Massachusetts Department of Higher Education
Commissioner’s Working Group on Mathematics Diagnostics for Elementary Teacher Preparation
Working Group Report (Abridged Version)
April 14, 2010
BACKGROUND
In 2007, the Board of Elementary and Secondary Education (BESE) passed new regulations for mathematics subject matter
knowledge for teachers at the elementary level1, issued a guidance document to higher education preparation programs
detailing recommendations for mathematics course content and quantity (suggesting 9-12 credits)2, and developed a new,
separately scored mathematics subtest for the General Curriculum MTEL (03)3 required for initial license for all new
elementary and special education teachers, first administered in spring 2009. Prior to 2007, most elementary and special
education undergraduate teacher preparation programs required at most one appropriate mathematics course and most postbaccalaureate preparation programs required none. Between 2007 and 2009, many of the undergraduate preparation
programs developed new mathematics courses and some proposed new program requirements to meet the demands
presented by the revised MTEL; however, it will be a few years before the new program requirements will take effect. On the
other hand, most post-baccalaureate programs still don’t require any mathematics content courses.
The first test administration for the revised General Curriculum MTEL was in March 2009. The low pass rate (27%) attracted
much publicity and prompted BESE to develop a short-term solution; they dropped the cut score of the General Curriculum
Mathematics Subtest MTEL to allow another 15% of candidates to pass “conditionally” for initial licensure, with the condition
that these candidates will need to retake the mathematics test within five years for the professional license. The BESE will
award conditional licenses for the next three years and then revert to the higher cut score, doing away with the conditional
passing scenario. BESE’s short-term conditional license approach solves the lag time problem with program revisions intrinsic
to the undergraduate case, but the post-baccalaureate case remains problematic. Since half of the State’s new elementary
teachers and nearly all of the special education teachers come from post-baccalaureate programs4 and these programs have
stricter time constraints, they require unique solutions.
While the pass rate on the General Curriculum MTEL is a near-term concern to the Commonwealth, the longer term challenge
of producing enough qualified elementary and special education teachers prompted the Department of Higher Education
(DHE) and the Department of Elementary and Secondary Education (DESE) to sponsor the Joint Convening on Mathematical
Preparation of Elementary Teachers5 at Lesley University in September 2009, bringing together 150 higher education
preparation program administrators and faculty. The meeting highlighted the differences between program requirements in
undergraduate and post-baccalaureate programs and identified some additional strategies that could help increase the pool of
new teachers with the requisite knowledge and skills to teach elementary mathematics well. Feedback from this meeting
indicated the 9-12 credit requirement approach is manageable within undergraduate programs, but not within postbaccalaureate programs, which, as previously stated, are often very tight. Moreover, discussions and feedback from the Joint
Convening indicated an interest for a diagnostic instrument to assist in the advising of students entering post-baccalaureate
programs. Thus, the DHE commissioned a working group of ten members (see Appendix A) to evaluate the potential of five
mathematics diagnostic instruments for assisting the post-baccalaureate admissions/advising process. Support for this work
was provided by the Massachusetts STEM Pipeline Fund.
Working Group
The working group met three times between December 2009 and January 2010 for product presentations from Pearson
Education, Lesley University, ALEKS, Mary DeSouza/MTEL Prep, and a short presentation on the University of Louisville’s
Diagnostic Mathematics Assessments for Elementary Teachers by a member of the DHE staff. Following each presentation, the
group discussed initial reactions and then evaluated the products in depth privately, before completing an evaluation rubric on
each (see Appendix B). At the last meeting, the working group members discussed the strengths and weakness of all products
and developed final recommendations.
The group feels strongly that students preparing to teach at the elementary level, including post-baccalaureate students, must
have attained a level of mathematics content knowledge, as outlined in the BESE guidance document2, before pursuing
mathematics methodology courses, and all students should have the opportunity to take mathematics courses specifically
1
designed for prospective teachers. In order to obtain this level of content knowledge, some post-baccalaureate students may
need to take more time to complete their programs, which is preferable to allowing candidates with inadequate mathematics
understanding to teach the children of the Commonwealth. To this end, the group resisted pursuing a diagnostic that was too
closely aligned with the MTEL and which could be perceived as an MTEL practice test; instead they resolved to recommend
tools which assess student readiness for a mathematics methodology course in a post-baccalaureate program. It is
