Efficient and Effective STEM Curricula
Jonathan Johnston
This paper was completed and submitted in partial fulfillment of the Master Teacher Program, a 2-year faculty
professional development program conducted by the Center for Faculty Excellence, United States Military
Academy, West Point, NY, 2012.
Perhaps the greatest benefit and challenge of the United States Military Academy
curriculum is its adherence to covering both a depth and breadth of topics to produce well
rounded leaders. When complemented with intense military and physical training, the four-year
experience, routinely rated top among undergraduate institutions throughout the world, develops
innovative adults capable of leading small teams in the most uncertain of conditions. However,
with the four-year time constraint amidst several majors offerings, military missions abroad, and
the near continual transitory state of the Army, it becomes exceedingly challenging to balance
the curriculum. The framework often applied for curricular development is Bloom’s Taxonomy,
which suggests progressive objectives among the cognitive, affective, and psychomotor domains.
Though integration of all three domains is critical for the well rounded leaders we produce,
individual evaluation of each domain presents significant areas for improvement. From the
perspective of cognitive development, it appears that the primary role of West Point is to
introduce cadets to cognitive levels of analysis, synthesis and evaluation. That is, graduates must
be prepared to classify situations, generalize similarities to previous knowledge or relationships,
synthesize solutions, and evaluate outcomes (Bloom, 1956), which is far from the cognitive
levels with which they arrive as fourth class cadets. With a four-year time constraint for such a
significant progression, it is critical to develop the most efficient and effective curriculum to
accomplish this objective.
Curricula efficiency has been the sources of several recent studies, particularly in the
international assessment of primary and secondary school STEM programs. The challenge with
children of the primary and secondary age groups is very similar to the challenges faced in
undergraduate curricula, as students struggle to extend previous factual information to more
abstract concepts. One such study, the 2007 Trends in International Mathematics and Science
Study (TIMSS) assessed eighth grade math and science competencies from different countries,
and compared a number of efficiency metrics, from class room sizes to number of topics
covered, to determine similarities between better performing countries. The results of the study
showed a slight relative decline in American math and science performance compared to
emerging Asian curricula, and more importantly, a generally negative trend in the number of
topics covered to performance (NCES, 2009). Furthermore, time spent on homework, funding,
facility capabilities, classroom sizes, and teacher credentials were all in American favor
(Schmidt, 2009). The logical conclusion for several academics was that structural differences in
curricula afforded greater efficiencies within the top performing countries.
The curriculum structure among top performing countries differs significantly from the
American education system. Topic content reduction alone contributed greatly to student math
and science proficiencies. The reduced content afforded teachers more opportunity to cover
material in depth, thereby allowing full derivation instead of cursory introductions. Study results
suggest a range of 60-80% of material coverage in depth optimized the breadth and
understanding of concepts (NCES, 2009). This supports similar undergraduate evaluations that
found the emphasis of material covered to be overly procedural to the exclusion of conceptual
instruction (Curtler, 2008). In addition to increasing the depth of material, the reduction in topics
also afforded teachers the opportunity to better integrate topics. Whereas American teachers
often search for small spaces to briefly revisit often forgotten material for redundancy, Asian
teachers rely on derivations of new concepts to reinforce previously covered topics (Leung,
1987). As a result, those curricula cover the same total number of topics within the secondary
curriculum, but introduce fewer each year (Stevenson, 1990). Another benefit of integrated
curricula was a collaborative environment between faculty that vastly improved faculty
development (Froyd, 2005). This in itself would be invaluable in an institution where the
majority of experience among the faculty is three years or less. Thus, synergistic effects of an
integrated curriculum foster a much more efficient academic program with an improved faculty.
