AC 2008-1277: FRESHMAN-LEVEL MATHEMATICS IN ENGINEERING: AREVIEW OF THE LITERATURE IN ENGINEERING EDUCATION

Wendy James, Oklahoma State UniversityWendy James is a PhD student in the College of Education at Oklahoma State University.Currently she has a fellowship promoting collaboration between the College of Education andOSU's Electrical and Computer Engineering department on an NSF funded curriculum reformproject called Engineering Students for the 21st Century. She has her M.S. in Teaching, Learning,and Leadership from OSU, and her B.B.S. in Mathematics Education from Hardin-SimmonsUniversity in Abilene, Texas. She has taught math and math education classes at both the highschool and college levels.

Karen High, Oklahoma State UniversityKAREN HIGH earned her B.S. from the University of Michigan in 1985 and her M.S. in 1988and Ph.D. in 1991 from the Pennsylvania State University. Dr. High is an Associate Professor inthe School of Chemical Engineering at Oklahoma State University where she has been since1991. Her main research interests are Sustainable Process Design, Industrial Catalysis, andMulticriteria Decision Making. Other scholarly activities include enhancing creativity inengineering education, critical thinking, and teaching science to education students andprofessionals. Dr. High is a trainer for Project Lead the Way pre-Engineering curriculum. Dr.High is involved with the development of an undergraduate entrepreneurship minor at OklahomaState University.

© American Society for Engineering Education, 2008

Page 13.627.1

Freshman-Level Mathematics in Engineering: A Review

of the Literature in Engineering Education

Abstract

Mathematics is part of the life-blood of engineering. While it is one of the essential tools

for doing engineering, it is believed to be one of the confounding variables tripping students in

their learning of the subject. In synthesizing the history of projects and research concerning

freshman-level mathematics as studied by engineering educators, this paper provides a report of

the patterns and themes engineering faculty have identified with algebra, trigonometry, and

calculus and provides a call for topics in future research. Because of a lack of published, peer-

reviewed journals connected to the topic, the exploration of themes in this preliminary report

focused on ASEE conference proceedings papers.

The papers reviewed will be analyzed to answer the following questions: What aspects of

freshman-level mathematics did the authors identify as problematic in their courses? What

interventions or changes served as the impetus for publishing? What literature is being used as

the context and foundation for engineers for their projects? What direction should future research

take?

Introduction

During the 1990s, congress, industry, and forums began to pressure universities to

increase the number of engineering graduates and their knowledge and abilities for the sake of

the US economy. Part of the pressure came from reports calling for reform not only of

engineering education but also of undergraduate education at the nation’s research universities.1

More recently in 2002, a report by Building Engineering & Science Talent (BEST) opened with

the statement,

There is a quiet crisis building in the United States — a crisis that could jeopardize the

nation’s pre-eminence and well-being. The crisis has been mounting gradually, but

inexorably, over several decades. If permitted to continue unmitigated, it could reverse

the global leadership Americans currently enjoy. The crisis stems from the gap between

the nation’s growing need for scientists, engineers, and other technically skilled workers,

and its production of them.2

As a result, engineering faculty have been looking at how and at what they teach in order to

address this quiet crisis.

For the past two years, the Journal of Engineering Education (JEE) has trumpeted the

need to establish engineering education as a rigorous-based field of study. Rising pressure in its

editorials mention the need for engineering faculty to equip and develop the best pedagogical

practices, make adjustments to enhance diversity, collect and employ foundational theory

knowledge, switch from behaviorist to constructivist paradigms in teaching, and provide

educational research that is as rigorous as their engineering-content research.3,4,5,6

Thus, there is

a call for engineering faculty to develop their understanding of teaching and learning theory and

its applicable practices along with developing as engineering-educational researchers.

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In trying to recruit and strengthen engineering programs, many engineering faculty

choose to research and receive grants that investigate mathematics, science, and engineering in

the K-12 system and university-level mathematics courses. Mathematics is seen as the

foundation and life-blood of engineering. While engineering faculty view it as one of the

essential tools for doing engineering, it is also one of the confounding variables tripping students

in their learning of engineering. Engineering faculty are often able to perceive the problems with

algebra, trigonometry and calculus in their students’ coursework.

Students learn mathematics in courses during high school and college. Mathematics

courses at the high school level concern themselves with the subjects of algebra, geometry,

trigonometry, and calculus. Freshman-level mathematics courses at the university level concern

themselves with three of the same topics: algebra, trigonometry, and calculus; however,

occasionally, universities will choose to designate calculus as a sophomore level mathematics

course. Despite how courses are named or organized at the high school or college level, the

mathematics content is very similar, and for the purposes of brevity for this paper, the subjects

of algebra, trigonometry, and calculus will be grouped together and referred to as freshman-level

mathematics.

