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Numeric and Symbolic Reasoning Assessment in Freshman Mathematics Courses

Abstract Universidad de las Américas Puebla (UDLAP) is a Mexican private institution of higher learning. Since 1959, the Commission on Colleges of the Southern Association of Colleges and Schools (SACS) has accredited UDLAP in the United States. SACS comprehensive standard 3.5.1 states: “the institution identifies college-level general education competencies and the extent to which graduates have attained them”. Therefore UDLAP had to clearly define its college-level general education competencies, and develop an assessment plan to learn about the extent to which graduates have attained UDLAP’s college-level general education competencies as well as to enhance student learning and development of these competencies. As a result, UDLAP’s General Education Committee identified the following competency areas: Written and Oral Communication in Spanish and English, Critical Thinking, Information Technology Literacy, and General Studies and Culture. Competencies from every area were clearly identified as well, including for the competency area of General Studies and Culture that UDLAP graduates will have an understanding of how knowledge is acquired and applied through the intellectual traditions of the arts, humanities, or social sciences; engineering or natural sciences; and business or economic sciences. As part of UDLAP’s General Education Curriculum our students have to take three General Studies courses (3 credits each), one from each school (School of Engineering and Sciences, School of Business and Economy, and School of Social Sciences, Arts, and Humanities). In particular for the School of Engineering and Sciences this course is a Mathematics course, which has to focus on developing numeric and symbolic reasoning skills, and students select from a list of approved General Studies courses. Development of the Mathematics Assessment Plan consisted of three major parts: determining UDLAP’s expectations; determining timing, identifying cohort(s), and assigning responsibilities; and interpreting and sharing results to enhance general education effectiveness. Particular competencies (and expected outcomes) for the Mathematics courses were defined following SUNY at Geneseo as follows: Symbolization (ability to convert a problem into a setting using symbolic terminology), Relationships (ability to connect quantities and find relationships among symbolic quantities), Formulation (ability to construct an appropriate symbolic framework), Analysis (ability to carry out algorithmic and logical procedures to resolution), and Interpretation (ability to draw valid conclusions from numeric/symbolic evidence). The Mathematics Committee chose to use rubrics as primary means of assessment to evaluate representative samples of student work (individual and group written and oral work products including quizzes, exams, homework, presentations, problem solving exercises) as well as teacher written and oral work products (presentations, problem solving exercises). Once students are assessed in a pre-test to determine his or her skill levels in the five chosen competencies, guided practice and training (both in the course and related problem solving sessions) is provided to every student. Students are required to reach a level of mastery (in a post-test) as measured by an average of meeting the expectations of the Numeric and Symbolic Reasoning Rubric. Up to date more than 300 students and 7 teachers have participated. The majority of the students have shown weakness in one or more of the targeted numeric and symbolic reasoning skill competencies.

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Yzasmendi Arellano, R., & Palou, E., & Gazca, L., & López-Malo, A. (2009, June), Numeric And Symbolic Reasoning Assessment In Freshman Mathematics Courses Paper presented at 2009 Annual Conference & Exposition, Austin, Texas. 10.18260/1-2--5296