Teaching Algebraic Model Construction: A Tutoring System, Lessons Learned and an Evaluation
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Teaching Algebraic Model Construction: A Tutoring System, Lessons Learned and an Evaluation Kurt VanLehn 1
& Chandrani
Banerjee 1 & Fabio Milner 1 & Jon Wetzel 1
# International Artificial Intelligence in Education Society 2020
Abstract An algebraic model uses a set of algebra equations to precisely describe a situation. Constructing such models is a fundamental skill required by US standards for both math and science. It is usually taught with algebra word problems. However, many students still lack the skill, even after taking several algebra courses in high school and college. We are developing a short, intensive course in algebraic model construction. The course combines human teaching with a tutoring system. This paper describes the lessons learned during the iterative development process. Starting from an existing theory of model construction, we gradually acquired a completely different view of the skills required as we modified the tutoring system and the instruction. We close by describing encouraging results from a quasi-experimental study. Keywords Model construction . Intelligent tutoring system . Algebra word problems .
Mathematics learning
Introduction Teaching students how to construct and use models is undeniably important. According to the Next Generation Science Standards (NGSS, 2013), “developing and using models” is one of 8 key scientific practices. According to the Common Core State Standards for Mathematics (CCSSM) (NGA & CCSSO, 2011), “modeling with mathematics” is one of its 8 key mathematical practices. Model construction, and solving algebra word problems in particular, are notoriously difficult for students. A 2007 survey of 743 high school algebra teachers rated word problem solving as the most difficult topic for incoming students (Hoffer, Venkataram, Hedberg, & Shagle, 2007).
* Kurt VanLehn [email protected]
1
Arizona State University, Tempe, AZ, USA
International Journal of Artificial Intelligence in Education
According to the CCSSM (NGA & CCSSO, 2011), the process of constructing a model has four sub-processes, shown in Fig. 1. When the model is a set of algebra equations, the Formulate process is writing the equations, the Compute process is solving them, and the other two processes check the numerical answer. The Compute process can be performed by a Computer Algebra System (CAS). A CAS will solve equations entered by students. CAS are available on calculators (e.g., Casio 9970Gs or TI-92) as well as computers. Algebra students are often allowed to use a graphing calculator during exams but not a CAS. On the other hand, students in university engineering and science classes are often allowed to use a CAS and sometimes even required to use one. Although a CAS can perform the Compute process of Fig. 1, it takes a human to do the other processes. Thus, the non-Compute processes are likely to remain important skills throughout the twenty-first century. To assess just those skills, our assessments have students use a CAS for the Compute process. Prior Work on Teaching Mo
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