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The California State University / University of California

Mathematics Diagnostic Testing Project



NOVEMBER 2 0 0 4


MDTP's New Prealgebra Readiness Test Available

In August MDTP's newest test became available to California teachers. The MDTP Workgroup developed the Prealgebra Readiness test (PR40A04) in response to many requests for a test that could be given to students beginning a prealgebra course, meaning a course immediately preceding a first-year algebra course. Teachers may request copies of the test from their regional site by phone or using the MDTP website. The PR40A04 is most appropriately given near the beginning of a prealgebra course. The suggested time for the 40-question, multiple-choice test is 45 minutes. Students should not use calculators while taking the test. The test has six topics: Integers; Fractions, Decimals, and Percents; Proportional Reasoning; Literal Symbols; Measurement of Geometric Objects; and Co-ordinate Plane, Graphical Representation, and Data Analysis. Question (item) specifications are based upon some of the California mathematics standards for grades 4 through 6. Each item is written to address a specification, but may require additional knowledge. MDTP test result reports identify the overall strengths and weaknesses of classes in the topics of the test. They also provide detailed information about the performance of the class on each item. Teachers can use this information to identify areas that will require more intensive review and to identify possible sources of common student misunderstandings. The test results include topic scores for each student. These may be used to help direct the review or other study for individual students, possibly in groups formed based on common needs or in tutorial settings. If several teachers in a school administer the PR40A04 at about the same time, MDTP recommends they share their results with each other to help plan ways to address any identified weaknesses. PR40A04 results can stimulate collaboration between Prealgebra teachers and teachers of more elementary mathematics classes at the same school or at feeder schools. The favorable reactions of many of the 273 middle school teachers who administered a field test version of PR40A04 in fall 2002 or fall 2003 provide some evidence of face validity-- which means that the test looks like it tests what it should. The statistical analyses of the field tests provide evidence of content validity. Strong correlation of test scores with future measures of student achievement is a powerful indication of the appropriateness of a diagnostic test. The following table lists correlation of test scores for the PR test given to students near the start of a 7th grade prealgebra course in fall 2002 with some later measures. Teachers were asked to evaluate each student's preparation for algebra near the end of their prealgebra course and after about six weeks in their algebra course.

Measure Algebra Readiness Test Teacher Evaluation Teacher Evaluation Geometry Readiness Test Date Spring 2003 Spring 2003 Fall 2003 Spring 2004 Number 908 Correlation 0.83

751 762 737

0.64 0.66 0.78

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MDTP Relations with Schools Office 2341 Math Sciences Bldg., Box 951555 Los Angeles, CA 90095-1555

Nonprofit org. U.S. Postage PAID UCLA

Continued from page 1

The strong correlation with the Geometry Readiness test 20 months later not only shows that the PR40A04 tests concepts and skills needed for success in Algebra I, but also shows that a solid understanding of mathematics taught in Grades 4­7 is essential for success in Algebra I. In fall 2000 the MDTP workgroup decided to develop a Prealgebra Readiness test. By the end of spring 2001, preliminary item specifications had been developed and three middle school mathematics teachers had agreed to work on the new tests as consultants. During summer 2001 the workgroup and the consultants wrote and refined 50 items that were field-tested in prealgebra classes in 2001-2002. During summer 2002, the results of those field tests were used to select 18 items, refine 7, and write 15 new items to create the first version of a PR test. That test was field-tested in 2002­2003. Those results were used to significantly modify 10 of the items on this test and replace three others. The other 27 items on the 2003 field test were essentially the same as items on the 2002 field test. The results of all the field tests were used to compose PR40A04. Thirty-four of the 2003 field test items appear on the released form. One distractor of another item was changed to improve that item for PR40A04. Each of the remaining five items was replaced with an item that had been field-tested earlier and that fit better in the released test. We are grateful to the hundreds of teachers who participated in the three field tests and the three middle school consultants for their essential help. We also appreciate the longstanding financial and other support of The California State University, the University of California, and the California Academic Partnership Program.


Upcoming Users' Conferences

Why not plan to attend a users' conference this year? Those who have done so recently expressed the feeling that it was invigorating to meet other teachers and build new professional relationships. Consider bringing a colleague from your department so that you both can share the excitement. CSU Fullerton: Wednesday, January 19, 2005 3:30­8:00 p.m. Contact: Christine Brackett (714) 278-2691 [email protected] CSU San Bernardino: Spring 2005 Contact: Tiffany Hughes (909) 880-7670 [email protected] UC Berkeley: Wednesday, March 2, 2005 2:15­6:30 p.m. Contact: Judie Welch (510) 642-0846 [email protected]

[Note: This is a joint conference held with other math projects on the Berkeley campus.]

