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Using Assessment to Improve Mathematics Methods Courses
Sue Brown
University of Houston-Clear Lake
browns@uhcl.edu
Using Assessment to Improve Mathematics Methods Courses
Background: In the Unites States, multiple sets of professional and content standards form the basis of what is taught in a university mathematics methods course. The mathematics methods course at UHCL relies on three sets of standards: National Council of Teachers of Mathematics Professional Standards for Teaching (NCTM, 1990), Principles and Standards for School Mathematics (NCTM, 2000), and Everybody Counts (National Research Council, 1989). These documents advocate mathematics teaching as actively engaging students in doing mathematics. They provide insight into teacher preparation and professional development. The NCTM 1990 standards have defined the major roles of any mathematics teacher as:
(a) Creating a classroom environment to support teaching and learning mathematics.
(b) Setting goals and selecting or creating mathematical tasks to help students achieve these goals.
(c) Stimulating and managing classroom discourse so that students and teachers are clearer about what
is being learned.
(d) Analyzing student learning, the mathematical tasks, and the environment in order to make ongoing
instructional decisions (p. 4).
A challenge to teacher educators is to prepare preservice students to be effective mathematics teachers so their students are proficient in their mathematics learning and understanding (Kilpatrick, Swafford, & Findell, 2001). At the University of Houston-Clear Lake all students seeking elementary teacher certification are required to take a three-hour mathematics methods course. Prerequisites to this course are a three-hour college algebra course and two three-hour mathematics for elementary teachers courses. Four different faculty members teach five sections of the elementary math methods course with a maximum of 24 students/section each semester. In an attempt to provide consistency across the sections, all faculty have adopted common assignments. The major assignment is writing lesson plans and teaching the plans. Students spend five class sessions in an area elementary school. Three students are assigned to an elementary school teacher, and the teacher assigns mathematics topics for the university students to teach to her students. The entire School of Education (SOE) has adopted a standardized lesson plan template so all SOE lesson plans have the same components. Each student writes her mathematics lesson plan, which is graded by the university faculty. Each student makes the required revisions and teaches her 30-minute lesson to 1/3 of the teachers children. Then the university students rotate twice, each time teaching another 1/3 of the teachers children. Thus in one and a half hours, each elementary student has participated in three different mathematics lessons taught by three different university students. When students complete the math methods course they will have taught 12 mathematics lessons to elementary school students.
Assessment System: Three years ago, it was determined that the assessment system in the School of Education was not as effective as it should be, and that evolving national accreditation processes would require much greater sophistication in the collection, analysis, and use of data. Under the old system, data collection and aggregation was cumbersome, not sufficiently consistent across the full breadth of School of Education programs, and relied too heavily on manual effort. Therefore, a new Unit Assessment System (UAS) was designed.
The UAS is written in a dialect of Java, a language for developing applications that can be deployed across the Internet. Student work products, scoring rubrics and the scores themselves are entered using these applications in one of several common Internet browsers. All UAS data entered, either from students or faculty, are stored in raw form on a UHCL server, which has extremely limited access. Only three individuals can access the data. The School of Education Director of Planning and Assessment downloads the raw data, which consists of thousands of records, from the UAS into Microsoft Office Access. Additional data about students and courses are imported from the universitys student management system. All queries, calculations, and reports are prepared in Access on the Directors PC, which uses the Microsoft Windows XP operating system
Results: With the implementation of the Unit Assessment System, faculty were asked to identify course-based assessments that would be uploaded into the UAS. The mathematics methods faculty decided that each student would upload into the assessment system, the revised third lesson plan, the graded rubric, the reflection on the lesson plan, and the classroom teachers evaluation of the lesson. Therefore, at the end of each semester, all lessons, graded rubrics, reflections, and teacher evaluations are available electronically. Thus, the faculty can aggregate the data and use the data for course improvement. Table 1 presents the data on 44 lesson plans written in fall. The data are presented in percents where U denotes unacceptable, A is acceptable, and O is outstanding.