recommended that readers consider Appendix C, which lists the highlights for each diagnostic instrument.
RECOMMENDATIONS AND CONSIDERATIONS
Recommendation 1: The working group recognizes a strong potential in Pearson Education’s concept for an online
mathematics diagnostic package (including test, feed-back report, and tutorials) to assist post-baccalaureate teacher
preparation programs in advising incoming students about their needs for mathematics coursework based on proficiency in the
areas of number and operations, functions and algebra, geometry and measurement, and statistics and probability. The
working group recommends that DHE ask Pearson Education to develop a commercial product based on the proposed concept
reflecting the objectives and learning outcomes of the aforementioned content areas as outlined in: (1) the Massachusetts
Guidelines for the Mathematical Preparation of Elementary Teachers2, (2) the Conference Board of the Mathematical Sciences
report Mathematical Education of Teachers6, Chapter 3, and (3) General Curriculum MTEL3 mathematics subtest objectives.
Furthermore, they recommend that DHE reconvene the working group to review the final product with a target of September
2010.
Consideration: During working group discussions, the concern was raised that there may be a perceived conflict of
interest with Pearson because the current MTEL vendor is also a division of Pearson. After further clarification from
Pearson Education, it was determined that there are no internal connections between Pearson Education – Higher
Education Division (the division with the concept for an online mathematics diagnostic package) and Pearson –
National Education Systems Division (the current vendor of the MTEL).
Recommendation 2: The working group recommends Pearson Education develop a diagnostic package that incorporates the
following considerations:
a. It should include test questions of three types: procedural, conceptual, and multi-step (MTEL–like), with the
understanding that a student’s performance on questions in each category will signal different advisement
possibilities, as outlined in Appendix D. Furthermore, Pearson’s writing team should consider questions like
those contained in the University of Louisville test.
b. It should include a robust feedback report (see ALEKS), with components for students and components for
program administrators. The student feedback should contain an annotated answer key, information about
what questions were right and wrong, an assessment report about indicated degree of competency on each of
the content strands, and a study guide tailored to individual performance.
The administrator feedback report should focus on the student’s performance broken down by content strand
(see endnotes 2, 3, and 6).
Furthermore the working group members recommend that the DHE and DESE provide links on appropriate websites to
information about Pearson’s online diagnostic package so that individuals not associated with a higher education preparation
program may also directly access the diagnostic package from Pearson.
Recommendation 3: The working group members assert that colleges and universities should use the diagnostic package to
determine whether a student is prepared to enroll in an elementary mathematics methodology course in a post-baccalaureate
preparation program and not as a substitute for a needed mathematics course.
Recommendation 4: The working group recommends that the Lesley University diagnostic be reevaluated in a year to see if
sufficient revisions have been made and that the diagnostics from ALEKS, De Souza, and University of Louisville be no longer
considered.
2
Appendix A - Working Group Charge and Members
Charge:
The Commissioner’s Working Group on Mathematics Diagnostics for Elementary Teacher Preparation will respond
to a call from the higher education community for help in assessing the mathematical preparation of new
students in post-baccalaureate elementary teacher preparation programs via a common mathematics diagnostic
instrument. The Working Group will evaluate five available diagnostic instruments and submit recommendations
to the Commissioner of Higher Education about their usefulness for this purpose and related applications.
Working Group Members:
•
Katherine Ariemma, Doctoral Student, Lynch School of Education, Boston College
•
Jeff Beaulieu, MEd., Senior Lecturer, Mathematics and Statistics Department, UMass Amherst
•
Donna Beers, Ph.D., Professor, Mathematics and Statistics Department, Simmons College
•
Debra Borkovitz, Ph.D., Associate Professor, Mathematics and Science Department, Wheelock College
•
Mary Caddle, Ph.D. Candidate, Department of Education, Tufts University
•
Volker Ecke, Ph.D., Assistant Professor, Mathematics Department, Westfield State College
•
Margaret Kenney, Ph.D., Professor, Mathematics Department, Boston College
•
Rebecca Metcalf, Ph.D., Assistant Professor, Department of Mathematics and Computer Science,
Bridgewater State College, Working Group Chairperson
•
Maura Murray, Ph.D. Associate Professor, Mathematics Department, Salem State College
•
Steve Rosenberg, Ph.D., Professor, Mathematics and Statistics Department, Boston University
Working Group Facilitator:
•
Eileen Lee, Director for Educator Policy, Department of Higher Education
3
Appendix B - Diagnostic Evaluation Rubric
4
Appendix C – Highlights of Diagnostic Instruments
Pearson Education
Lesley University
ALEKS (Assessment and LEarning
Mary DeSouza/MTEL Prep
University of Louisville