Rationale and Purpose of this Study

In working with students while teaching their courses, many engineering instructors are

able to know, recognize, and report the mathematical knowledge their course requires as well as

their students’ struggles and weaknesses in remembering or applying the mathematical content or

processes. Because coursework is often divided among disciplines, students’ mathematical

instruction is out-sourced to mathematics courses as a pre-requisite to engineering instruction.

Thus, if NSF and other funding agencies support the work of engineering faculty in investigating

mathematics to develop educational projects and research for possible solutions, student learning

can be better streamlined. This is because engineering faculty have the advantage of recognizing

the mathematical content and processes necessary for their course as well as students’ current

weaknesses in understanding this mathematics. It can be argued that they who receive funding

or acceptance for published works must have identified problems with students’ understanding

and developed strong arguments for possible solutions to mathematical weaknesses.

In synthesizing the literature concerning freshman-level mathematics as studied by

engineering educators, this paper intends to contribute a report of the patterns and themes

engineering faculty have identified with freshman-level mathematics and what they have

attempted to change or research. In providing these summarized themes from the literature, this

paper intends to provide guidance for future research and projects by answering the following

research questions:

� What do engineering faculty perceive and/or identify in their courses as problematic with

students’ understanding of freshman-level mathematics?

� What do the authors suggest as the direction for future research?

The audience for recognizing and understanding the problems engineering faculty have

identified in their courses concerning freshman-level mathematics are high school math teachers,

Page 13.627.3

university math instructors, mathematics-education researchers, engineering-education

researchers, and mathematics curriculum designers.

Methodology

Due to a lack of literature and leads found in PRISM, Journal of Engineering Education

(JEE), and on-line journal web-databases concerned with freshman-level mathematics, ASEE

conference proceedings papers were analyzed. Conference proceedings papers were chosen

because they are known sources for including current projects in improving science, technology,

engineering and mathematics (STEM) education in K-12 and college-level mathematics courses.

In using the conference proceedings papers, the author hoped first to find initial themes

concerning algebra, trigonometry, and calculus as a goal of this paper and secondly to use the

cited references as a spring board for finding and further broadening the literature review into

published journal articles.

For this preliminary report, conference papers from the 2006 American Society for

Engineering Education (ASEE) conference proceedings archives were analyzed.9-31

While the

search engine was used to locate papers with mathematics in the title, it was not used

exclusively. Since some related papers may be tucked into non-mathematical, content-specific

sessions without mathematical words in the title, all titles for papers published for the 2006

conference were examined for possible connections to the purposes of this paper. To be included

in this analysis, the conference paper must have some connection to improving the learning or

teaching of algebra, trigonometry, or calculus. Topics connecting to other mathematics, such as

differential equations, were not included. The mathematics did not have to be the focus of the

paper, but the paper had to serve directly to the purposes of improving the learning or teaching of

mathematics in algebra, trigonometry, or calculus.

Twenty-three papers fit the criteria for inclusion in the analysis and are referenced in the

appendix. Each paper was analyzed for the how it answered the following questions:

1. What aspects of freshman-level mathematics did the authors identify as problematic in

their courses?

2. What did the paper position as the underlying problem?

3. What interventions or changes served as the impetus for publishing?

4. What was studied?

5. What did the paper suggest as direction for future research?

6. What sources of literature did the paper reference?

7. To what degree was the paper and study situated in literature?

The greatest goal while analyzing the papers was to list any problematic areas authors mentioned

about freshman-level mathematics. The goal of the remaining six questions was to explore and

report the assumptions, actions, and future vision of the authors for the use of researchers

building from these initial works. Thus, the second and third questions elaborated on what the

authors perceived as the root of the problem and how they attempted possible interventions,

changes, or studies to address the problem. The fourth question, concerning what was studied,

helped support the second question and was necessary because, for example, while two papers

may evaluate the success of teacher workshops, one may study future student learning and the

other may study teachers’ perceptions of the program on survey responses. The fifth and sixth

questions developed themes for future work, and the last two questions served as gauges for

Page 13.627.4

determining the reliability and strength supporting the claims made by the papers. The last two

questions also served as points of reference in broadening this literature review toward published

articles later.

In classifying references, a 5-point rubric was created to assess the degree to which the

argument and theoretical framework is situated in existing literature and the degree to which

substantial claims are supported by needed references. In this manner, the caliber of the

reliability for the claims and conclusions in the paper can be reported. The logic of each paper

was noted, and the claims and supporting evidence within the logic were analyzed for reliability.