In addition to the timing and integration of topics covered, the methods of instruction
contribute greatly to the effectiveness of a curriculum. Problem-based learning includes a borad
category of teaching methods of varied informational requirements and objectives (Lowman,
2010). Studies suggest an improved perception of relevancy of and interest in a topic as a result
of problem-based instruction (Fielding-Wells, 2008). Though interest in a subject may not
necessarily result in improved competency, several studies suggest a strong correlation between
the two. Comparisons of American and Chinese curricula demonstrate much of Chinese
curricular success is the result of problem-based instruction currently deficient in American
programs (Wang, 2005). In addition to improved interest in the material, there are potentially
several other reasons for the success of problem-based learning. Several argue that problembased learning is the approach most natural to students. Providing students with complex
situations and requiring them to identify the problems, study contextual relationships, develop a
solution, and evaluate its outcome reinforces the method used to solve everyday complex
problems. Such an approach also forces students to evaluate different aspects of a problem with
varying levels of taxonomy (Hiebert, 1996). As stated previously, the approach of covering
different subjects at varying levels of taxonomies creates curricular efficiencies within Asian
programs (Stevenson, 1990). Some academics have evaluated the effectiveness of introducing
realistic problems to students who have no existing background knowledge of the situation. One
study found a significant benefit in improving the adaptability and general competencies of high
school students using such epistemic games. Upon identifying the underlying problem, students
quickly learned contextual relationships through trial and error, and adapted a successful
solution. Furthermore, student interest improved significantly (Shaffer, 2005). However,
educators practicing such methods emphasize the importance of realistic problems, as well as
developing the constraints and restrictions of given situations to achieve the desired learning
outcomes (Azad, 2003). Thus, realistic problem-based learning for students with and without
previous knowledge of the problem provides another opportunity for improving the effectiveness
and efficiency of a time-constrained curriculum.
In conclusion, the author recommends further evaluation of the integration of topics and
problem-based learning within the United States Military Academy curriculum. Though
prioritizing content for reduction may be particularly challenging with the variety of majors, its
benefit in reinforcing core science and mathematics principles within the majors is likely to
exceed the consequences of reduced breadth of topics in those areas. Further assessment of the
timing of courses, particularly pushing specific discipline (majors) courses earlier in the cadets’
academics may also reveal added reinforcement of key topics. While, save for a few branches,
development of specific technical competencies may not be a curricular priority, the problem
based instruction offered within specific disciplines will likely promote better retention of
fundamental topics, and provide students with more practice in naturally solving complex
problems. The end effect is likely to be both a more efficient and effective program for
developing junior leaders.
References:
Azad, Abul KM. Teaching of Control for Complex Systems Through Simulation. Proceedings
of the ASEE/WFEO International Colloquium. 2003.
Bloom, Benjamin S. Taxonomy of Educational Objectives. Handbook I: The Cognitive Domain.
New York: David McKay Co Inc., 1956.
Curtler, Sue. Action Learning Project #9: Getting to the Root of the STEM Problem- Math
Literacy. St. Paul, Minnesota : Luoma Leadership Academy, 2008.
Fielding-Wells, Jill. Student (dis)engagement in Mathematics. The University of Queensland.
2008. Accessed on-line at http://www.aare.edu.au/08pap/mak08723.pdf.
Froyd, Jeffrey. Integrated Engineering Curricula. Journal of Engineering Education. January
2005.
Hiebert, James. Problem Solving as a Basis for Reform in Curriculum and Instruction: The Case
of Mathematics. Educational Researcher. May 1996 vol 25 no. 4. 12-21.
Leung, F.K.S. The Secondary School Mathematics Curriculum in China. Educational Studies in
Mathematics. 1987, Vol. 18, 1, pp. 35-57.
National Council for Educational Statistics (NCES). Special Analysis 2009 International
Assessments. [Online] 2009. [Cited: December 24, 2009.]
http://nces.ed.gov/programs/coe/2009/analysis/tablea08.asp.
Nilson, Linda B. Teaching at its Best: A Research-Based Resource for College Instructors. San
Francisco: John Wiley & Sons, 2010.
Schmidt, William H. The Quest for a Coherent School Science Curriculum: The Need for an
Organizing Principle. [Online] Education Policy Center, Michigan State University. [Cited: 12
19, 2009.] http://ustimss.msu.edu/coherentscience.pdf.
Shaffer, David Wiliamson and Gee, James Paul. Before every child is left behind: How
epistemic games can solve the coming crisis in education. Madison : Wisconsin Center for
Education Research. School of Education, University of Wisconsin-Madison, 2005.
Stevenson, Harold W. Mathematics Achievement of Children in China and the United States.
Child Development. 1990, Vol. 61, 4.
Tiller, Michael. Introduction to Physical Modeling with Modelica. London: Kluwer Academic
Publishers, 2004.
Wang, Jian and Lin, Emily. Comparative Studies on U.S. and Chinese Mathematics Learning
and Implications for Standards-Based Mathematics and Teaching Reform. Educational
Researcher. June, 2005, Vol. 34, 5.
Annotated Readings:
Azad, Abul KM. Teaching of Control for Complex Systems Through Simulation. Proceedings
of the ASEE/WFEO International Colloquium. 2003.