in Knowledge Spaces)

Web-based MTEL
preparation course and
stand-alone book designed
specifically to provide
support for teacher
candidates taking the
General Curriculum
Mathematics subtest.


Online course offers lessons
& quizzes, along with final
exam and email access to live
tutor.
Series of four “paper and
pencil” diagnostic exams
which assess students
understanding of 4 types of
mathematical knowledge:
memorized, conceptual
understanding, higher-order
thinking/application, and
pedagogical content
knowledge.

Online course currently
offered by UMass Boston’s
Division of Corporate,
Continuing, and Distance
Education ($400 per
student).
Tests include both multiple
choice and open response
questions which are closely
aligned with national
recommendations for the
preparation of elementary
teachers2.

Product developers are
willing to make adjustments
based on customer need.
Exam must be returned to
testing center for grading and
feedback.

Significant discount likely for
other high volume market.
Price per exam is $10, total
$40 for all 4 exams.

Described at:
http://louisville.edu/educatio
n/research/centers/crmstd/d
iag_math_assess_elem_teac
hers.html



Concept of a “canned” online
diagnostic instrument
equipped with individualized
study plan tutorials.
Concept is similar to
MyMathTestTM, currently
used for college algebra and
precalculus markets.
Enormous question bank for
test and tutorial questions
available. (Pearson has the
ability to use questions from
three popular textbooks with
e-resources in MyMathLabTM
they publish for
undergraduate math courses
for preservice teachers Billstein, et al.7; Long, et al.8;
O’Daffer, et al.9)
Permits individuals to work
with diagnostic/tutorial
independent of a particular
prep program or facilitator.

When final product is
developed it will be available
directly to students for $10
(access for a semester).

Described at:
http://www.mymathtest.co
m/support/mmt/product_inf
o.html




In-house diagnostic package
recently developed by faculty
with significant experience
teaching mathematics
courses for elementary
teachers and currently used
for advising purposes at
Lesley.
Product links a new online
diagnostic assessment with
existing online MTEL prep
workshops. Students can
participate in online
workshop, along with face to
face workshop.
Product developers are
willing to make adjustments
based on customer need.
Cost for access is currently
$300 for non-Lesley students
(subscription length is
variable, depending on when
next MTEL is scheduled).

Web-based artificially
intelligent assessment and
learning system designed for
K-12 students.

Test is integrated with selfstudy tutorial component.

Product has been piloted in
some teacher preparation
programs in state as a course
supplement for basic
computation practice.

Cost ranges from $20 (access
for a month) to $40 (access
for a year).

Described at:
http://www.aleks.com/about
_aleks



Described at:
http://www.lesley.edu/soe/c
ertification/gc_mathsupport.
html

Note: Product is not currently
available, but Pearson Education
has begun development with
September 2010 target date for
availability.
5
Described at:
http://ccde.umb.edu/testpre
p/mtel
Appendix D – Diagnostic Advising Paths: Inputs and Outputs
Input: Diagnostic Question Type
Output: Advisement Possibilities
•
Procedural items in the following areas
 Number and Operations
 Functions and Algebra
 Geometry and Measurement
 Statistics and Probability
•
Students who are unable to demonstrate mastery of
procedural computations in these areas may be advised to
consider taking a developmental mathematics, college
algebra, statistics, and/or geometry course.
•
Conceptual items in the following areas
 Number and Operations
 Functions and Algebra
 Geometry and Measurement
 Statistics and Probability
•
Students who are unable to demonstrate mastery of
conceptual understanding in these areas may be advised to
consider taking a college algebra, statistics, and/or geometry
course.
•
Or, they may be advised to take content courses designed for
elementary teacher preparation, depending on their level of
competency.
•
Or, they may be advised to practice the available tutorials,
depending on their level of competency.
•
Students who are unable to demonstrate mastery of multistep problems requiring problem-solving and advanced
reasoning may be advised to take courses designed for
elementary teacher preparation.
•
Or, they may be advised to practice the available tutorials,
depending on their level of competency.
•
Or, they may be advised to take an MTEL prep course to
brush up problem solving and mathematical reasoning,
depending on their level of competency.
•
Or, they may be advised to take the MTEL and enroll in a
methodology course.
•
Multi-step items involving elementary school
mathematics content, which require
 Problem-solving abilities
 Mathematical reasoning
6
Appendix E – Endnotes
1
Board of Elementary and Secondary Education. (August, 2009). Regulations for Educator Licensure and
Preparation Program Approval. Massachusetts Department of Elementary and Secondary Education:
(http://www.doe.mass.edu/lawsregs/603cmr7.html?section=06).
2
Massachusetts Department of Education. (2007). Guidelines for the Mathematical Preparation of Elementary
Teachers. Malden, MA: Author. (http://www.doe.mass.edu/mtel/MathGuidance.pdf).
3
Massachusetts Department of Elementary and Secondary Education. (2008). Massachusetts Test for Educator
Licensure® (MTEL®) Test Objectives Field 03: General Curriculum Test Objectives.
(http://www.mtel.nesinc.com/PDFs/MTELobjs_newfld03_2.pdf), 10 – 15.
4
Data obtained from the Massachusetts Department of Elementary and Secondary Education’s 2008 Annual
Report on (Teacher Preparation) Program Completers.
5
Massachusetts Department of Higher Education, (September, 2010). Mathematical Preparation of Elementary
and Special Education. Meeting at Lesley University:
(http://www.mass.edu/meetings/MathResources20090930.asp).
6
Conference Board of the Mathematical Sciences. (2001). The Mathematical Education of Teachers. Providence RI
and Washington DC: American Mathematical Society and Mathematical Association of America.
(http://www.cbmsweb.org/MET_Document/PDF_Files/chapter3.pdf), 15 – 24.
7
Billstein, R., Libeskind, S., & Lott, J. (2010). A Problem Solving Approach to Mathematics for Elementary Teachers.
Boston: Pearson Education.
8
Long, C., DeTemple, D., & Millman, R. (2009). Mathematical Reasoning for Elementary Teachers. Boston:
Pearson Education.
9
O’Daffer, P., Charles, R., Cooney, T., Dossey, J., & Schielack, J. (2008) Mathematics for Elementary School
Teachers. Boston: Pearson Education.
7