What has this got to do with NCEA? SOLO taxonomy What has this got to do with NCEA?

What is SOLO? SOLO stands for the Structure of Observed Learning Outcomes. It was developed by Biggs and Collis (1982) as “a framework for understanding”. SOLO identifies five stages of understanding. Each stage embraces the previous level but adds something more.

Prestructural Unistructural Multistructural Relational The stages of SOLO Prestructural Unistructural Multistructural Relational Extended abstract

Prestructural the student acquires bits of unconnected information that have no organisation and make no sense. Unistructural makes simple and obvious connections between pieces of information Multistructural a number of connections are made, but not the meta-connections between them Relational sees the significance of how the various pieces of information relate to one another Extended abstract can make connections beyond the scope of the problem or question, to generalise or transfer learning into a new situation

Questions that assess thinking Use of SOLO allows us to balance the cognitive demand of the questions we ask and to scaffold students into deeper thinking and metacognition.

Multistructural questions Students need to know or use more than one piece of given information, fact, or idea, to answer the question, but do not integrate the ideas. This is fundamentally an unsorted, unorganised list. 8

Relational questions These questions require students to integrate more than one piece of given knowledge, information, fact, or idea. At least two separate ideas are required that, working together, will solve the problem. 9

Extended abstract questions These questions involve a higher level of abstraction. The items require the student to go beyond the given information, knowledge, information, or ideas and to deduce a more general rule or proof that applies to all cases. 10

A change of focus in mathematics The SOLO hierarchy shifts us from the situation in maths of “doing more” and “ doing longer tasks” to qualify for a higher grade. This change recognises and rewards deeper and more complex thinking along with more effective communication of mathematical ideas and outcomes. It is these that are fundamental competencies to mathematics. . 14

Algebra: Patterns in number Houses 1 2 3 Sticks 5 9 __ Given: How many sticks are needed for 3 houses? (unistructural) How many sticks are there for 5 houses? (multistructural) If 52 houses require 209 sticks, how many sticks do you need to be able to make 53 houses? (relational) Make up a rule to count how many sticks are needed for any number of houses. (extended abstract)

Algebra: Patterns in number AS1.1 Apply numeric reasoning Algebra: Patterns in number Achieve = uni and/or multistructural thinking involves using a range of methods in solving problems and demonstrating knowledge of number concepts and terms or communicating solutions which would usually require only one or two steps.

Algebra: Patterns in number AS1.1 Apply numeric reasoning Algebra: Patterns in number Merit = Relational thinking involves one or more of: selecting and carrying out a logical sequence of steps connecting different concepts and representations demonstrating understanding of concepts forming and using a model, and the student will relate findings to a context, or communicate thinking using appropriate mathematical statements.

Algebra: Patterns in number AS1.1 Apply numeric reasoning Algebra: Patterns in number Excellence = Extended abstract thinking Involves one or more of: devising a strategy to investigate or solve a problem identifying relevant concepts in context developing a chain of logical reasoning, or proof forming a generalisation, and the student will use correct mathematical statements, or communicate mathematical insight. 

References References Hattie, J.A.C., & Brown, G.T.L. (2004, September). Cognitive processes in asTTle: The SOLO taxonomy. asTTle Technical Report #43, University of Auckland/Ministry of Education. http://www.tki.org.nz/r/asttle/pdf/technical-reports/techreport43.pdf Biggs, J.B. (1999). Teaching for Quality Learning at University. Buckingham: SRHE/Open University Press. Biggs, J.B., & Collis, K.F. (1982). Evaluating the Quality of Learning: the SOLO taxonomy New York: Academic Press. Pam Hook and Julie Mills http://hooked-on-thinking.com/solo-taxonomy/