The Importance of Talk for Mathematical Learning in the Early

Years

Denise Neal

November, 2014

Image sourced from: http://docs.education.gov.au/system/files/doc/other/belonging_being_and_becoming_the_early_years_learning_framework_for_australia.pdf

Everyday Learning about Maths and Numeracy

http://www.aamt.edu.au/Webshop/Newest-resources/Maths-and-Numeracyhttp://www.earlychildhoodaustralia.org.au/shop/product/everyday-learning-about-maths-and-numeracy/

Key Message from the book

If we talk about mathematics and numeracy and show positive attitudes to using their ideas to solve everyday problems, children will want to learn more about it and understand that learning isn’t always easy, but when we solve problems and get past the confusion, we have the satisfaction of learning something new.

When children tackle new challenges with appropriate levels of support, they develop as curious, persistent, highly engaged and successful learners. ….

Talk supports and extends this learning

IntroductionOverview

• The importance of talk• Links to curriculum frameworks• Promoting talk in the learning environment

(strategies and prompts)• Talk as way to assess student learning• References/resources• Conclusion• Questions

Source: Tracey Muir webinar- Connect with Maths, August 26th, 2014

Talk is Important!

• Research clearly tells us that oral language is crucial for learning and that oral language is the key to reading success. This involves not only speaking but also the capacity to listen (PALL)

• Vocabulary is another foundation for reading and learning. In the case of mathematics, there is a wealth of vocabulary specific to the learning area that helps build understanding and enables learners to explain, justify and extend their thinking.

Talk Matters

Klibanoff and colleagues discovered that teacher-facilitated “math talk” in the early years significantly increased children’s growth in understanding of mathematical concepts (2006, p. 59).Knowledgeable educators recognize that although young children may have a beginning understanding of mathematical concepts they often lack the language to communicate their ideas. By modelling and fostering math talk throughout the day and across various subject areas, educators can provide the math language that allows students to articulate their ideas. It is also important to encourage talk among students as they explain, question and discuss their strategies whileco-operatively solving problems.

http://www.edu.gov.on.ca/eng/literacynumeracy/inspire/research/cbs_maximize_math_learning.pdf

Examples…

http://www.earlychildhoodaustralia.org.au/nqsplp/wp-content/uploads/2012/05/EYLFPLP_E-Newsletter_No22.pdf

http://www.dreamstime.com/royalty-free-stock-photo-rolling-out-dough-pizza-child-making-fresh-beginning-image35196585

Curriculum

Both the Early Years Framework for Australia and the Australian Curriculum value and promote the importance of communication.

The EYLF

..educators are also responsive to children’s ideas and play, which form an important basis for curriculum decision-making. In response to children’s evolving ideas and interests, educators assess, anticipate and extend children’s learning via open ended questioning, providing feedback, challenging their thinking and guiding their learning. They make use of spontaneous ‘teachable moments’ to scaffold children’s learning.

Australian Curriculum

http://www.australiancurriculum.edu.au/mathematics/Curriculum/F-10?layout=1

Proficiencies and Content Strands

• Understanding

• Fluency

• Reasoning

• Problem solving

• Number and Algebra

• Measurement and geometry

• Statistics and Probability

through and with……

Both the proficiencies and the content work together to build mathematical understandings and ways of working… this begins in the early years- all learners can be expected to problem solve and reason

Building Dispositions

…enduring habits of mind and actions, and tendencies to respond in characteristic ways to situations, for example, maintaining an optimistic outlook, being willing to persevere, approaching new experiences with confidence. (Carr, 2001)

Reasoning

Reasoning mathematically is a habit of mind, and like all habits, it must be developed through consistent use in many contexts.

From children's earliest experiences with mathematics, it is important to help them understand that assertions should always have reasons. Questions such as "Why do you think it is true?" and "Does anyone think the answer is different, and why do you think so?" help students see that statements need to be supported or refuted by evidence. Young children may wish to appeal to others as sources for their reasons ("My sister told me so") or even to vote to determine the best explanation, but students need to learn and agree on what is acceptable as an adequate argument in the mathematics classroom. These are the first steps toward realizing that mathematical reasoning is based on specific assumptions and rules.

http://www.fayar.net/east/teacher.web/math/standards/document/chapter3/reas.htm

Mathematizing

The educator can play an integral role by making meaningful connections between the mathematical strands, the real world and other disciplines, and most importantly, “between the intuitive informal mathematics that students have learned through their own experiences and the mathematics they are learning in school” (For example, as a child naturally creates and extends a pattern while making a necklace, the educator can effectively pose questions that provoke the student not only to describe the pattern, but also to make predictions and generalizations). http://www.edu.gov.on.ca/eng/literacynumeracy/inspire/research/cbs_maximize_math_learning.pdf

The importance of discussion

Research has shown, however, that “manipulatives themselves do not magically carry mathematical understanding. Rather, they provide concrete ways for students to give meaning to new knowledge”Students need the opportunity to reflect upon their actions with manipulatives, and through discussion, articulate the meaning they generate, so that the link between their representations and the key mathematical ideas is apparent (Clements & Sarama, 2009, p. 274).

Pause and talk…

• Questions?

• Comments?

• Your experiences?

Talking AND Listening

We have a lot of talk and attention to speaking and listening and while many classrooms have gone a long way to improving children’s speaking in mathematics lessons, I think we still have a way to go in promoting deep listening (Askew, 2012)

Classrooms can support student learning by ensuring that solutions proposed by students are built on.Collective mathematical meaning is built when teachers carefully listen to students and select solutions to be shared which will build and develop collective understanding.