This article emphasizes the user interface in the development of a simulation program to target
desired learning objectives. The author briefly introduces methods for modeling a flexible
manipulator, and then covers in depth his practices in teaching various open and closed loop
control techniques for a flexible manipulator. The modeling aspect alone far exceeds the
technical capabilities of his undergraduate students, and as a result, is completely transparent
within the user interface. The author was very careful in his graphical user interface (GUI)
design to allow students to first identify and classify control system strategies, and through trial
and error, comprehend the effects of different parameters within a given control system, apply
various techniques, and evaluate the performance of each. The simulation environment also
offers users the ability to synthesize and test new control systems on a given model. Though the
connection was not provided by the author, the benefit of such a framework reinforces and
educational framework based on Bloom’s Taxonomy.
Bloom, Benjamin S. Taxonomy of Educational Objectives. Handbook I: The Cognitive
Domain. New York: David McKay Co Inc., 1956.
The original text defining Bloom’s taxonomy levels provides a framework for preparing
academic curricula and assessment throughout a scholar’s development. It classified learning
objectives according to six levels of increasing cognitive complexity: Knowledge;
Comprehension; Application; Analysis; Synthesis; and Evaluation. As material is newly
introduced to students, key learning objectives and assessments must characteristic of
knowledge-based cognitive complexity, such that the students should merely be required to
recall the information. With increasing familiarity of the material, the student should be
expected to demonstrate an understanding of the provided information, typically by organizing
and describing presented ideas. With further presentation, students should be able to apply the
previous knowledge to solve new problems, and possibly analyze given information to establish
relationships and generalizations between problems. Synthesis requires significant cognitive
power, as scholars are able to establish new patterns and solutions based on their analysis of
existing and new problems. This tends to be just beyond the upper limit of undergraduate
students, and is often the result of practical experience within a field. As familiarity further
develops, scholars are able to evaluate ideas and/or solutions by presenting and defending their
opinions. The text augments the six categories with a series of action verbs for each category
that further aid faculty in developing learning objectives and assessments. Faculty implementing
curricula based on Bloom’s Taxonomy would simply select actions verbs based on the students’
familiarity with the material, cognitive ability, and desired outcome. By providing sample
objective verbs for taxonomy levels from novice to expert, the method provides a scalable and
linearly progressive instruction framework. Bloom’s Taxonomy gained considerable traction
within the education communities in the 1980’s, with several scholars since attempting to update
it. One such scholar was Dr. Lorin Anderson, a former student of Dr. Bloom, who believed it
was more appropriate to switch the top two cognitive levels. To him, it was more cognitively
demanding to synthesize a new point of view or solution than to present an opinion about an
existing idea or solution. Nonetheless, Bloom’s Taxonomy is still widely in use in its original
form presented in 1956.
Curtler, Sue. Action Learning Project #9: Getting to the Root of the STEM Problem- Math
Literacy. St. Paul, Minnesota : Luoma Leadership Academy, 2008.
In 2007-2008, Minnesota State Colleges and Universities conducted a series of research projects
on a variety of topics to improve the state undergraduate program. The ninth project involved
assessing the current and desired levels of graduate STEM competencies. While providing
recommendations for faculty professional development and pre-screening exams, the most
actionable recommendations regarded improvements on the instruction within the classroom.
They concluded that current undergraduate curriculum were overly formulaic, with instruction
and learning objective focused on procedural understanding (calculation) to the exclusion of
conceptual understanding (derivation) and problem solving. However, the projects findings left
the reader searching for areas to cut in order to make room the additional required of derivations
and problem solving.
Fielding-Wells, Jill. Student (dis)engagement in Mathematics. The University of Queensland.
2008. Accessed on-line at http://www.aare.edu.au/08pap/mak08723.pdf.
This article studies the effect of inquiry-based learning on student activity and interest within a given
subject. The work cites various examples of the rising disengagement in mathematics directly related to
lack of interest and perceived irrelevancy of the material. Inquiry-based learning was chosen as the
control variable as its aim is to relate the material directly to authentic problems, so as it give the material
context and relevancy. Survey data collected from students between ages 8 and 12 indicated improved
engagement, attentiveness, and decreased frustration with mathematics among students with experience in
inquiry-based instruction. While the study does not assess the mathematical competencies of the students
prior to, during and after inquiry-based learning curricula, it does reflect a positive motivation to learn the
material, which many other studies have concluded as the primary reason for reduced mathematical
competency.
Froyd, Jeffrey. Integrated Engineering Curricula. Journal of Engineering Education. January
2005.
