1. DEFINE / REFINE student learning outcomes based on input from stakeholders.

In the fall of 2004, our mathematics department came together and refined the learning outcomes for Mathematics for Elementary Education Majors I and II. The following is a list of these learning outcomes:

Math 100 (Mathematics for Elementary Teachers I) Expected Learning Objectives: Upon completion of this course, the student shall be able to:

• Apply learned problem-solving techniques to problems that require applications of deductive and mathematical reasoning, while handling the details of arithmetic with appropriate use of the calculator.
• Use sets and set operations as a basis for whole numbers and whole number arithmetic using Venn Diagrams.
• Organize set relations.
• Classify numeration systems as additive or place-value systems.
• Write and operate with numerals in non-decimal positional systems.
• Demonstrate algorithms for basic arithmetic operations using various manipulatives such as base ten blocks, units, strips and mats and place-value cards.
• Demonstrate techniques for mental arithmetic and estimating results of arithmetic operations.
• Define and apply the Fundamental Theorem of Arithmetic.
• Compute LCD and GCD using various methods.
• Perform fundamental operations of arithmetic through the real numbers, using the calculator where appropriate.
• Interpret the key components of the NCTM curriculum standards for grades K-4 and grades 5-8.

 

Math 200 (Mathematics for Elementary Education Majors II) Expected Learning Objectives:

• Generate various graphical representations of data sets.
• Compute measures of central tendency and variability.
• Define population, sample, random sample and normal distribution.
• Contrast theoretical and empirical probability.
• Calculate comparable probabilities using counting techniques.
• Define the basic concepts and principles of plane and 3-D geometry.
• Determine if an Euler Path exists within a graph and, if so, identify one.
• Use both English and metric units of measurement.
• Apply area and perimeter formula for rectangles, parallelogram, triangle and circle.
• Apply the Pythagorean theorem to solid figures that contain triangles.
• Calculate surface area and volume of prisms, cylinders, pyramids, cones and spheres.
• Identify the three basic rigid motions of translation, rotation, and reflection.
• Identify patterns and symmetries in plane figures and Escher-like tilings.
• Define congruence and similarity of figures and identify the four principles for congruence of triangles (ASA, SSS, AAS, SAS) as well as five properties for similarity of triangles (ASA, SSS, AAS, SAS, AA).
• Identify the basic geometric constructions and demonstrate these through the use of compass and straightedge, the Mira, and patty paper.
• Analyze articles from professional journals and publications in the field of elementary school mathematics.

2. DESIGN assessment tools, criteria and standards directly linked to each outcome.

The first two assessment tools, Concept Maps and Journaling are classroom assessment tools. The third assessment tool is a course-level assessment tool.

CONCEPT MAPS: To assess the learning objective listed for Math 100 which states, 'Perform fundamental operations of arithmetic through the real numbers, using the calculator where appropriate' a concept map was utilized. Using a research article written by Bobbye Bartels (1995), "Promoting Mathematical Connections with Concept Mapping," Mathematics Teaching in the Middle School, NCTM. A concept map uses a flowchart to describe a mathematical idea. Students initially filled in a concept map on whole number arithmetic. (View Whole Number Concept Map) Students were then asked to produce their own concept map for rational numbers (fractions). (View Fraction Concept Map)

JOURNALING: Based on the previous concept map assessment tool, students were asked to write a paragraph describing the advantages of creating the fraction concept map.

END OF COURSE ASSESSMENT: To assess all learning objectives for the Mathematics for Elementary Education Majors I course, an end of course assessment tool in the form of a questionnaire was developed. Students were asked to analyze each learning objective and produce evidence of having been provided with the opportunity to meet each objective.

3. IMPLEMENT assessment tool(s) to gather evidence of student learning.

CONCEPT MAPS: Students were given 10 minutes to work in groups during class. They were then provided with a list of terms and the already organized flow chart to fill in.

JOURNALING: Immediately following the group work, individuals were asked to respond to the journaling prompt, "describe the advantages of creating the fraction concept map."

END OF COURSE ASSESSMENT: On the last day of the semester, students came to class with all course material. They formed groups with students they had most interacted with over the course of the semester. For each learning objective students were required to provide evidence of the opportunity to learn the required objective. In addition, students also noted next to the objective whether the opportunity to meet that objective was met or not.

4. ANALYZE and evaluate the collected data.

CONCEPT MAPPING, JOURNALING, END OF COURSE ASSESSMENT: All data provided by these assessment tools was analyzed and summarized by the instructor after the in-class activity was completed.

5. IDENTIFY gaps between desired and actual results.

The following questions will be addressed for each assessment tool:

1. What was learned from the collected data?
2. What were the strengths and weaknesses of the activity?
3. What were the gaps between desired and actual outcomes?
4. What changes are necessary to improve the activity?

CONCEPT MAPS:

1. Students had previously shown the ability to add, subtract, multiply and divide fractions. But this activity uncovered students' lack of ability to see the connections between these operations.
2. Initially, students were not given enough time to discover the connections between these operations on the concept map, because they were provided with the already organized flow chart.
3. The instructor discovered that students were unable to demonstrate their conceptual knowledge of operations with fractions.
4. Students were given 10 minutes (as opposed to 5 minutes) to construct their own group's concept map prior to being provided with the organized flow chart to fill in. This resulted in a significant improvement of students' conceptual knowledge of fractions as evidenced by follow-up testing.

JOURNALING:

1. Students had not been aware of the connections between operations of fractions. Many students indicated that looking at these concepts without actual numbers allowed them to focus on the conceptual connections.
2. A strength of the activity was that students were allowed to journal immediately following the concept mapping activity.
3. None
4. In the initial implementation of the activity, one class was allowed to journal at home and the other class journaled immediately following the activity. The take home journals were incomplete and not as focused.

END OF COURSE ASSESSMENT:

1. Students indicated that the opportunity to meet 3 of the learning objectives had not been met.
2. Strengths: WOW! The instructor now knew that three learning objectives needed more opportunity for learning.
3. None.
4. When the activity was initially performed, students were not asked to make a 'met' or 'not met' judgment call. Also, students are now provided with a section on the assessment to make additional comments about classroom format (ie. group work, lecture, online support, etc.).

6. DOCUMENT results and outline needed changes in curriculum, instructional materials or teaching strategies.

CONCEPT MAPPING, JOURNALING, and END OF COURSE ASSESSMENT. The results of each evaluation were used to revise the course. For the concept mapping and journaling the activity is now included as a part of the course. For the end of course assessment, the course was revised to include more opportunities for the three areas of noted weakness. Note: the next time that the course was taught (with these improvements) the three areas were shown to have met the opportunity for learning.

All members of the department are updated on assessment outcomes during each department meeting. Also, the Teaching Learning Center at Black Hawk College, Moline, IL publishes a college-wide link of best student learning practices for all faculty.