Both the quality and quantity of sources were considered. In research, originality is favored;

however, the audience expects formal research papers, like the ones found as conference papers,

to situate their research projects in existing literature and argue how their project builds from and

extends beyond prior efforts. In this way, research informs itself and systematically develops

cumulative knowledge in order to advance the field. Thus, the papers were first evaluated on

whether the current work was situated within existing literature and then further evaluated on

whether claims were supported by appropriate of evidence within existing literature. The rubric

is as follows:

A. Positions current work within prior work and existing

literature? (Knows what’s been done before?)

B. Backs claims with evidence from prior research or existing

literature?

Yes

No

1: Surface

references

2: Supports

Arguments

3: Lacks some

references

4: Backed by

Literature

0: No

references or

only to self

A.

B.

B.

Figure 1: Assessment Rubric for Gauging Use of Literature

Each paper was first scored whether it couched its work within earlier literature. If it did,

then it was assessed for its ability to back its supporting claims with appropriate literature. If the

paper did not couch its study in the literature, then its ability to support its arguments with

references in the literature were also assessed. The support any particular claim requires can be

moderately subjective and based on the intended audience. The nature of some claims requires

only one valuable reference as evidence; other times, the nature of a claim requires several

references as sufficient support. The rubric was used with the assumption that the intended

audience for these conference papers was people associated with academia, who would require

substantial evidence for all claims and that evidence come from reliable sources.

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Problems Reported with Freshman-Level Mathematics

Because the papers were chosen as having a connection to the teaching and learning of

mathematics, the problems reported with freshman-level mathematics did not have to be central

to the purpose or logic of the overall paper. Thus, the problems found concerning the

mathematics can be different than the overall problem the paper seeks to explore.

Four themes surfaced within reporting the problems engineering faculty describe with

freshman-level mathematics. Two of the 23 papers (9%) concerned themselves with Calculus as

problematic for retention within STEM, and nine papers (39%) addressed students’ inability to

apply and connect mathematical content and/or processes within engineering courses. One paper

(4%) focused on the need for the conceptual understanding of a topic. Eleven papers (48%) left

the problem unstated or unclear.

Both papers concerned with retention in Calculus served to create theory. The first

looked at whether help-seeking behavior could be a possible predictor for success in the course,

and the second looked at whether a web-based tutorial program could serve as a method of

predicting proper student placement into Calculus I.

Of the nine papers attributing the problem to an inability to apply the mathematics,

several reasons were given. As examples, the papers asserted their goals to address “engineering

students [as] better problem solvers” across STEM courses,20

students’ “lack of mathematical

skills,”27

students’ ability of “connecting mathematics with context-rich content and processes in

science and engineering,”23

and students’ lack of “ability to put mathematics knowledge and

skills to functional use in a multitude of contexts.”9 The difficulty with these claims is that all

but two papers lack details and/or evidence to support such claims. The claims lack the specifics

of the contexts in which engineering faculty refer, which is problematic because it leaves the

reader unsure of whether it is mathematical content, mathematical processes, or a combination of

both.

Interestingly, seven of the nine papers argue that mathematical knowledge and processes

are best gained through applications. They argue the need to teach or re-teach mathematics

within applications of STEM topics in order to increase student success. It is unsubstantiated by

theory and supporting research, but it is a valuable theme for the exploration of this paper

because the research question asks what engineering faculty perceive as the problems with

freshman-level mathematics.

Unable to be classified with the others, one paper argued the need for students’

conceptual understanding of infinity based on personal experiences with engineering students.

The paper proposed a framework along with practical activities to promote students’ conceptual

development.

Overall, six papers mentioned specific content knowledge, which is helpful because it

helps readers know what mathematics is used in engineering. Topics included “mathematical

function and covariation,”23

“percent, measurement, area, and perimeter,”13

“matrix

Page 13.627.6

manipulation, conic sections, series, and linear regression,”10

“topics covered in College Algebra

and Trigonometry,”12

“concept of infinity,”22

and “tessellations, curve surfaces, and subdividing

space by solids.”31

All but one of these topics were chosen by either experts or instructors based

on their knowledge that engineers use this content in their field. Only one topic, mathematical

function and covariation, was chosen in direct connection to a study recognizing student

difficulties. Thus, for the purposes of this exploration, content topics are mentioned but only one

paper supported as problematic within engineering coursework.

Proposed Direction for Future Work

The second research question focused on reporting themes across the papers in regard to

what engineering faculty propose as possibilities in future work. Of the 23 papers, fifteen papers

mentioned direction for future work, but all but two detailed future work to be done by the

authors. Of the two that offered future work to its readers and other researchers, both were calls

for larger sample sizes in order to further test the work of the current author.

