepts in the context of the geosciences. Providing context for quantitative skills seems to be essential to helping students to succeed in introductory geoscience courses (e.g., Bailey 2000). To date, there are seven modules that address quantitative skills associated with geoscience concepts (Density, Graphing, Hypsometric Curve, Rearranging Equations, Slopes, Trigonometry, and Unit Conversions). Each online module contains an explanation page (introducing the quantitative concept and associated algorithm), a set of practice problems with worked answers (Figure 1), and an instructor page (providing instructors with relevant information). The modules can be used in any order and are designed to provide review of quantitative concepts that will be used in a preexisting geoscience course. TMYN resources remediate quantitative skills using online/multimedia theory and pedagogical research in mathematics. As the name implies, The Math You Need, When You Need It uses a just-in-time approach. Similar to the manufacturing notion of just-in-time inventory, a just-intime approach sequences applicable Vol. 41, No. 1, 2011

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skills immediately prior to concept formation or problem solving and has been successfully used in mathematics (Kaseberg 1999; Mueller and Brent 2004) and other academic and workplace education textbooks (Brandenburg and Ellinger 2003; Modesitt, Maxim, and Akingbehin 1999; Phillips 2005). Each TMYN module places a mathematical concept in multiple geoscience contexts, drawing on Harel’s (1998) necessity principle—that students are better poised for deep learning when certain mathematical skills or concepts

are necessary to tackle the problem at hand. An online, asynchronous, justin-time and necessity approach to infusing quantitative concepts into introductory geosciences courses illustrates immediate application of a quantitative skill and provides opportunities for repeated exposure to mathematical concepts, enhancing long-term retention (Steen 2004; Stevens 2000; Kenyon 2000). This approach can increase student motivation to engage with the modules by bolster-

ing perceptions of relevance and usefulness (Barkley 2010; Wigfield and Eccles 2002). In addition, teaching mathematics in a geoscience context can improve transfer of learning by exposing students to contexts and discourse (words, tools, representations) that they may also encounter when applying mathematics in future coursework (e.g., Adams and Hamm 1998; Bailey 2000; Bransford, Brown, and Cocking 1999; Evans 1999; Ganter and Barker 2004; HallWallace 2000; Lutz and Srogi 2000; Salomon and Perkins 1989).

FIGURE 1 Screenshots of student portions of the unit conversions module in The Math You Need When You Need It. Students are instructed to begin on the explanation page to learn the algorithm for completing similar problems. At the bottom of the page, there is a link to the practice problems, geologically relevant exercises in at least three contexts. Practice problems have worked answers (using the algorithm on the explanation page). On completing the practice problems, students may take a post-module quiz (at WAMAP.org; not shown) or link to other practice problems. Other quantitative topics may be found at http://serc.carleton.edu/mathyouneed.

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The Math You Need, When You Need It TMYN modules are multimedia presentations involving the juxtaposition of words, tools, and representations, with information presented in more than one format (e.g., words and pictures; Mayer 2001). Designing effective multimedia online resources requires reducing the cognitive load or limits on working memory that are major impediments to learning (Cooper 1990; Sweller 1994). TMYN modules use three main principles of effective multimedia presentations: that students learn better (1) from words and pictures than from words alone (multimedia principle); (2) when corresponding words and pictures are presented near rather than far from each other on page or screen (spatial contiguity principle); and (3) when extraneous words, pictures, and sounds are excluded (coherence principle; Mayer 2001). The modules adhere to these three principles.

Description of pilots TMYN modules were piloted at HCC and University of Wisconsin Oshkosh (UWO) by eight different instructors (Table 1). The following two models were used: 1. Stand-alone course: At HCC in 2008–2009, students who received less than 80% on a skills assessment took a concurrent, standalone, one-credit course taught by a separate instructor. Students chose either an online or face-to-face version of the class. The online version used four to five TMYN modules, and students received a separate grade for the course based on online quiz scores. The course spanned the first half of the quarter, meaning that in some cases the mathematical skills were not immediately applied to geoscience. 2. Integrated with geoscience course: In all pilots at UWO and in the spring 2010 pilot at HCC, TMYN modules were integrated

into a geoscience course, mainly as prelab assignments. Modules were assigned approximately two to five days before the quantitative concept arose in a lecture or laboratory setting. Students completed the modules outside of class, and their scores on the postmodule quiz accounted for a small fraction of their grade. Table 2 includes detailed information about the eight pilots. The eight pilot instructors varied in their familiarity with the modules, history of including quantitative content in their courses, and experience with teaching with technology. To explore the flexibility of TMYN, the pilots varied in the number of modules used, grading stakes, and the geoscience topics connected to the quantitative concepts. In addition, the pilots differed in the temporal proximity of module completion to skill use in class and instructors introduced modules at different times during the course.

