CADGME, Hagenberg July 2009 Christian Bokhove FISME, St. Michaël College Assessing symbol sense in a digital tool

Context Christian Bokhove 11 yr Teacher maths/ict secondary school St. Michaël College, Zaandam, the Netherlands, tradition math/ict projects Phd research. ( aimed at math curriculum. Freudenthal Institute of Science and Mathematics Education, Utrecht University, the Netherlands Supervisor: Paul Drijvers and Jan van Maanen Educational research

Problem statement Transition secondary  higher education Lack of Algebraic expertise Entry exams Use of ICT “Use to learn” vs. “Learn to use” Position statement NCTM (2008): ICT can be a valuable asset

Research question In what way can the use of ICT support acquiring, practicing and assessing relevant mathematical skills

Key topics / conmceptual framework Assessment - Formative (for) v Summative (of) - Feedback (Black & Wiliam, 1998) ICT tool use - Instrumentation - Task, technology, theory (Lagrange, 1999) Algebraic skills - Basic skills - Symbol Sense (Arcavi, 1994)

Criteria for tools Evaluation instrument Externally validated First formulate want we want, then see what there is A selection: Assesses both basic skills and symbol sense; Provides an open environment and feedback to facilitate formative assessment; Stores both answers and the solution process of the student; Steps; Freedom to choose own strategy; Authoring tool for own questions; Intuitive interface (‘use to learn’ vs. ‘learn to use’) Close to paper-and-pencil notation;

Digital prototype (enter as guest, at the moment in dutch) Digital Mathematics Environment (DME) 30 items basic skills & symbol sense Designer: Peter Boon, always in close collaboration with teacher’s field. Store results in environment SCORM, so every module can be used in VLE’s including Moodle

Case studies / 1-to-1s Qual. analysis (video, camtasia, atlas TI) Symbol SenseQoT (no focus) Feedback 6 multihour think-aloud 1-to-1 sessions with 17/18 year olds I want to know what’s going on in their minds

Symbol Sense Four example exercises 1. Equations with common factors Solve 2. Wenger, 1987 Rewrite as v=

Four examples (continued) 3. Does the student recognize the quadratic terms? 4. Recognize common factors when rewriting

First example: student’s work more clips

Feedback Feedback is part of formative assessment. Types of Feedback (Hattie & Timperley, Uni. Waterloo) Corrective Procedural Syntactical Meer.. From the 1-to-1’s we distilled modifications for our protoype (Matrix items vs. Feedback) Content Tool itself Feedback to be added Logging feature (for research) Second cycle with large group

DEMO module 1.Random vars. I forget one solution, and get the above 2.Custom feedback. a.Just divide by quadratic term. b.Work towards form x 3 3.Added random variables but fixed 4.Random variables Note: this adds complications. The author has to think about the implications. 5.Feedback rules 6.Features 7.Features: applets This feedback can be authored

Improving the tool Latest developments Mathematica enables: (Note: secondary school algebra in the Netherlands only needs a small amount of traditional CAS) Notation d/dx (Chain Rule) Limits (left, right, infinite) Substitutions (e.g. Chain Rule) Integrals (also +C) More sophistication in feedback Feedback rules (webservice connection with research Jeuring, Open University) Integration of tools like Geogebra, graphing tool, rotating cubes (All benefits of a close collaboration with the designer)

New developments: integrals

New developments: rule feedback

New developments: GeoGebra

Wrapping up Educational research: CAS serves education and not the other way round More info:

Second example: student’s work

Third example: student’s work

Fourth example: student’s work

Student work: clips First example Martin tries to solve the first exercise Movie clip Movie clip Second example Barbara tries the Wenger exercise. Movie clip Movie clip