Thus, there were no themes—neither mathematical nor otherwise—across the papers where

engineering faculty proposed direction to their audience to extend and generate new research

other than the possibility of providing larger sample sizes to current work. This can partly be

explained by the impetus for publishing, which is described later in the paper.

Description of the Papers

In most cases, each paper opened by describing a significant problem of interest to the

audience which would be addressed by the study. Sometimes the problem lay unstated but easily

surmised by the goal of the paper, other times it was stated openly. In suggesting the problems,

several papers ascribed multiple points; however, all but one paper centered its argument on just

one particular problem. Figure 3 shows the patterns that emerged.

Page 13.627.7

The problem mentioned most often (41.7%) was the need for increased student interest and/or

exposure to STEM related topics. The theme of interest and exposure could not be further

subdivided because the papers seemed to assume increased interest would result in further

exposure and increased exposure would further interest. Eight papers (33%) attributed the

problem as students’ weakness in either mathematical content or process skills. Five of the

eight papers did not elaborate as to what weaknesses they observed. Only three papers noted

specific difficulties for students. These included an understanding of mathematical function and

covariation, a conceptual understanding of infinity, and a lack of problem solving ability. Of

the four papers that cited retention as the problem (16.6%), two concerned themselves with

retention in and past calculus, one addressed retention past mathematics courses in general until

the junior year, and one looked at high school retention and also in STEM fields during college.

Lastly, one paper concerned itself with student engagement in group activities based on gender

differences, and the last addressed questioning as a more beneficial sequencing of student

content as a result of how students learn.

It could be easily argued that 5 of the 8 papers attributing the problem to students’

weaknesses in mathematics along with 2 of the 4 papers pertaining to retention could also be

grouped under exposure. The logic of these seven papers follows that if students had further

exposure to mathematics, then their mathematical weaknesses could be eliminated and concern

toward their retention in STEM courses would be reduced. Thus, 17 of the 24 (70.8%) of the

papers could be classified as pertaining to interest/exposure.

Interestingly, only one paper stated the need for students to recognize connections

between STEM topics within the mathematics course; however, this theme seemed to be an

assumption which surfaced in many of the papers. With only one paper attributing the lack of

connections as the primary source for the problem while many other papers seemed to point in

that direction also, it may be possible that engineering faculty believe that exposure to STEM

topics is central to increasing retention and content knowledge. By using this collection of

papers, a reader could strongly argue that engineering faculty believe students who lack

exposure to STEM will lack interest and have weak content knowledge, and this in turn causes

Page 13.627.8

students not to enter STEM related fields or causes them to drop-out of high school because of

high-stakes testing. In believing a lack of exposure to STEM creates the problems with

retention and knowledge of the subject, the authors of the papers indirectly make the statement

that exposure to STEM topics will serve to recruit and build greater learning.

Having stated their problems, the papers then argued the need for their choice of intended

study, intervention, or change in order to address or better understand the significant problem.

In attempting to address the above mentioned problems, the interventions or changes which

served as the impetus for publishing fell into six basic categories with the sixth category

requiring subdivision (see figure 4).

The most common impetus for publishing was professional development for teachers

where the goal was to increase teacher content knowledge and provide the teachers experiments

for their classes. Eight papers addressed professional development for teachers either through

week-long workshops or professional development classes.13,14,19,21,23,25,26,30

Two of these studies

also included interactions with students during the workshop or professional development

days.21,26

Six of the eight papers used teacher development programs as the intervention of

choice in increasing student interest and exposure to STEM topics, and the remaining two papers

were classified as either attributing retention or weaknesses in mathematical ability as the

problem, but both of them could also argue to be classified as attributing the need for increasing

exposure and interest as the problem.

The second largest category was the seven papers which did not center on reporting an

intervention or change. These could be sub-divided into two chategories: research-driven

questions and assertions. Five papers were exploratory and driven by research

questions.10,15,20,21,29

For example, one paper investigated the correlation between help-seeking

behavior and student performance in a large calculus class. Other topics explored were the

ability to predict student preparedness for calculus, problem-solving vocabulary similarities and

Page 13.627.9

differences across all STEM courses, gender performance differences in different group

activities, and the nature of a high school curriculum to prepare for engineering course work. Of

the two papers in the second subcategory characterized as being assertions by the authors, one

was a statement by the author for how infinity should be taught, and the other posed the

usefulness of a tree diagram in helping instructors decide the sequencing student learning should

take. 18,22

All seven of these papers did not attribute interest and exposure as the problem, but

were evenly spread among the remaining themes from the attributed problem.