TABLE 1 Courses that used TMYN with aggregated engagement and remediation data.

School/course

Semester/ quarter offered

UWO Physical Geology

Fall sem. 2008

UWO Physical Geology UWO Physical Geology

Spring sem. 2009 Spring sem. 2010

Students enrolled

No. of posttest attempts allowed

Completion rate

Average change pre- to posttest (percentage points)

154

1

90%

28**

13.64

.000

166

unlim.

95%

42**

28.08

.000

164

unlim.

84%

28**

13.67

.000

t

p

UWO Environmental Geology

Fall sem. 2008§

180

1

67%

19**

6.77

.000

HCC Physical Geology

Fall qtr. 2008§

5

1

40%

−33

2.24

NA


Spring qtr. 2009

10

1

80%

18*

4.98

NA


Fall qtr. 2009§

5

1

60%

−13

0.96

NA

HCC Shaping the Earth

Spring qtr. 2010

23

1

83%

32**

7.88

.000

Note: Italics indicate stand-alone course. TMYN = The Math You Need When You Need It; UWO = University of Wisconsin Oshkosh; HCC = Highline Community College; sem. = semester; qtr. = quarter; unlim. = unlimited. *p ≤ .05 **p ≤ .01 § Instructor included significant quantitative material for the first time.

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Evaluation and results The success of TMYN hinges on two factors: (1) student participation/completion and (2) successful quantitative skill remediation. Remediation of mathematics with TMYN was evaluated in two ways: (1) improvement of students’ skills and (2) students’ perceptions of the modules. Because successful remediation requires students to

complete the modules, these two indicators of success are largely inseparable, yet they varied significantly across the pilots. Following, we present completion rates and skills remediation data. We supplement our quantitative findings with qualitative data collected through faculty interviews, student surveys, and focus groups.

Completion rates Table 1 shows overall completion rates (percentage of students completing all or all but one module). In pilots using the integrated model, completion rates were generally strong, ranging from 67% to 95%, averaging 84%. Completion rates for pilots using the stand-alone model were generally lower, ranging from 40% to 80%, averaging 60%. It is

TABLE 2 Individual modules and aggregated pilot data with associated student attitudinal survey results. Attitudinal data includes positive responses to the statements: “I found this module helpful” and “I found this module difficult.”

School/implementation description University of Wisconsin Oshkosh (UWO): UWO is a 12,000 FTE, 4-year public comprehensive university located in northeast Wisconsin. Introductory geoscience courses are taught as large (>170 student) generaleducation lecture sections with small (24 student) laboratory sections. Implementations at UWO: All students in a course were required to complete a pretest, three to five TMYN modules and associated postmodule quizzes as “prelab” assignments. Students’ pretest scores did not affect their course grade. Posttest attempts varied from one (to measure effectiveness of modules) to unlimited (to encourage mastery). Scores on postmodule quizzes made up a small fraction of the students’ overall grades in the course.

Course and semester (total enrollment) Physical Geology F08 (n = 154)

Modules used (in sequential order)

Students who completed module

% of students responding with agree or strongly Completion agree to questions about: rate helpfulness

difficulty †

Unit Conversions

151

98%

†

Plotting Points

142

92%

58%

5%#

Best Fit Line

140

91%

47%#

17%#

Rearranging Equations

132

86%

63%#

33%#

Physical Geology S09 (n = 166)

Unit Conversions

160

99%

76%

82%


160

99%

87%

54%

Graphing

156

96%

73%

29%

Physical Geology S10 (n = 164)


156

95%

84%

59%

Density

146

89%

89%

56%

Unit Conversions

134

82%

91%

77%

Slopes

139

85%

69%

62%

Graphing

134

82%

78%

21%

Slopes

175

97%

46%#

44%#


166

92%

49%#

35%#

Unit Conversions

119

66%

34%#

61%#


614

—

86%

57%

Unit Conversions

564

—

84%

80%

Graphing

571

—

76%

25%

Environmental Geology F08§ (n = 180)

Aggregated data for most-used modules in integrated course

#

Note: Italics indicate stand-alone course. FTE = full-time equivalency; TMYN = The Math You Need When You Need It; F = fall; S = spring. † Attitudinal questions inadvertently left off postmodule assessment. # Before spring 2009, surveys were a 5-point Likert scale (with an option to choose “neutral”) instead of the forced Likert scale used after spring 2009. § Instructor included significant quantitative material for the first time.

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The Math You Need, When You Need It noteworthy that most students opted for the face-to-face version of the stand-alone course, leading to small class sizes in these pilots. In all pilots, student comments suggest that instructions for module use and connections to geoscience were sufficient to complete the assignments. Interview data coupled with completion rates suggest in-

structors who had more experience teaching quantitative concepts had higher completion rates, as did instructors who directly encouraged students to complete modules and who referred to modules when covering associated geoscience topics in lecture or lab. In the stand-alone model involving two separate instructors, survey and interview data suggest

that explicit connections between the one-credit stand-alone course and the associated geoscience course were not often made clear to the students, particularly given the temporal gap between module completion and skill use. In addition, many students in the stand-alone model expressed resentment at having to take, and to pay for, an additional course.

