Visible Learning for Mathematics: What Works Best to Optimise Student Learning – Hattie, Fisher, Frey

Some notes:

According to The National Council of Teachers of Mathematics (NCTM) publication ‘Principles to Action: Ensuring Mathematical Success for All’ (2014) the 8 high leverage teaching practices that support meaningful learning are:

  1. Establish mathematics goals to focus learning
  2. Implement taks that promote reasoning and problem solving
  3. Use and connect mathematical representations
  4. Facilitate meaningful mathematical discourse
  5. Pose purposeful questions
  6. Build procedural fluency from conceptual understanding
  7. Support productive struggle in learning mathematics
  8. Elicit and use evidence of student thinking

Similarly the 2012 National Research Council report Education for Life and Work identifies the following essential features of instruction:

  • Engaging learners in challenging tasks, with supportive guidance and feedback
  • Using multiple and varied representations of concepts and tasks
  • Encouraging elaboration, questioning, and self-explanation
  • Teaching with examples and cases
  • Priming student motivation
  • Using formative assessment

Focus on rigor defined as a balance among conceptual understanding, procedural skills and fluency, and application with equal intensity.

Mathematics instruction should be intentionally designed and carefully orchestrated in the classroom, and should always focus on impacting student learning. Start with appropriately challenging learning intentions and success criteria. Teachers need to be clear about where their students are, where they need to go, and what achievement of learning milestones looks like. Good mathematics learning is embedded in discourse and collaboration – both with teachers and among peers – and is orchestrated around appropriately challenging tasks. Students should be doing more of the thinking and talking than the teacher. Must be partners in understanding with metacognition (thinking about their own thinking).

Surface, deep and transfer learning

Surface – initial development of conceptual understanding, procedural skills, and vocabulary of a new topic

Deep – begin to make connections among conceptual ideas, and practice and apply procedural skills with greater fluency. Plan, investigate, elaborate on their conceptual understandings and begin to make generalisations. Can facilitate transfer.

Transfer – ability to more independently apply deeply understood concepts and skills to new and novel situations

 

 

Maths – Staff Meeting

Reflect on the things you do not like people to say and do when you are working on maths in a group

  • This is easy
  • This isn’t useful
  • Someone dominating the group
  • Hurry up!
  • I can’t do it
  • This is boring
  • That’s not right
  • I do not want to do this
  • Put downs
  • Competitiveness
  • Distracting
  • Off task behaviour
  • Sitting in rows
  • Silence
  • Worksheets
  • This is too easy
  • Talking about other things – off task
  • That’s wrong
  • I don’t want to work with him/ her
  • Not engaged
  • I don’t understand
  • I don’t like this
  • This isn’t useful
  • It’s easy
  • Rather than take risks, students use their group as a resource for answers
  • Someone else doing everything
  • Too complicated task

Reflect on the things you do like people to say and do when you are working on maths in a group

  • I’ve worked this out
  • I’ll give you more time
  • If you need help I’m happy to lend a hand
  • Time to consider and then work collaboratively
  • Keep trying
  • Let’s work it out together
  • I love Maths
  • This is fun
  • Keep trying
  • Supportive comments
  • I like a challenge
  • Asking questions
  • Collaborating
  • Fun
  • Interactive
  • Lots of talk
  • Groups
  • Tricky
  • I have to think about that
  • Lots of chatter
  • Work with buddies
  • A challenge
  • Building off others’ ideas
  • That’s a good idea
  • Mistakes seen as opportunities to grow
  • On task
  • I like that idea
  • Could you try
  • Can I help you?
  • This is so much fun
  • I like going in this pit
  • You can do it
  • The strategy I used was…
  • Busy
  • Engaging conversations about how to solve the problem

Reflection:

What stuck with you today?

There is more than one way to do the task.

