Abstract:

Most scholars in curriculum development agree that there are four components of curriculum development: objectives (learning outcomes), content, teaching strategies (methods), and assessment [1]. Based on the data analysis by Freeman and his co-authors [2] who reviewed more than 300 published and unpublished studies on active learning, there is no doubt that active learning can be very successful and students benefit from it. However, analyzing Freeman’s list of references, as well as results of internet search, we found much fewer references to the assessment of active learning compared to organizing active learning references. We can assume that either the science of assessment of active learning has to be developed to reach the same level as active learning per se, or there is no significant difference between assessing traditional learning and active learning though in the published literature we came across statements like “active learning requires active assessment”[3]. Based on our experience integrating major specific lab component into the calculus curricula, we are planning to discuss active learning and formative assessment of active learning.

A major specific lab component to calculus was developed in the framework of the US Department of Education Minority Science and Engineering Improvement Program grant that has enabled the University of Texas at Brownsville, one of two legacy institutions for the University of Texas Rio Grande Valley, to embark on an ambitious agenda of activities that increased the number of minority students entering into and retaining in the fields of sciences and engineering. Development of labs have been a collective effort of faculty from Mathematics, Biology, CS, and Physics departments under the leadership of the grant’s director and co-director. Faculty developed discipline specific lab problems proved to be successful in improving student learning outcomes. In the inaugural year students in the specialty labs posted a GPA that was 29% higher than those of students in traditional lecture based teaching. In the following year, the differential was an increase of 50%.

Some scholars in cognitive research argue that assessment should be based on psychological ideas and can be only as good as those ideas. [Ginsburg, 2009]. We are going to discuss our experience from the perspective of constructivism, SSDMA (Stage-by-Stage Development of Mental Actions theory as developed by Bouniaev [5] in application to higher education mathematics teaching), and recent developments in Bloom’s taxonomy [6].

References:
[1] Tyler, R. (1949). Basic Principles of Curriculum and Instruction. Chicago; University of Chicago Press
[2] Freeman S., et al. (2014). Active learning Increase student performance in science, engineering, and mathematics. Proc. Natl. Acad. Sci. USA. 111(23) 8410-8415
[3] Runte, R. (2004). Designing Assessment for Active Learning, CORE(13)(3) 1-2, 6.
[4] Ginsburg H. P. (2009). The challenge of Formative Assessment in Mathematics Education: Children’s Minds, Teachers’ Minds; Human Development, 52:109-128.
[5] Bouniaev, M. (2004). Stage-by-Stage Development of Mental Actions and Online Mathematics Instruction, Society for Information Technology and Teacher Education International Conference 2004, Vol. 1, pp. 4366-4373.
[6] Anderson, L. et al. A taxonomy for learning, teaching and assessing: A Revision of Bloom’s Taxonomy of Educational Objectives. N.Y.:Longman 2001.

Keywords:

Calculus, assessment, learning theories, mathematics, constructivism.