TABLE 2 (Continued)

School/implementation description Highline Community College (HCC): HCC is a 5,600 FTE community college located in a suburb of Seattle, Washington. Physical Geology is a low-enrollment (24-student) course that meets the lab-science requirement for an associate’s degree. Implementations at HCC: Only Physical Geology students (except S10) who did not receive 80% on the pretest were required to complete TMYN online as a one-credit, stand-alone course taught by a separate instructor. The online course included three to five TMYN modules in the first half of the quarter, though the mathematical skills were not always addressed immediately in the concurrent course. The course grade was calculated from scores on postmodule quizzes and affected a student’s GPA. In S10, implementations were more like UWO— all students were required to complete TMYN and had one attempt to complete the online quiz.

Course and semester (total enrollment) Physical Geology (F08)§ (n = 5) Physical Geology (S09) (n = 10)

Physical Geology (F09)§ (n = 5) Physical Geology (S10) (n = 23) Aggregated data for mostused modules in stand alone course

% of students responding with agree or strongly agree to questions about:

Students who completed module

Completion rate

Unit Conversions

3

60%

0%#

67%#

Hypsometric Curve

1

20%

†

†

Plotting Points

3

60%

67%#

0%#

Density

3

60%

67%#

33%#

Unit Conversions

8

80%

63%

63%


7

70%

57%

29%

Density

8

80%

88%

50%

Hypsometric Curve

7

70%

57%

14%

Plotting Points

8

80%

88%

38%

Hypsometric Curve

5

100%

40%

20%

Unit Conversions

5

100%

20%

20%

Plotting Points

4

80%

25%

25%

Density

4

80%

67%

33%

Slopes

21

91%

64%

65%

Density

16

70%

85%

29%

Hypsometric Curve

16

70%

53%

47%


7

—

57%

29%

Unit Conversions

16

—

42%

42%

Graphing

15

—

57%

32%

Modules used (in sequential order)

helpfulness

difficulty

Note: Italics indicate stand-alone course. FTE = full-time equivalency; TMYN = The Math You Need When You Need It; F = fall; S = spring. † Attitudinal questions inadvertently left off postmodule assessment. # Before spring 2009, surveys were a 5-point Likert scale (with an option to choose “neutral”) instead of the forced Likert scale used after spring 2009. § Instructor included significant quantitative material for the first time.

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Table 2 reveals that, in six of eight pilots, completion rates for individual modules dropped throughout the semester by an average of 17 percentage points, from a low of 3 percentage points (UWO, spring 2009) to a high of 31 percentage points (UWO, fall 2008).

Skills remediation In all implementations, pretests were given at the beginning of the course, and postmodule quizzes were completed online through Washington Mathematics Assessment and Placement (WAMAP) software (www. wamap.org). The pilots varied in whether students were allowed single or multiple attempts at the postmodule quizzes (Table 1). Posttest scores were calculated by totaling student points on all post-module quizzes and dividing by the total points possible on these quizzes. If students failed to take a postmodule quiz, a score of 0 was given for that quiz. Whereas pretest and posttest questions were not always identical, they tested a student’s ability to apply identical quantitative concepts and were equivalent in difficulty. For each pilot, we used the paired t-test to test the null hypothesis of no change between pre- and posttest. Table 1 shows a statistically significant increase (p < .01) in students’ pre- to posttest scores across all pilots that used the integrated model. When students were allowed only one chance at the postmodule quiz, mean pre- to posttest increases ranged from 19 to 32 percentage points. In the two pilots in which students were allowed unlimited attempts, average posttest scores were 28 and 42 percentage points higher than pretest scores. A limitation of our findings is the lack of uniform posttest administration and the inability to correlate posttest results with other course assessment. Additionally, in pilots that allowed unlimited attempts, our analysis did not explore the number of attempts a student took to complete the posttest. Nonetheless, the overall positive pre– 22


post change, regardless of method of administration, provides evidence that the modules are effective in remediating mathematics when integrated with a geoscience course. The results in stand-alone models were mixed and ranged from a pre–post increase of 18 percentage points to a decrease of 33 percentage points. Small sample size precluded conducting a test of significance and should be considered when interpreting these results.