2,3,4 heads are better than just 1

Everyone can learn maths

Low Floor, High Ceiling – entry points and differentiation for all

Maths needs to be hands on – not sheets – to give children the opportunity to experiment

Planning for differentiation is much easier than we sometimes make it (when the task is well-designed)

Youcubed lesson plans and resources, easily accessible and ‘ready to use’

Great ‘Emoji sorting’ lesson – Will definitely try it out!

How many different ways there are to understand a simple concept like ‘what is half?’ Along with encouraging students to take those risks and make mistakes.

Who would have thought that a simple concept like ‘halving’ would result in rich conversations – growing our learning together.

I’m going to look up Jo Boaler’s Youcubed, Daily Inspiration and try some new tasks as feeling a little like the meerkat in Maths at the moment.

Youcubed week of Inspiration site excellent ideas using Emoji’s. So many things you can do with this one activity, also very relevant for kids current fads.

Importance of developing positive attitudes in maths

Open ended, collaborative maths tasks.

Finding ways of exposing misconceptions/ highlighting understandings, and things we do/ say as teachers which might create misunderstandings.

During today’s activities reinforced how everyone sees the same problem differently. Allowing students to explore and work collaboratively is extremely valuable.

The Youcubed Week of Inspiration in Maths – lesson ideas, videos and resources to use

A great Emoji task to do.

Collaborative dialogue is the key to group feeling successful.

Fun working together if group collaborative

Thanks for sharing – inspiring indeed!

Look at and explore Youcubed, Inspirational maths lessons, continue to inspire students in maths.

I have good ideas but my group has great ideas!

Once you convince yourself …convince others.

 

 

 

Good Maths Tasks – Reference Points

Low Floor – High Ceiling Tasks:

1. Open up the task so that there are multiple methods, pathways, and representations.
2. Include inquiry opportunities.
3. Ask the problem before teaching the method.
4. Add a visual component and ask students how they see the mathematics.
5. Extend the task to make it lower floor and higher ceiling.
6. Ask students to convince and reason; be skeptical.

Jo Boaler recommends these sites:

Youcubed: www.youcubed.org

NCTM: www.nctm.org (membership required to access some of the resources

NCTM Illuminations: http://illuminations.ntcm.org

Balanced Assessment: http://balancedassessment.concord.org

Math Forum: www.mathforum.org

Shell Centre: http://map.mathshell.org/materials/index.php

Dan Meyer’s resources: http://blog.mrmeyer.com

Geogebra: http://geogebra.org/cms/

Video Mosaic project: http://videomosaic.org/

NRich: http://nrich.maths.org/

Estimation 180: http://www.estimation180.com

Visual Patterns; grades K-12: http://www.visualpatterns.org

Number Strings: http://numberstrings.com

Mathalicious, grades 6-12; real-world lessons for middle and high school: http://mathalicious.com

7-8 Transition Resources

Resources that were used or referred to during the 7-8 Transition Workshop

ASMI – Are, Volume and Surface Area
http://amsi.org.au/teacher_modules/area_volume_surface_area.html
area_volume_surface_area-1jq97lm

– Introduction to Measurement 7-8
http://amsi.org.au/teacher_modules/introduction_to_measurement.html
introduction_to_measurement-xiso7q

Mathematics Assessment Project
Evaluating Statements About Length and Area
http://map.mathshell.org/lessons.php?unit=9310&collection=8
length and area r1-ts0bvx

A-E Reference

The BitL Tool – Mathematics Years F-10
BitL_maths_F_10-28eyfie

Transforming Tasks
Designing tasks where students do the thinking
Transforming_tasks_strategy_diagram-20twebn
Transforming_tasks_intellectual_challenge_v3-2evfc7p
Year_8_Maths_example-1aoqqzk
Transforming_tasks_Maths_closed_to_open-26fbvoc

Beliefs and Attitudes About Mathematics
DECD_BEST-ADVICE_1.0_Beliefs-and-attitudes-about-mathematics_v12-177kbx5

 

The learning progression in the area of measurement:

Measurement progression-1cacnil