Of the remaining eight, one paper mapped student learning to teachers hits on their

created web-library,11

two created entirely new courses to address mathematical needs,12,31

three

added activities to existing courses,9,27,28

and two papers addressed activities for students,16,17

specifically one was a week-long summer camp and the other was a science club. Of the two

that created new courses, one paper described a one-hour course studying applications of algebra

and trigonometry and the other described a three-hour course focused on the mathematical skills

needed for architecture. Of the three that added an activity to their existing courses, one included

more quizzes and two included projects in calculus courses. Half of these remaining papers

sought to increase interest and exposure while three sought to decrease student weaknesses in

mathematical ability and one sought to decrease dropouts within STEM related fields.

Knowing the intervention or change for each paper was not sufficient to categorize the

papers. For example, some of the papers which had teacher workshops as the intervention for

the impetus of publishing studied teacher attitudes toward the workshop while others studied

student learning during the school year. Thus, the question of what was studied is necessary for

the analysis.

Of the 23 papers studied, 12 studied student perception and/or learning, 9 studied teacher

perception and/or learning, one studied university STEM faculty, one studied curriculum, and

four did not study anything but instead were declarations of statements or descriptions. The

overlap results from some papers studying multiple sources in order to strengthen its findings.

Of these 23 papers, 15 focused on evaluating or describing an activity or program, five had the

purpose of being a research study, two were papers with the purpose of declaring a particular

statement of interest, and one sought to evaluate an on-line resource (see figure 5).

Page 13.627.10

Appropriate to the discussion is the need to compare evaluative research and basic

research studies. Michael Quinn Patton, a popular scholar on research, makes the distinction,

Evaluative research, quite broadly can include any effort to judge or enhance human

effectiveness through systematic data-based inquiry….The question of whether the

people involved are accomplishing what they want to accomplish arises. When one

examines and judges accomplishments and effectiveness, one is engaged in evaluation.

…Research, especially fundamental or basic research, differs from evaluation in that its

primary purpose is to generate or test theory and contribute to knowledge for the sake of

knowledge.7

Though research hopefully guides choices in future activities, its purpose of developing

knowledge is solely different from evaluation. The nature of the focus and purpose of the papers

divides the papers accordingly.

Of the 15 papers which had the purpose of describing or evaluating an activity or

program, three evaluated the success of adding an activity to a course. All three of which

included scores for student perceptions of the activities and their learning as a result. Two of the

fifteen had the purpose of evaluating newly created courses. Both evaluated the course success

with scores from class grades and surveys concerning student perceptions of the course.

The last ten described teacher workshops, professional development days, a student

science club, and student camps with eight of the papers including evaluations of the activities

using either surveys for perceptions, observations of pedagogical behavior, or tests to evaluate

learning. Three papers assessed the program with teacher perceptions, two assessed teacher

learning and then observed them in their classes, two assessed with both teacher and student

surveys for perceptions, and one assessed by asking teacher perceptions and evaluating later

student learning. Of the eight papers which included evaluations, three papers made broad

statements concerning the results of their surveys, but the rest included the anlaysis formally.

The five research studies were concerned with student performance on a gender basis on

four activities, whether a computer program could be a predictor of success in calculus, whether

student help-seeking behavior correlated with success in calculus, STEM faculty differenes in

uses of problem solving techniques and vocabulary through interviews, and whether students

were prepared in their mathematical content knowledge for engineering courses by interview

teachers, observing their classes, and testing college freshman content knowledge.

Description of the Papers’ Literature

Literature used to situate the context of each paper and to support claims within the

papers were from various sources. Just under half of the sources, 104 of 220, looked at

education in general coming from the disciplines of Cognitive Science, Psychology, or

Education, and 95 of of the remaining 116 were split among Engineering Education,

Mathematics Education, and STEM Education. Figure 6 reveals the types of literature cited.

Page 13.627.11

� 32: Engineering

Education

� Journal – 9

� Presentations - 21

� Book - 2

� 11: Math

� Book - 10

� 36: Math Education

� Paper/Report – 11

� Journal – 16

� Book – 8

� Dissertation – 1

� 104: Educ/CogSci/Psyc

� Paper/Report – 23

� Journal – 53

� Book – 15

� Presentation – 9

� Dissertation - 4

� 27: STEM Education

� Paper/Report – 6

� Journal – 13

� Book – 7

� Presentation - 1

� 10: Other/Unknown

Types of Literature Referenced

Figure 6: Breakdown of Literature Referenced into Categories

While the central theme for all twenty-three 2006 ASEE conference papers relates to

somehow improving freshman-level mathematics, a surprising low percentage (16%) of papers

referenced math-education research and literature, which comes from the discipline that studies

the learning and teaching of mathematics. Also a surprising number of references were reports

or conference papers (18%). Both were often referenced when describing the problem or

supporting arguments which served as the impetus for undertaking the project or paper.

