SOLO in MathematicsMitchell Howard

Lincoln High School

Activity : Discuss for 1 min with the person next to you

1. Why did you come to this presentation? 2. What do you hope to get from this workshop?

Aims for my talk1. A brief explanation of

SOLO2. Why SOLO in

Mathematics?3. Some SOLO Pedagogy4. Get you involved in

thinking about how to use SOLO in the learning of Maths

Thinking at Lincoln

The focus is on ensuring students achieve deep learning outcomes and “learn how to learn”.

Activity 2: Describe map - SOLO

• Much like a spider diagram or brainstorm

characteristic

characteristic

characteristic

characteristic

characteristic

Idea /thing

characteristic

DESCRIBE Map with SOLO coded self-assessment rubric

Students could do this on a template, or just sketch up in their books or on mini white boards or scrap paper

Activity : Describe map - SOLO

• Use the map to write what you know about SOLO?

• Then write a statement about what you think SOLO Taxonomy is

SOLOSOLO

Surname of HAN

What this talk is supposed to be about

The next passing FAD in education

SOLO is the surname of a cool space guy from Star wars. It is also a word which is being a used a lot in education at the moment. Today I’m attending a workshop about it.

We will come back to your statement soon

Everyday SOLO Language

UNISTRUCTURAL

MULTISTRUCTURAL

RELATIONAL

EXTENDED ABSTRACT

PRESTRUCTURAL

Prestructural What does it mean?

What do you know

about SOLO?

Err….. What??

Prestructural What does it mean?

At the prestructural level of understanding, the student response shows they have missed the point of the new learning.

Unistructural What does it mean?

What do you know about

SOLO?

Err….. It’s got some

funny symbols!?!

Unistructural What does it mean?

At the unistructural level, the learning outcome shows understanding of one aspect of the task, but this understanding is limited.

For example, the student can label, name, define, identify, or follow a simple procedure.

Multistructural What does it mean?

What do you know about

SOLO?

It’s a thinking taxonomy with funny symbols and a type of

mark scheme.

Multistructural What does it mean?

At the multistructural level, several aspects of the task are understood but their relationship to each other, and the whole is missed.

For example, the student can list, define, describe, combine, match, or do algorithms.

Relational What does it mean?

It’s a way of structuring your thinking. It follows on from having your ideas to being

able to link your ideas together by explaining or comparing & contrasting them to show a greater

understanding of a topic. Rubrics can be used to assess

their level of achievement.

What do you know about

SOLO?

Relational What does it mean?

At the relational level, the ideas are linked, and provide a coherent understanding of the whole.

Student learning outcomes show evidence of comparison, causal thinking, classification, sequencing, analysis, part whole thinking, analogy, application and the formulation of questions.

Extended abstract What does it mean?

It’s a way of structuring your thinking. It follows on from having your ideas to

being able to link your ideas together by explaining or comparing & contrasting

them to show a greater understanding of a topic. It then allows you to formulate your own prediction or generalisation,

discussing the topic in question.

I predict that if I use SOLO Taxonomy within my lessons, I will see an increase in Merits

and Excellences as students learn to structure their answers better and they can transfer

their knowledge to another context.

What do you know

about SOLO?

Extended abstract What does it mean?

At the extended abstract level, understanding at the relational level is re-thought at a higher level of abstraction, it is transferred to another context.

Student learning outcomes show prediction, generalisation, evaluation, theorizing, hypothesising, creation, and or reflection.

Self Assessment: So What Level do you think you were at with your initial statement about SOLO Taxonomy?

How do the symbols relate to NCEA?

ACHIEVED

MERIT

EXCELLENCE

The Verbs

The Hattie and Brown Asttle example: Algebra patterns

Given:

• How many sticks are needed for 3 houses?• How many sticks are there for 5 houses?• If 52 houses require 209 sticks, how many sticks do

you need to be able to make 53 Houses?• Make up a rule to count how many sticks are

needed for any number of houses

Houses 1 2 3

Sticks 5 9 ___

• In your notes is a copy of this generic mathematics and SOLO rubric.

• You can read at your leisure but it relates well to what is happening at level 1

• Planning a unit of work, making connections

Task : How many ways can you represent this fraction?

73

Some ideas:

• Diagram: Pieces of pie or divided grids• Number line or a scale• Mixed number• Decimal, Percentage, Ratio • A context: 7chocolates divided between three

people• A number sentence:

addition/subtraction/multiplication/division.

Activity: construct a SOLO rubric

Based on the responses you have made, and what you know of your students could you:• construct a hierarchy of understanding?• Measure understanding?• Show students where to go next?

0 21 43 5

3

12

3

7

Borrowed from Louise Addison

0 21 43 5

3

73

12

3

1

3

17

0 21 43 5

3

73

12

3

17

6 7

3

1

⅓ of 1

0 21 43 5

3

73

12

3

17

6 7

3

1

⅓ of 2

0 21 43 5

3

73

12

3

17

6 7

3

1

⅓ of 3

0 21 43 5

3

73

12

3

17

6 7

3

1

⅓ of 4

0 21 43 5

3

73

12

3

17

6 7

3

1

⅓ of 5

0 21 43 5

3

73

12

3

17

6 7

3

1

⅓ of 3

0 21 43 5

3

73

12

3

17

6 7

3

1

73

1of

⅓ of 7

0 21 43 5

3

73

12

3

17

6 7

73

1of37

3

73

12

3

17

73

1of37

Implications on teacher planning

• Multiple representations of mathematical ideas/concepts

• How do we help students to make the connections between them?