UC Davis: Wednesday, November 17, 2004 4:00­7:00 p.m. Contact: Trish Ramos (530) 752-2015 [email protected] UC Davis: Math Workshop Wednesday, March 23, 2005 4:00­7:30 p.m. UCLA: Effective Mathematics Instruction: Issues and Answers Saturday, March 12, 2005 8:30 a.m.­1:30 p.m. Contact: Jade Chien (310) 825-8030 [email protected] UC San Diego: Thursday, March 24, 2005 3:30­7:15 p.m. Contact: Jean Forsythe (858) 534-3373 [email protected]

Tom's Teasers

Tom Walters, former UCLA Site Director

1. Three math teachers play a game with the understanding that the loser is to double the money of the other two at the end of each game. After three games, each has lost just once, and each has $24. How much did each have to start? 2. A young algebra teacher is twice as old as her favorite student was when she was as old as the student is now. She is 24. How old is the student? 3. Fermat requires us to provide the remainder when 5^999,999 is divided by 7.

Mathematics Diagnostic Testing Project


This newsletter has been provided with the support of the Regents of the University of California, the Trustees of the California State University, and the California Academic Partnership Program. Produced by the MDTP Relations with Schools Office 2341 Math Sciences Bldg., Box 951555 Los Angeles, CA 90095-1555 Relations with Schools Coordinator: Barbara Griggs Wells See the MDTP Website:


Answers to last issue's Teasers: 1. Two squares are removed from opposite corners of a checkerboard, leaving 62 squares. Can the checkerboard be filled with 31 dominoes, each domino covering two adjacent squares? Answer: No; the opposite corners are the same color and each domino must cover one square of each color.

2. Which is larger, the 10th root of 10 or the cube root of two? Answer: Simply raise each to the 30th power, yielding 1000 and 1024 respectively. 3. The game of toe-tac-tic has the same rules as the standard game with one exception. The first player with 3 markers in a row loses. Can the first player always win? Answer: Yes; by taking the center square and then mirroring the second player's moves.


Spanish versions for all MDTP tests are available at the AR, EA, GR and SR levels, and for MR45A92 and PC40 test versions.

Test Level/ Test Name PR Prealgebra Readiness

Description Assesses some concepts needed for success in a course immediately preceding a first-year course in algebra and subsequent success in that first-year algebra course. This test should be given near the beginning of a course immediately preceding a first year algebra course. Tests readiness for success in a first course in algebra. The calculator-prohibited versions require more arithmetic facility.

Calculator Prohibited PR40A04 0814004

Calculator Optional

Calculator Required

AR Algebra Readiness

AR50/90 0715090 AR45A00 0714500

AR50X92 0775092

EA Elementary Algebra Diagnostic

Tests readiness for success in a second-year algebra course. Appropriate when the second course follows immediately after the first-year algebra course and students have not been exposed to a year of geometry. Tests readiness for a geometry course. Includes some informal geometry students should have encountered prior to and during algebra. Would most likely be given near the end of Algebra I or near the beginning of a geometry course. Tests readiness for success in a second-year algebra course that follows a geometry course. Measures first-year algebra and geometry topics critical for success in second-year algebra. Appropriate near the end of geometry or near the beginning of second-year algebra. Tests readiness for success in the second year of an integrated algebra curriculum. This test was based on the common content of two of the integrated curricula in use in California. Tests readiness for success in the third year of an integrated algebra curriculum. This test was based on the common content of two of the integrated curricula in use in California.

EA50A90 0315090

Scientific EA45X91 0374591

GR Geometry Readiness

GR45A93 0414593

GR45X94 0474594

SR Second-Year Algebra Readiness

SR45A93 0314593

Scientific SR45X94 0374594

IS Integrated Second Year Readiness

IS45A00 0414500

IT Integrated Third Year Readiness

IT45A00 0314500

MR Mathematical Analysis Readiness

Assumes two years of algebra and a year of geometry in preparation for a precalculus course. It has significant geometry content. It would ordinarily be given near the end of the prerequisite courses or near the beginning of the next course, typically trigonometry, precalculus, or mathematical analysis. Tests topics needed for success in a first calculus course. The CR versions contain more emphasis on geometry. Suggested times are 60 minute for 40 question tests and 90 minutes for tests with 55 or 60 questions. PC versions are still available on a limited basis. PC40 versions are available in Spanish. Designed for students in a first calculus course requiring graphing calculators. Students need to decide when to use a graphing calculator. The test can help identify strengths and weaknesses of students' mathematical skills and abilities and can provide information about students' facility with graphing calculators. Suggested time is 60 minutes.