This article identifies the lack of integration between science, mathematics, and engineering
disciplines as a possible area for improvement in engineering curricula. The work investigates
the freshmen and sophomore engineering curricula among several undergraduate institutions,
including student surveys, evaluation of grade point averages within engineering disciplines,
student workloads, student retention, diversity, and faculty collaboration. The study found that
faculty development was the most significant outcome of integrated curricula. Collaboration
among faculty significantly improved pedagogical techniques, and integrated learning objectives
created learning centers within the student community that significantly improved performance
based on the aforementioned metrics. However, the authors also discovered that though most
integrated curriculum programs were successful, they tended to be pilot programs, and the
scalability of integrated programs was limited to well less than an institutionalized curriculum.
The author closes by providing guidelines for assessment and outcome development,
longitudinal studies, alternative approaches, as well as meta-cognitive outcomes assessments to
overcome the scalability challenges of an integrated curriculum.
Hiebert, James. Problem Solving as a Basis for Reform in Curriculum and Instruction: The
Case of Mathematics. Educational Researcher. May 1996 vol 25 no. 4. 12-21.
This article identifies the critical shortcoming of current mathematics education as the distinction
of acquiring knowledge on a subject and then applying it. Existing approaches still suggest that
students must first acquire knowledge to a particular problem, and then apply it, which does not
develop the material sufficiently. The authors recommend a problem-solving approach, but
distinguish between existing problem-based approaches and their model, which is based on John
Dewey’s idea of “reflective inquiry.” After observing methods people ordinarily use to solve
complex, though common, problems, Dewey concluded that people naturally solve problems by
identifying, hypothesizing, studying through trial and error, developing solutions, and reflecting
on the outcome. By presenting situations that allow students to identify, study, and solve
complex problems, the paper contend they provide students with a better understanding of the
material. While some may argue this approach conflicts with Bloom’s Taxonomy and the paper
makes no mention of Bloom’s Taxonomy, it is apparent that cognitive level progression still
occurs, albeit with less structure imposed on the learning process.
Leung, F.K.S. The Secondary School Mathematics Curriculum in China. Educational Studies in
Mathematics. 1987, Vol. 18, 1, pp. 35-57.
This article argues that better performing countries in STEM subjects have more efficient
curricula as a second order effect of reduced content within the top performing secondary school
curricula. The reduced content particularly facilitates instructors the time required for properly
integrating subject material. The American practice of revisiting topics periodically and briefly
for redundancy of potentially forgotten material is contrasted to the spiral approach in better
performing curricula, which integrates concepts at staggered intervals to progress from
descriptive instruction to theoretical instruction. The paper concludes that the spiral approach
thus provides better understanding of the material. Though the author makes no mention of
bloom’s Taxonomy, the success can be attributed to allowing students to progress cognitively
within each subject, thereby improving achieving cognitively progressively learning objectives.
National Council for Educational Statistics (NCES). Special Analysis 2009 International
Assessments. [Online] 2009. [Cited: December 24, 2009.]
http://nces.ed.gov/programs/coe/2009/analysis/tablea08.asp.
This work includes a series of objective international curricular assessments of primary and
secondary education programs. Particularly useful in this report was the evaluation of the extent
to which average national curricula covered abstract concepts. The report ultimately discovered
that American curricula, in general, cover a greater breadth than depth of topics when compared
to other European and Southeast Asian countries. When combined with the council’s “Trends in
International Mathematics and Science Study,” the work correlates eighth grade STEM
competencies inversely to the breadth of material covered within the curriculum. While
providing excellent detail in topic developed within curricula, it also provides generalizations for
curricular development at other developmental levels. According to the report, there is an
apparent “sweet spot” in topics covered, with 60-80% of the material covered in depth instead of
simply introduced, which was the typical percentage of top performing countries. Thus, it
provides the argument to extend a general guideline of 60-80% coverage of topic in depth for
any curriculum.
Nilson, Linda B. Teaching at its Best: A Research-Based Resource for College Instructors. San
Francisco: John Wiley & Sons, 2010.
Though Teaching at its Best provides a framework for objectives-based course
development, cognitive taxonomy, teaching techniques, as well as assessment, it was most
helpful in evaluating problem-solving techniques for use in the classroom. The text presents
three approaches, each with different objectives and requirements: Inquiry-Guided Learning; The
Case Method; and Problem-Based Learning. Inquiry-Guided learning presents students with
open-ended problems, and typically requires cognitive levels within the synthesis and evaluation
categories. As such, it is recommended in multi-semester courses, where students can become
familiar enough with the material to achieve the higher taxonomy levels. Case studies are
perhaps the most flexible method, as they allow the teacher to pose questions ranging from openended problems similar to those used in Inquiry-Guided Learning, to simple case studies
(identified as bullet cases) helpful for allowing students apply previously learned material.