Conference presentations accounted for another 14% of the sources. The ten mathematical

references were mathematics textbooks. Only 41% of the references were published, peer-

reviewed journal articles.

In using the 5-point rubric to assess the degree to which the argument and theoretical

framework was situated in existing literature and the degree to which substantial claims are

supported by needed references, ten of the papers couched their study in literature (scoring a 3 or

4 on the rubric), and 4 of the 10 successfully backed its supporting claims with the needed

references (scoring a 4). Thus, only four papers (17%) offer literature and references of the

caliber needed for being highly reliable and valid. Of the 13 papers that did not situate their

research projects in existing literature and argue how their project builds from and extends

beyond prior efforts, three adequately supported arguments with needed evidence (scoring a 2),

four referenced sources on the surface but not integral to its logic and argument (scoring a 1),

and six had no references or only referenced other sources written by the author of the work

(scoring a 0).

Page 13.627.12

Summary & Discussion

Increasing the number of students entering STEM fields and the quality of STEM

graduates’ knowledge and skills when entering the workforce are practical problems which can

be solved by doing something to eliminate the causes leading to undesired outcomes. The

authors of these articles exampled for this study, with a focus on math, have sought to increase

desired outcomes by professional-development for teachers (39%), adding new components to

current courses (13%), camps and science clubs for students (8.7%), and developing entirely new

courses (8.7%). The most common practical problem (41.7%) was identified as interest and

exposure to STEM topics with another 29.1% of the papers containing the similar argument but

argueing that lack of exposure and interst causes the practical problems of weaknesses in

mathematics and low retention. Thus, 70.8% (17 of 24 topics) of the papers are argued to

increase interest and exposure to STEM topics.

Because engineering faculty have invested their time doing something to eliminate the

undesired outcomes, the purpose of 70% of the papers was to evaluate their efforts. Evaluation

papers are not meant to be generalizable because

good evaluation is quite specific to the context in which the evaluation object rests.

Stakeholders are making judgments about a particular evaluation object and have less

desire to generalize to other settings than a researcher would. …In contrast, because the

purpose of research is to add to general knowledge, the methods are designed to

maximize generalizability to many different settings. If one’s findings are to add to

knowledge in a field, ideally, the results should transcend the particulars of time and

setting.8

One of the leading reasons why it may be appropriate for the papers not to have proposed

direction for future research is the papers were not research oriented but rather evaluation

oriented. Describing the project and noting direction for future work by the authors is

appropriate for papers with purpose toward evaluation. Unfortunately, only two of the five

research studies offered direction for future work. This may be a result of authors feeling that to

offer advice for their readers for future work would undermine the strength and completion of

their own work—or any other multitude of reasons. However, engineering faculty have much to

offer to the field if they were to offer direction for future research stemming from their

participation in either evaluation or research studies, which is often done by educational

researchers in their articles. Engineering faculty also have much to offer in developing the field

of science if they were to complete research studies with the intent of gathering knowledge on

the problems underlieing STEM topics and processes in their courses. Research studies are

intended to be generalizeable, and they offer progress to a systematic study of the field, which in

turn also better informs practice.

Typically, conference papers are not judged as intently as peer-reviewed journal articles

are; however, surprisingly only 4 of the 23 papers (17.4%) situated their work in existing

literature along with the needed references as evidence for supporting claims. Without situating

current work in existing literature, the authors fail to help progress the systematic study of the

field. It is unrealistic, nor recommended, to expect engineering faculty to become experts in the

study of the learning and teaching of mathematics, but if grant money supports their efforts in

mathematcial projects such as professional development for teachers, experts in engineering

Page 13.627.13

should use the practical and theoretical research offered by experts and involve experts in

mathematics-education in creating the framework and direction for their work. Informed

decisions would advance the progress in both fields.

The quality and types of references also are important in progressing the field of study.

References from general education, cognitive science, and psychology comprised 47% of the

sources referenced; whereas, a surprising low percentage (16%) of papers referencing math-

education research and literature. The context of details provided by particular fields of

education, such as mathematics education, as compared to general education cannot be

underestimated. In terms of quality, a surprising number of references were reports or

conference papers (18%) and conference presentations (14%), which comprises a third of the

references. Only 41% of the references were published, peer-reviewed journal articles with

another 14% referencing books.