MR45A92 0214592

Scientific MR45X94 0274594

CR/PC Calculus Readiness

CR40A97 0114097 CR55A97 0115597

Scientific CR40X96 0174098 CR55X96 0175596

BC Beginning Calculus

Graphing BC30X97 0173097

MDTP tests were developed to provide students and teachers with diagnostic information. This information can help students identify specific areas where additional study or review is needed. It can help teachers identify topics and skills that need more attention in courses. MDTP tests are diagnostic, not comprehensive; they should not be used as final exams or as the only placement measure. MDTP provides a notebook of written response materials to supplement most of its tests.

MDTP Regional Sites


Berkeley Alameda, Contra Costa, Marin, Napa, San Francisco, San Mateo, Sonoma, and Stanislaus counties.

Emiliano Gomez Judie Welch [email protected]

(510) 642-0752 (510) 642-0846 Fax: (510) 642-6726

Chico Butte, Colusa, Del Norte, Glenn, Humboldt, Lake, Lassen, Mendocino, Modoc, Nevada, Plumas, Shasta, Sierra, Siskiyou, Tehama, Trinity, and Yuba counties.

Jack Ladwig [email protected]

(530) 898-6367

Davis Alpine, Amador, Calaveras, El Dorado, Placer, Sacramento, San Joaquin, Solano, Sutter, and Yolo counties.

Phil Knox Trish Ramos [email protected]

(530) 752-2021 (530) 752-2015 Fax: (530) 752-7706

Fresno Fresno, Inyo, Kern, Kings, Madera, Mariposa, Merced, Mono, southern San Benito, Tulare, and Tuolumne counties.

Peter Tannenbaum Diana Carmichael [email protected]

(559) 278-4029 (559) 278-4773

Fullerton Orange County, and schools in Los Angeles and Riverside counties near Fullerton.

David Pagni Christine Brackett [email protected]

(714) 278-2671 (714) 278-2691 Fax: (714) 278-3972

Los Angeles Los Angeles and Ventura counties except for schools near Fullerton.

Barbara G. Wells Jade Chien

(310) 206-8360 (310) 825-8030 Fax: (310) 825-8914

Shipping and Scoring John Hoover [email protected] San Bernardino Schools in and northwest of the city of Riverside in Riverside County and San Bernardino County.

(310) 825-2495 Fax: (310) 206-7261

John Sarli Tiffany Hughes [email protected]

(909) 880-5374 (909) 880-7670 Fax: (909) 880-7119

San Diego Imperial, San Diego, and Riverside counties, except for schools near Fullerton or in or northwest of the city of Riverside in Riverside County. San Luis Obispo San Luis Obispo, Santa Barbara, and southern Monterey counties.

Bruce Arnold Jean Forsythe [email protected]

(858) 534-3298 (858) 534-3373 Fax: (858) 534-1011

Steve Agronsky Dale Wilbur [email protected]

(805) 756-1683 (805) 756-2206 Fax: (805) 756-6537

Santa Cruz Northern Monterey, northern San Benito, Santa Clara, and Santa Cruz counties.

Bruce Cooperstein Karen Quinn [email protected]

(831) 459-2150 (831) 459-2400 Fax: (831) 459-3260

MDTP Users' Survey

MDTP produces two major products for the instructional use of California mathematics teachers. These are the multiple-choice diagnostic tests scored at regional sites and the written response materials scored by teachers using provided general and specific rubrics. We can readily ascertain usage data for the former since we do the scoring ourselves. Such is not the case with the latter. For some time now, we have been struggling to determine to what extent and in what manner teachers are using these materials. This survey is an attempt to obtain that information. If you use MDTP materials, please take a moment to answer the questions. We hope you will be kind enough to assist us with this endeavor. 1. Do you know what the MDTP Written Response materials are? Yes No

[If `No', do not answer the remaining questions but please return the survey to us. Then if you are interested, contact your MDTP site director for more information about MDTP Written Response materials.]