Problem-Based Learning proves most successful when applied with unclear and uncertain
challenges. In engineering disciplines, these typically manifest as semester-long, team design
problems that require students to organize their own teams, research solutions to existing
problems, and develop their own solution. Students benefit greatly from the social interaction
and tend to take better ownership of learning the material. The requirement to recall and apply
existing knowledge to solve the problem ultimately better reinforces the material.
The text also addresses shortcomings specifically within science education directly from
excessive content covered in too little time, as well as a greater reliance of lectures and
memorization over discussion, theory, and creativity. Two of several advisements included
helping students understand the overarching hierarchical knowledge structure of the discipline,
as well as recognizing patterns across concepts, principles, and patterns.
Schmidt, William H. The Quest for a Coherent School Science Curriculum: The Need for an
Organizing Principle. [Online] Education Policy Center, Michigan State University. [Cited: 12
19, 2009.] http://ustimss.msu.edu/coherentscience.pdf.
This article assesses the validity of arguments suggesting that several non-curricular factors have
caused American students to fall behind contemporaries in science and mathematics by the end
of secondary school. The authors reviewed weekly homework requirements, teachers’
credentials, classroom sizes, facility capabilities, and educational funding, and found these
variables were either similar among American and excelling countries, or in American favor.
They concluded by suggesting centralized curricula within the top performing countries provided
better fundamental understanding of the material. The primary difference in the curricula was
the temporal integration of topics; subjects would be continually reinforced once introduced by
their application in their application of more complex subjects.
Shaffer, David Wiliamson and Gee, James Paul. Before every child is left behind: How
epistemic games can solve the coming crisis in education. Madison : Wisconsin Center for
Education Research. School of Education, University of Wisconsin-Madison, 2005.
This is an exceptional article that documents a unique method for devloping thinking skills
among high school students. The works’ fundamental critique of existing education porgrams is
that they are too formulaic, and as a result, are not developing innovative young adults. The
proposed solution is to inject high school students into simulated professional environments
without formal training. The premise of this approach is that students adapt quickly through trial
and error, and as a result, develop the cognitive capacity to quickly assess and perform in
unfamiliar environments. Though not mentioned in the paper, this approach appears to fit well
within Bloom’s Taxonomy, as students are required to analyze, evaluate, and synthesize
solutions to unfamiliar problems based solely on generalizations from existing knowledge.
While the results presented in the article seemed a bit subjective, the article is invaluable in both
identifying a key shortcoming of, and providing an alternative method for, current education
practices.
Stevenson, Harold W. Mathematics Achievement of Children in China and the United States.
Child Development. 1990, Vol. 61, 4.
This work also assesses the improved efficiency of Asian STEM curricula. Its greatest
contribution over the other works listed is a graphic that best depicts the efficiency of a the spiral
approach over typical American curricula applied from primary to secondary education levels,
recreated below. The graphic demonstrates both the fewer concepts introduced annually, as well
as the integration of topics based on increasing complexity, thereby allowing reinforcement of
lower complexity subjects through higher cognitive learning objectives.
Top-Performing Curriculum
American Curriculum
Tiller, Michael. Introduction to Physical Modeling with Modelica. London: Kluwer Academic
Publishers, 2004.
The text is a technical reading on incorporating multi-physics modeling of a system. It provides
a problem-based approach to teaching students the relevant patterns between engineering
concepts across multiple disciplines, including mechanical, electrical, biological, chemical,
thermal, and hydraulic systems. Its particular strength is in simultaneously reinforcing material
at different levels of Bloom’s Taxonomy to demonstrate similarities between disciplines.
Wang, Jian and Lin, Emily. Comparative Studies on U.S. and Chinese Mathematics Learning
and Implications for Standards-Based Mathematics and Teaching Reform. Educational
Researcher. June, 2005, Vol. 34, 5.
This article presents several studies on the differences in math instruction between the United
States and China. The work concludes that Chinese instruction, characteristic of several other
better performing STEM curricula, is predominantly problem-based. Whereas American
mathematics education focuses on acquiring the applying knowledge of different perspectives
individually (computation, algebra, geometry, trigonometry, etc.), Chinese students are taught to
practice and develop proficiency in solving problems through simultaneous solutions involving
several perspectives. As a result, they are better able to connect the concrete, representational,
and abstract concepts of various solution methods.