Another complication with the papers was the lack of detail supporting how mathematics

is problematic within engineering courses. Six mathematics content topics were mentioned,

which is powerful for informing the audience of what mathematics is needed in the field, but

only one content topic, mathematical function and covariation, was chosen having been

supported by evidence from a prior study as being problematic for students. Engineering faculty

have much to offer audiences from mathematics education concerning mathematics use in their

courses. Possible questions include: What mathematics is used in your courses? How is it

used? How is the mathematics in engineering courses used differently than in mathematics

courses? What about mathematics is problematic for students when they are called to apply their

mathematical knowledge and processes? It should be noted, one complication for answering

these questions is they would require qualitative methods because they are inductive and seek to

explore and describe the situation. It is highly recommened for systematic progress within the

field that engineering faculty work to understand the nature of the problem and collaborate with

educators who are trained in qualitative research methods—especially those who are familiar and

trained within research concerning the teaching and learning of mathematics.

An example of a possible research paper which would be of great value to STEM

education was referenced in “Project Pathways: Connecting Engineering Design to High School

Science and Mathematics in a Mathematics Science Partnership Program” by faculty at Arizona

State.23

Mentioned briefly within the paper but offering richness if fleshed out in a full research

study, the authors noted “between disciplines, there are gaps in knowledge, issues in

terminology, and differences in ways of thinking about function and covariation and its

applications.”23

If these “language and notation barriers between math and science teachers”23

were studied and reported, issues with student learning could be identified. Thus, this evaluation

report concerning teacher workshops discovered an issue that could be a very valuable research

topic.

Noted earlier, 70.8% (17 of 24 topics) of the papers argued to increase interest and

exposure to STEM topics. Of these 17 papers, 41% argued that the problem with freshman-

level mathematics is its need to be taught through application. In other words, 77.8% of the

papers which argued the percieved student problem with freshman level mathematics is their

inability to apply mathemtical content and processes across STEM disciplines also aruged

Page 13.627.14

interest and exposure as the overall significant problem. The difficulty with these descriptive

statistics is they do not offer an answer as to why engineering faculty believe applications

increase student learning and understanding of mathematical topics. For future research, this

attitude among engineering faculty should be explored and compared to mathematics-education

research focusing on learning in context.

Thus, possible questions to be answered: Do engineering faculty believe students

practice of applying math in STEM topics increases students’ learning of mathematical content

and/or process skills? Is there a correlation between people choosing engineering as their field

of study and those who enjoy applications of mathematics? In developing their own

mathematical understanding with success, has applications of mathematics been a leading cause

for people choosing engineering as their field of study? What about applications with STEM

topics increases student learning of mathematics? In studying students learning of mathematics,

is there literature to support that increased interest and exposure to STEM topics would increase

student learning and recruitment into STEM related fields? Is the correlation between increased

exposure and gains in retention, recruitment, and learning significant? What does literature

report as the sources of interest for current experts in engineering choosing the field?

Conclusions

It is possible that many of these questions posed here are already within existing

literature. This paper serves to be exploratory and an initial excursion to understand the

problems concerned with freshman-level mathematics and engineering. Overall, the two

research questions were not able to be answered. Engineering faculty have not reported in these

papers with enough detail the problems with students’ understanding of freshman-level

mathematics as identified in their engineering courses, and there were no suggestions for future

research springing from their current work except to repeat their work with larger sample sizes.

This literature lacks specifics of what can be identified as the problems with freshman-level

mathematics. The following three questions remain:

• What mathematics do engineering faculty use in their courses?

• With what aspects of mathematics do engineering faculty see their students

struggle?

• What do engineering faculty observe students doing/saying as they struggle with

the mathematics in their courses?

Despite the lack of success in answering the research questions, this analysis reports

70.8% of the papers display engineering faculty’s perceptions that interest and exposure are the

leading problem to be tackled, and 47% of these papers sought to address the issue of interest

and exposure by conducting professional development programs for teachers, which was 35% of

all the papers in the analysis. In analyzing the nature of the research, 82.6% of the papers

demonstrated neglect in supporting the logic and claims within existing literature, and 70% of

the papers were evaluative in purpose, which does not contribute to the systematic study of the

problems within the field and has little generalizability for other works.

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Engineering faculty seem to participate and get funding for programs and interventions

without identifying the problem with the mathematics in their courses. There seems to be a

belief among the papers when taken together that a lack of exposure to STEM is the problem.

Many of the papers where teachers and students participated in a camp or workshop provide data

reporting positive beliefs in the learning gains from participating in the workshops or camps.

Teachers also report desiring to implement projects from workshops into their courses, but they

report lacking the time. If teachers claim learning from the workshops and desire to implement

the projects into their courses, engineering faculty must be creating useful workshops for the

teachers. Unfortunately, the details of their workshops are not part of the literature, which keeps

a larger audience from benefiting from the content of their workshops. Practical activities and

worksheets are sought by teachers participating in the professional development, but the nature

of the content and purposes of the activities are valuable knowledge within research literature.

