said about the problem solver's possible meanings, knowledge structures, cognitive processes, affect, or changes in these in the course of the interview ...
Using collaboratively framed dynamic assessment to develop a method for the analysis of adult students’ conceptual understanding of measurement. Pamela Vale Rhodes University
Presentation of paper at the 22nd Annual Meeting of the South African Association for Research in Mathematics, Science and Technology Education (SAARMSTE): New avenues to transform Mathematics,
Science and Technology education in South Africa. Hosted by the Nelson Mandela Metropolitan University.
An examination of the conceptual understanding of measurement of first year National Certificate (Vocational) engineering students Pamela Vale
An examination of the conceptual understanding of measurement of first year National Certificate (Vocational) engineering students An exploratory study to inform our understanding of the prior knowledge of the students
Using collaboratively framed dynamic assessment to develop a method for analysis of adult students’ conceptual understanding of measurement
Introduction • Located in the FET college sector • NC(V) students • Adult learners RATIONALE • Lack of knowledge about adult learners in South Africa, particularly in NC(V) • The descriptions of these students are largely from a deficit perspective, extending into the policy documents for this sector • Described in terms of what they lack, and seldom, if ever, in terms of what they bring • Common theme in all of the NC(V) Engineering subjects is measurement • Change deficit view to a more abilities-based focus on student capabilities
Mail and Guardian, 14 December 2012
National Certificate (Vocational)
Typology of NC(V) students • Young people who have a Grade 12 ‘pass’ (NSC) but who wish to pursue vocational education • Young people who have not passed Grade 12 due to either dropping out or failing the examinations • Young people who have left school at Grade 9 to enter the NCV route • Adults who wish to access further education FET Round Table (2010)
• Mixture of second chance and first choice • Different motivational ‘profiles’/ ‘orientations’
• Mixture of socio-economic circumstances • 36% are funded through NSFAS
• Average age: 22 years (for NCV Level 2)
• Practical skill and vocational knowledge are regarded as pursuits for those young people who are felt to be less able when it comes to academic study, or for young people who have become disaffected and who need to be coerced into participating in further education and/or employment (Unwin, 2004) • Perceived as a post-compulsory education system to be avoided
Unwin argues for a more ambitious interpretation of vocational education
Measurement in NC(V) Engineering • In every programme, the following outcomes are mentioned in at least one compulsory subject: • • • • • • • • •
“Explain the concept ‘measuring’ and indicate the purpose of measuring” “List equipment and methods used for meaning” “Define basic units of measurement” “Define SI derived units” “Define the physical quantities that are measured by SI units” “Derive new units from the relationships between the SI units” “Describe the origins and purpose of …. measurement” “Describe the principles of …. measurement“ “Explain the importance and reasons for using a standardised unit system for …. measurement” • “List the factors that affect the accuracy of measuring equipment” • “Describe errors in measurement and explain how to reduce these errors”
Measurement in NC(V) Engineering • Ambiguity evident in how measurement is addressed in the curriculum documents • Go right back to the basics, but do them so quickly
• Johri & Olds (2011): What engineers need is adaptive expertise which allows them to be both innovative and efficient at what they do.
Key concepts in measurement Measurement is a concept and not just the memorisation of formulae. Conceptual understanding allows transfer of skill across measurement domains. • Iteration or repeating a unit • Partitioning or subdividing • Number and measurement (Measurement is more than counting) • Transitivity and Conservation
Measurement domains • Area
• Volume • Force • Magnitude • Direction
• Flow rate • Two measurements with different unit • Rate of change, most commonly per unit time
• Key concepts are also transitivity and unit iteration (Long & Kamii, 2001)
3 Research Aims • 1. To explore the stable measurement conceptualisation of the students as evident in their capacity to engage with measurement-related tasks • 2. To explore the developing measurement conceptualisation of students as evident in their capacity to engage with mediated measurement-related tasks THIS REQUIRES A THIRD AIM • 3. To develop an analytical tool that enables the analysis of students’ mathematical conceptual understanding through mediation
Stable vs Emerging Knowledge • CANNOT view adult students as having NO knowledge of, in this case, measurement • Key theoretical distinction between the learner’s spontaneous bringing to bear of any particular competency, or the student’s doing so only when prompted. • Scaffolding: encompasses processes where experts use means that are contingent on students' performance to assist students in the realization of intentions relevant to task success (Howe, 2013)
Stable vs Emerging Knowledge • The notion of met-before was introduced to focus on how new learning is affected by the learner’s previous experiences. A met-before is a mental structure that we have now as a result of experiences we have met before. • This notion applies both to supportive aspects of previous knowledge that form a basis for new learning and to problematic aspects that cause confusion and may impede progress. • We need not only to identify these problematic aspects, but also to complement this activity with the development of a supportive strategy that seeks to improve the learning experience. (Tall & McGowen, 2013draft)
Stable vs Emerging Knowledge • Vygotsky (1978) • “Any learning a [student] encounters in school always has a previous history”
• Zone of Proximal Development • Stable understanding/conceptualisation – independent engagement and accurate response • Emerging – Requiring mediation to arrive at the accurate response
How do we access emerging knowledge? • Dynamic assessment • Traditionally involves a test-teach-retest approach • Full potential of dynamic assessment is realised through “collective, transformative activity undertaken with the learner” • Characterised by mediation negotiated with the individual and adjusted accordingly, rather than rigidly prefabricated clues and hints
How do we access emerging knowledge? • Collaborative Framing • Foregrounds engagement with assessment task • The assessor works with the learner on this task • Kinds of mediation to which student is responsive • Careful observation of learners’ responses form part of the diagnosis of their development • Can indicate how close they are to being able to function more independently
How do we access emerging knowledge? • Implicit vs Explicit mediation • Implicit mediation would include a prompt as simple as a pause. • Explicit mediation would include instances in which the researcher might need to point out that an error has occurred. • Students requiring only a small amount of implicit mediation may be considered to be closer to possessing stable knowledge than those requiring much explicit mediation
Structured task-based interviews
• Used in research for twin purposes: • Observing mathematical behaviour in an exploratory problemsolving context • Drawing inferences from the observations to allow something to be said about the problem solver’s possible meanings, knowledge structures, cognitive processes, affect, or changes in these in the course of the interview
Example of interview task • FIND THE AREA OF THE FOLLOWING SHAPE:
• Given the following unit:
Example of interview task • FIND THE SURFACE AREA OF THE FOLLOWING OBJECT:
• Given the following unit:
Example of interview task • Which object has the larger SURFACE AREA?
Analysis • Interaction analysis - ICM (Koichu & Harel, 2007) • Line by line analysis, multiple iterations
• Cognitive analysis (Simon et al., 2010) • The useful data segment – the end-point where there is compelling evidence that the student has a particular understanding and a beginning point where there is compelling evidence of the student not having that understanding • Line-by-line analysis, multiple iterations
• Analysis guided by a ‘capability grid’
Analysis • GENERIC CAPABILITY GRID: Iteration
Partitioning/ subdividing
Accumulation
Number and measurement
Transitivity
Conservation
Use of Use of SI units Structuring an measuring tool array
Using collaboratively framed dynamic assessment to develop a method for analysis of adult students’ conceptual understanding of measurement