Conclusion: The data were somewhat surprising. The highest percentage of unacceptable responses, 30%, was for Input/Procedure: Check for Understanding. The mathematics methods faculty are very detailed in their expectation for this category. Students are to give two specific questions with anticipated answers that will check the childrens understanding of the mathematics taught and include a description of how an answer will be given by each student. Oral responses or simply walking around the room are not acceptable. It should be noted that on the first day of class, the instructor gives each student a detailed lesson plan and models how she would teach the lesson to children. It was very disappointing to note that on the third lesson plan, students were still having trouble with checking for understanding. Students were including checks to see if children understood how to play a game, checks to see if children understood some aspect of the concept that had not been taught, etc. Some students were not including two questions, not indicating the anticipated answer, or not indicating how they will get an answer from each child. The faculty decided that in the spring, in each class, they will ask each student to write one check for understanding question with an anticipated response, and how they will get an answer from each child. For example, the day multiplication is taught, students will write a check for childrens understanding of multiplication. The university students are sitting at tables and the students will work together to critique the answers. Finally, each table will report on one question, anticipated answer, and how they will get an answer from each child. It is anticipated that this focused approach implemented in each class over a 14 week period will improve the university students ability to check childrens understanding of mathematics. The data from spring 2008 will be presented at the conference.
The major problem students experienced in guided practice was continuing with the input/procedure (modeling) section of the lesson plan. In some cases, the university student was doing all the talking and practicing while students simply watched. The same approach used to improve check for understanding will be used for guided practice. In every session, each university student will indicate one approach that could be utilized to give children practice with the concept taught.
The implementation of the Unit Assessment System has provided an effective means to collect data, aggregate data, and use data for program improvement. In past semesters, lesson-planning data was used by university students to improve the lesson plans they write. Now the university faculty have the means to use the lesson plan data for course improvement.
Selected Literature
Kilpatrick, J., Swafford, J., & Findell (Eds.). (2001). Adding it up: Helping children
learn mathematics. Washington, DC: National Academy Press.
National Council of Teachers of Mathematics (1990). Professional standards for
Teaching mathematics. Reston, VA: Author.
National Council of Teachers of Mathematics (2000). Principles and standards for
school mathematics. Reston, VA: Author.
National Research Council. (1989). Everybody counts: A report to the nation on the
future of mathematics education. Washington, DC: National Academy Press.
Table 1: Evaluations of the Third Lesson Plan
ComponentsUAOStudent Population: Achievement and grade level, any special needs identified.00100Materials/Resources: All materials needed for the lesson are listed; copies or sketches of all teacher-made materials used are provided; well constructed and free from error.51184Safety: Safety should be addressed.
00100Texas State Standards: Written in entirety.2791Instructional Objective(s): Written in behavioral terms; The student will be able to . . . must be specific, addition is not, adding sums to 5 is.111177Anticipatory Set: Gains students attention; brief and related to the lesson; NOT a series of questions, a statement of the objective of the lesson, or a lecture.
142066 Input or Procedure (Instruction/Modeling): Provides all information for student success teacher demonstration of what students are to do; step-by-step of what will happen in the lesson; includes specific questions for students; enough detail so that a substitute could teach the lesson. (Word count: 300+).
145532Input or Procedure (Check for Understanding): at least two specific questions with anticipated answers; description of how an answer will be given by EACH student (an oral response is not acceptable; neither can you simply walk around the room and observe students) Assume you are teaching a class of 24 students.
303436Guided Practice: Provides each student the opportunity to practice the mathematics taught in the Input sections under the direct supervision of the teacher. All students should be active. Assume you are teaching a class of 24 students.
231661Independent Practice: Provides each student the opportunity to practice the mathematics taught in the Input sections without the direct supervision of the teacher. Assume you are teaching a class of 24 students. A worksheet is not outstanding.
91180Assessment: Matches the objectives; includes anticipated student answers; this must include a rubric, checklist, or scored student performance task that shows how well the student understands the math objective taught in Input/Modeling. (Because of time constraints, you will not be required to assess the students you teach.)
181170Reteach: Aligned to objectives, uses new strategies, addresses learning styles.
20970Enrichment/Extension: Must relate to the lesson objective.
00100Closure: Includes a brief activity that has the student(s) state or demonstrate the lessons main objective; state how the knowledge is related to real life or the future.21682
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