There is a need for engineering faculty to note the differences between what engineering faculty

perceive as differences between their current courses and what K-12 schools already do in their

courses.

This paper sought to summarize engineering faculty’s views on their students’ uses of

algebra, trigonometry, and calculus. In the initial search for articles, few articles were found of

use to the topic of interest; therefore, the project was reshaped to analyze only the 2006 ASEE

conference papers for possible themes and leads for further exploration. To broaden the

literature review into published journal articles, the following journals associated with science

and engineering should be explored: International Journal of Engineering Education,

International Journal of Mathematics Education in Science and Technology, Journal of College

Science Teaching, Journal of Research in Science Teaching, Journal of STEM Education, and

Science. Other journals not directly related to the STEM field but containing articles of interest

to this topic include American Journal of Education, Cognition & Instruction, Cognition &

Science, Educational Researcher, Journal of Education, and New Directions for Teaching and

Learning. Lastly, journals directly linked with the study of mathematics should be explored for

authors or co-authors who are faculty within engineering.

In conclusion, five audiences would benefit from both practical and research literature:

high school math teachers, university math instructors, mathematics-education researchers,

engineering-education researchers, and mathematics curriculum designers. There are many

possibilities for future research taken from themes found in this paper. Many possible questions

are mentioned in the discussion section. Overall, there is a need to explore through research

what mathematics is used in engineering courses and how it is used, which would be a valuable

resource for the five audiences in systematically building, studying, and understanding the field.

Some of the research questions would be best explored by a math-educator who can look through

their lens of expertise of common students’ K-12 experience based on current policies on

content, the theories of semiotics, and theories of cognitive development in a social environment.

Other questions are best tackled by engineering faculty, especially those which describe the

nature of student misconceptions and lack of abilities in using mathematics in engineering

courses.

Page 13.627.16

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Appendix The following papers were used for the analysis of this paper and were presented at the 2006 American Society for

Engineering Educators Conference. All papers were retrieved October 2007, from

http://www.asee.org/conferences/v2search.cfm

9. Aroshas, S., Verner, I., Berman, A. (2006). Integrating applications in the Technion calculus course: A

supplementary instruction experiment.

10. Bottomley, L., Hollebrands, K., Parry, E. (2006). How does high school mathematics prepare future

engineers?

11. Bremmer, D., Carlson, P. (2006). An assessment framework for a large-scale, web-delivered resource project

for middle school teacher of math, science, and technology.

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development.

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summer institute participants.

15. Carpenter, J., Hanna, R.E. (2006). Predicting student preparedness in calculus.

16. El-Hakim, O. (2006). Middle school math science engineering summer camp.

17. Fisher, A. (2006). Integration of mathematics, science, and competition to promote engineering educational

development.

18. Grossfield, A. (2006). The roadmap of arithmetic: Summing it up.

19. Hamann, J., Hutchison, L., Moore, A. (2006). Thinking and doing math and science with engineering: A

partnership.

20. Harper, K., Demel, J., Freuler, R. (2006). Problem solving in engineering, mathematics, and physics – part 2.

21. Hunter, K., Matson, J., Elkins, S. (2006). Preparing for emerging technologies: A grass-roots approach to

enhancing K-12 education.

22. Klass-Tsirulnikov, B., Katz, S. (2006). The concept of infinity from K-12 to undergraduate courses.

23. Krause, S., Burrows, V., Pizziconi, V., Culbertson, R., Carlson, M. (2006). Project pathways: Connecting

engineering design to high school science and mathematics in a mathematics-science partnership program.

24. Kukreti, A., Allen, J., Daniel, M. (2006). Gender performance assessment of unique hands-on inquiry based

engineering lessons in secondary mathematics and science classrooms.

25. Kukreti, A., McNerney, P., Soled, S., Obarski, K., Lu, M., Miller, R., et al., (2006) An engineering research

experience for teachers: implementation and assessment.

26. Lumpp, J., Bradley, K. (2006). Math and science across the board: connecting professional development to

classroom practices via an embedded research initiative.

27. Osorno, B. (2006). Student engagement through mathematical applications in electrical power systems.

28. Tapp, B., Farrior, D., McCoy, J., Keiser, L., LoPresti, P., et al., (2006). Enhancing interdisciplinary

ineteractions in the college of engineering and natural sciences.

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29. Thompson, D., Mwavita, M. (2006). Help-seeking behavior among freshman engineering students: A

predictor of calculus performance.

30. Trenor, J., Ruchhoeft, J., Claydon, F., & Long, S. (2006). Improving K-12 teaching through the research

experiences for teachers program at the University of Houston.

31. Verner, I., Maor, S. (2006). Two mathematics courses for architecture college students: from context

problems to design tasks.

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