MDTP Written Response Items used in last two years, check all that apply. AR­Algebra Readiness Items AR96BLOX AR94CAKE AR94FLAG AR96ILND AR94PNCH AR96LINE AR94WIRE I do not recall the specific names but used ____ AR item(s). GR­Geometry Readiness Items GR97HGHT GR96LINE GR97PZZA GR97SLRY GR01CUBE GR01INEQ GR01PATH GR01TRIP I do not recall the specific names but used ____ GR item(s). SR­Second Year Readiness Items SR98PYTH SR98QUAD SR97RING SR97ROOT SR01AREA SR01RTRI SR01SMLR I do not recall the specific names but used ____ SR item(s). MR­Mathematical Analysis Readiness Items MR98GOAT MR98TANL MR01CNSC MR01LINE MR01SHAD MR01TNGT I do not recall the specific names but used ____ MR item(s). Calculus Readiness Items CR01DIST (Only item at this level)

2. Have you ever used any MDTP Written Response Items with any of your classes? Yes No 3. When you used an item, did you try to score it by applying the MDTP rubrics or did you use your own grading criteria? Attempted to apply MDTP rubrics Used my own grading criteria If you did not use the rubrics, please tell us a little about why you did not: _________________________________________________________________ _________________________________________________________________ 4. On the list of item abbreviations in the column to the right, please check all items that you have administered to at least one class during the last two years. 5. Do you currently have access to an MDTP Written Response binder? Yes No 6. Is the binder shared among people in your department or is it your own individual copy? My own copy Shared copy 7. Did you (or the person with whom you share the binder) return the first page in it so that you might receive additions as they are designed and released? Yes No Don't know 8. Have you received any additions since you originally obtained your binder? Yes No Don't know 9. In your opinion, should MDTP continue to produce more written response materials? Yes No Please give us a little of your thinking regarding your response to #9: ____________________________________________________________________ ____________________________________________________________________ Optional: Name:_____________________________________________________________ School Name:________________________________________________________ City:_______________________________________________________________ Please mail the completed survey to the MDTP Relations with Schools Office, the address is on page 2 of this newsletter. THANK YOU.

From a 2004 MDTP Teacher Institute Participant...

Emiliano Gomez, UC Berkeley MDTP Site Director

The MDTP Teacher Institute was held at UCLA this summer from August 8 through 12. Teachers from all over California came for what turned out to be a feast of professional development, interesting conversations, and (what we hope to be) the beginning of long-lasting collegial relations. Oh, yes, and good food. As one of the newest site directors, I had never attended an MDTP Teacher Institute, so I signed up as a participant. It was a wonderful learning experience in a very friendly and professional atmosphere. There were presentations, discussions, and workshops led by Barbara Wells (UCLA), Alfred Manaster (UC San Diego) and John Sarli (CSU San Bernardino). Among other themes, we discussed general information about the project, analysis of class reports, aspects of low-stakes diagnostic assessment, presentations about MDTP, test development (including field testing and data analysis) and written response materials (including creation of items, usage, grading and rubrics). One of the most valuable activities was the assignment of small group presentations about some aspects of the project. Each group was free to choose the topics and structure of the presentation they designed. This resulted in very productive collaborations and gave us an opportunity to get to know each other better. The long-term goal of the Teacher Institute is to encourage all teachers to administer our tests in a low-stakes setting to obtain a true, accurate description of their students'

strengths and weaknesses in various topics. And then, of course, to look carefully at the class reports so they can make informed decisions about their teaching and curricula. This is an ambitious objective. We hope that the participants of our Teacher Institutes will lead their colleagues by example and by advocating for good uses of our materials. We also hope that they will help us by making presentations about MDTP and their experiences at our Users' Conferences and other professional development opportunities. If you are an experienced user of MDTP materials and/ or a leader in your department, and if you are interested in collaborating with our project, then you are the very reason for the existence of our Teacher Institutes! Call your nearest site if you think you would like to join us for the next one.

Student Letters Now in Spanish by Request

We are pleased to announce that a recent update of our scoring software now allows teachers to request the student letters (that are included in the teacher report) in Spanish. Some sites had requested the student letters be available in Spanish as well as English for students whose parents do not read English. The new software includes a Spanish version of the individual student letter as an added report. If you would like to have the student letters in Spanish then please include a note requesting them when you return your answer sheets for scoring. Your site will then print the Spanish letters in addition to the English letters and return both to you. You will then determine which version(s) you want to distribute to your students and their parents.


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