Student perception At the end of each postmodule quiz, students were asked to respond to the statements “I found this module . . . ” (1) helpful and (2) difficult, using a forced-response Likert scale (1 = strongly disagree, 4 = strongly agree). During the initial pilots, we included a “neutral” category, which was omitted in later pilots. Table 2 shows student responses to helpfulness and difficulty questions, by pilot and module type. To facilitate presentation, we aggregated the data across pilots and focused on three modules that were common to most of the pilots: Unit Conversions, Plotting Points/Graphing, and Rearranging Equations. Student survey responses show that 77% of students in the integrated model and 56% in the stand-alone course found these modules helpful. For individual modules, students in the integrated model generally indicated that they found modules more helpful (Table 2; Rearranging Equations, 86%; Unit Conversions, 84%; Graphing, 76%) than did those students in the stand-alone course (Rearranging Equations and Graphing, 57%; Unit Conversions, 42%). Perception of difficulty is similarly higher for students in the integrated course (53%) than in stand-alone versions (32%). Students found Unit Conversions most difficult (80%, integrated; 42%, stand alone), followed by Rearranging Equations (57% and 29%, respectively) and Graphing (25% for both models).

Discussion TMYN’s just-in-time (Kaseberg 1999) and necessity approach (Harel 1998) to online modules presents one effective solution to the challenge of teaching introductory geoscience quantitatively. Positive changes in pre- to posttest scores (Table 1) and students’ perception of helpfulness (Table 2) demonstrate that TMYN is successful in remediating mathematics skills in both a community college and regional university setting. Our findings suggest that successful use of TMYN hinges less on institution type, course characteristics, number of quantitative concepts covered, or grading stakes and more on instructional methods that lead to higher levels of student participation and completion. Higher levels of student completion resulted when instructors gave adequate introduction to modules, including clear directions for navigating the modules and testing websites, and reinforced to students that modules provided sufficient practice to prepare them for the postmodule quizzes. We believe these instructional methods increased students’ self-efficacy or expectancy for success, which can positively influence students’ motivation to complete a task—in this case, the modules and postmodule quizzes (Barkley 2010; Wigfield and Eccles 2002). Furthermore, there was a trend toward higher and sustained levels of student completion in pilots in which instructors made immediate and explicit connections between TMYN modules and course topics and regularly reinforced to students that completing the modules would help them succeed in the course. Together, this may have heightened students’ perception of the usefulness and relevance of the modules, which bolstered student motivation to complete the modules (Barkley 2010; Wigfield and Eccles 2002). No clear trend appeared between grading stakes and completion rates in the pilots. We maintain, however, that modules should at least

The Math You Need, When You Need It modestly affect students’ course grades in order to inspire completion (Astin 1998; Brint 2002; Cox 2009). The pilots using the stand-alone model were more variable and generally less successful than those using the integrated model, particularly in terms of completion rates. Students’ perception of module helpfulness may have been diminished because, in contrast to the integrated pilot, mathematical skills were not always immediately applied in the course. The immediacy of application, in combination with concerns about additional student costs and the challenge of coordination between two instructors, needs to be considered in weighing the merits of configuring TMYN modules into a stand-alone course as opposed to integrating them into a single geoscience course. In six of eight pilots, completion rates decreased as the course progressed (Table 2). We speculate that students’ perceptions of the value of the modules may diminish unless reinforced by the instructor. Moreover, as the semester progresses, students make “cost” choices about how to spend their time and energy (Wigfield and Eccles 2002) and may decide that TMYN is too costly. Alternatively, it is possible that students with adequate mathematical skills choose not to complete the modules, or students who find modules difficult may lose their expectancy for success, which can negatively influence completion rates. Future research should explore the influence of student preparation, module difficulty and perceived cost of completion on module completion rates using multivariate analysis, controlling for pretest scores, time spent on modules, and prior computer experience.

Conclusions Given the increasing need for college-level mathematics remediation and the lack of appropriate prerequisite courses, TMYN (http:// serc.carleton.edu/mathyouneed) represents a promising solution to

the challenge of teaching quantitative material that is contextually framed in introductory geoscience courses. Just-in-time and necessity approaches that sequence mathematics concepts followed closely by associated geoscience context successfully remediated students’ quantitative skills at two distinct institution types in diverse courses. Our results suggest that the success of TMYN hinges on instructional methods that reinforce to students the value of the modules to their learning and that bolster students’ perception that they can successfully complete the modules and online quizzes. TMYN may also speak to students’ difficulties in transferring mathematical knowledge across academic domains; thus, TMYN’s online modular approach to remediating quantitative problem solving could serve as a model for addressing similar challenges in a wide variety of science disciplines. n Acknowledgments This work was supported by the National Science Foundation’s Course, Curriculum and Laboratory Improvement program under grants DUE-0633402, -0633755, -0920583 and -0920800. The authors are grateful for the support provided by the Science Education Resource Center at Carleton College, especially by Cathy Manduca, John McDaris, and Sean Fox. In addition, we thank several anonymous reviewers for suggestions that greatly improved this paper.

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