• Differentiation – different types of learners will bring different ideas/experiences and connect with different representations.

• Differentiation – How do we cater for the ability range in our classes?

Equivalent Fractions: Doing versus Understanding

• Pictures

• Algorithm– Double top and bottom– × or ÷ numerator & Denominator by same

number• Relate to +/- Fractions of different denominator • Relate to ratio• Algebraic Fractions

Fraction Tiles

characteristic

characteristic

characteristic

characteristic

characteristic

Idea /thing

characteristic

DESCRIBE Map with SOLO coded self-assessment rubric

I can’t find any combination of tiles that are equal to ½

I can find sets of tiles that have the same denominator (or are of the same colour) that add up to ½.

I can find sets of tiles of different denominators that add to ½

I can explain how to find combinations of tiles (of different denominators) that add to ½

I can explain and relate fraction tiles to other representations of fractions such as Number sentences. I can write a general rule about the mathematics involved in this activity which makes it quicker and easier to do this kind of task with fractions that are not included on this set of fraction tiles.

Next

• We repeated the exercise for Which made connections for the algorithm of adding fractions.

Giving structure to open ended tasks

A Dan Meyer inspired task

In impoverished rural areas, clean water is often miles away from the people who need it, leaving them susceptible to waterborne diseases. The sturdy Q Drum is a rolling container that eases the burden of transporting safe, potable water—a task that falls mostly to women and children.

SOLO Level Criteria

Pre I don’t know where to startI don’t know what volume or capacity is

Uni I can estimate the dimensions orI can calculate the area of a circle

Multi I can calculate the volume of the water container.

Relational I can calculate the capacity of the water container as well as the weight. I can calculate the dimensions needed for the container to carry a given capacity

Extended abstract

I can design an alternate shapes or purpose for the container. Or I can make a formula that can be used to calculate the volume or capacity given any dimensions.

Using the terminology and referring to the symbols in class discussion:

The Picture (graph)

The Numbers

The Context

A Guide for responses in Level 3 Statistics internals

The Points on the graph are going down hill from left to right

The gradient of my regression line is

negative

As one of my variables increases the other

decreases

My smoothed data looks non-linear

But I have a high r squared

smoothed data will tend to get increased r

squared value

The equation

The Number pattern

The Picture (graph)

The Context. (dot diagram or skateboard ramp etc)

Level 1 - Understanding quadratic patterns and graphs

I have two answers for x when y=0

I have one positive and one negative

answer

The parabola cuts the x –axis twice

(2 roots)

I can only have a positive answer for

the number of people

Has an x squared

Differences not the same

Is a parabola

Some of the dots form a square shape

1.3 Investigate relationships between tables, equations and graphs

Initial amount and the rate of Increase/decrease

Y = c + mxm is the gradient or ratec is the initial value

Is it discrete - counted (e.g. matchstick pattern) So Dots on graphContinuous – Measured (e.g. liquid filling a container) So Solid line

What happens at x = 0What do values increase/decrease by each time

A taxi has a flag-fall of $2.00 and charges $2.60 per km

Draw the pattern as well as the next few

SOLO level

Uni-structural I can represent/ interpret the pattern in one way

Multi-structural I can represent/ interpret the pattern in more than one way

Relational -structural I can choose the best representation to solve a problem

Extended abstract-structural I can generalise a pattern and use it to solve a problem or make a prediction.

Level Success criteria Explanatory notes

Achieved Make links between various representations of a linear pattern.Quantitative

Write a formula or form a linear model.Demonstrate knowledge of gradient and intercepts

Merit Make links between various representations of a pattern in contextQualitative.

Forming and/or using a quadratic model.

Excellence Forming a generalisation.Evaluate effects of a change in particular pattern.

Form a model and correctly solve a problem.Cope with unusual models such as piecewise or exponential.

v

v

Next

• Did the regular theory of graphing linear functions.

• Contextual questions• Some quadratic theory.• Then

Some key ideas

• Different representations – making connections

• Differentiation - different types of learners• Common language to describe understanding• Self assessment – real power is from students

self assessing from a rubric

Where to next for me

• Learning experiences which lend them selves to relational and extended abstract thinking.

• Malcolm Swan

Card match activities Malcolm Swan

Malcolm Swan Classify in a 2 way table

Malcolm Swan Classify in a 2 way table

Evaluating statements about fractionsAlways true, sometime true or never true?• Statement 1: A fraction is a small piece of a whole• Statement 2: When you multiply one number by another the

answer must always be bigger• Statement 3: You can't have a fraction that is bigger than one• Statement 4: Five is less than six so one fifth must be smaller

than one sixth• Statement 5: Any fraction can be written in lots of different

ways• Statement 6: Fractions don't behave like other numbers• Statement 7: Decimals and fractions are completely different

types of numbers• Statement 8: Every fraction can be written as a decimal

Thanks for listening

• mho@lincoln.school.nz

Classifying mathematical objectsi. Odd one outii. Classifying using two-way tables

Interpreting multiple representationsCard match activitiesEvaluating mathematical statements – always true sometime true never true

Creating problemsi. Exploring the ‘doing’ and ‘undoing’ processes in mathematicsii. Creating variants of existing questions

Analysing reasoning and solutionsi. Comparing different solution strategiesii. Correcting mistakes in reasoningiii. Putting reasoning in order