Supporting maths talk

Suzanne Chapin proposes five effective talk moves which help to create meaningful mathematics discussions. Revoicing is one move that is particularly useful when a student’s explanation is confusing or hard for others to understand. The teacher repeats all or some of what the child said and then asks for clarification, which in turn provokes the child to clarify and offer further explanation. This also gives the educator an opportunity to embed mathematics vocabulary so the child can further explain his/her thinking (2009, p. 14).

http://www.edu.gov.on.ca/eng/literacynumeracy/inspire/research/cbs_maximize_math_learning.pdf

A recommended read

Askew, M (2012) Transforming Primary Mathematics, Milton Park, UK: Routledge.

A recommended read

Supporting Maths Talk- Talk Moves

http://www.edu.gov.on.ca/eng/literacynumeracy/inspire/research/cbs_maximize_math_learning.pdf

Building talk

• Making sense of problems by explaining them to someone else, putting them into your own words and comparing your answers with others all helps meaning to emerge.

• Talking mathematics means that mathematical vocabulary becomes part of the classroom discourse- much more than a list of words!

Askew, M (2012) Transforming Primary Mathematics, Milton Park, UK: Routledge

Our actions and interactions are key

Responsive learning relationships are strengthened as educators and children learn together and share decisions, respect and trust. Responsiveness enables educators to respectfully enter children’s play and ongoing projects, stimulate their thinking and enrich their learning.

Image sourced from: http://www.earlychildhoodaustralia.org.au/nqsplp/wp-content/uploads/2012/05/EYLFPLP_E-Newsletter_No22.pdf

Planning for talk

• Maths talk time- turn to your maths talk partner and chat about this (as problems are posed, during the lesson and at the end)

• Sharing or reflection time- built into the planning of a lesson (not always at the end of the lesson)

• Plan for explicit teaching and use of subject specific vocabulary in each sequence

What do we do to promote good maths talk?

1. Try to use tasks that engage the pupils in thinking for themselves and allow you to work alongside them on occasions.

2. Find time to listen and communicate with pupils as they work on these tasks.

3. Try to avoid controlling the communication to get to a mathematical end that you have predetermined but encourage mathematical thinking instead. "Go with the flow.“

4. Wait at least 5 seconds for a response before speaking further.

5. Help pupils to speak and listen to each other in a constructive way.

6. Do not make assumptions.

7. Watch body language and voice intonation in order to minimise a power imbalance.

http://nrich.maths.org/6662

Asking Open Questions

http://www.edu.gov.on.ca/eng/literacynumeracy/inspire/research/cbs_askingeffectivequestions.pdf

Building a Learning Culture

Learning cultures either promote or constrain talk…

TasksTasks either promote or constrain talk…carefully select tasks for a mathematical purpose.

http://nrich.maths.org/content/id/8863/Incey%20Wincey.pdf

Use Props and Prompts for Talk

http://www.dreamstime.com/stock-photography-toy-microphone-close-up-image18830572

Props

Props

Props

Prompts

Prompts

Books can prompt and extend mathematical talk

Vocabulary is Important

We support children’s mathematical vocabulary development by:

• Using and modelling correct mathematical language

• Planning for the language required in units of work/lessons

• Expecting children to use correct mathematical language

Vocabulary

ICTs can prompt and extend talk

Capturing Talk Informs our Work

Talk becomes evidence of learning or misconceptions in children’s learning.Capturing childrens’ talk enables us as educators to gather evidence to share with parents and others. Technology enables us to easily capture talk- smart phones, ipads and other devices enable us to record audio and/or video files in ways that were not possible in the past.

http://postmediacalgaryherald.files.wordpress.com/2012/03/ipad.jpg

Talk is important for assessment

We once thought that it was what children could put on paper that mattered. We made assessment decisions based on this. We now know that we need to value and promote talk as a way of both communicating and assessing mathematical understanding.

Talking to assess

We learn so much about what children know, understand and are able to do through interacting with them and listening to their explanations. Many assessment tools such asCount Me in Too http://www.curriculumsupport.education.nsw.gov.au/countmein/assesment.html

The Early Years Numeracy Interview https://www.eduweb.vic.gov.au/edulibrary/public/teachlearn/student/mathscontinuum/onlineinterviewbklet.pdf

Assessment for Common Misunderstandingshttp://www.education.vic.gov.au/school/teachers/teachingresources/discipline/maths/assessment/pages/misunderstandings.aspx

Use talk and one-on-one interviews to assess childrens’ mathematical thinking. Such opportunities provide a window into childrens’ thinking as they explain their answers and the processes they have used.

Assessing through talkFormal interviews are not necessary though, as informal discussions, overheard conversations and effective questions from adults can also provide valuable information about childrens’ thinking, reasoning and understanding of mathematical ideas.

Image: http://www.childhoodnannies.com/teachers-presents/

Our Aim: Mindful mathematics learning

In mindful mathematics lessons the shift is to:

- Someone explaining

- Everyone following the explanation

- It’s not that the teacher never explains, but that everyone in the community gets to be the teacher and learner, whether they are adult or child.

Conclusion

Good maths classrooms are talking classrooms!

Effective talk requires thoughtful planning and careful listeningStudents should be expected to reason and explain from the early years and can be assessed on their capacity to reason and justify using mathematical language.

The mathematical proficiencies help us to plan for tasks , to make assessment judgements and to build mathematical behaviour and dispositions.

ConclusionOne of the most valuable ways an educator can support young children’s developing numeracy is to provide the language to talk about maths and mathematical ideas. That means that educators need to understand mathematical concepts and to recognise the potential of situations for rich numeracy learning .http://www.earlychildhoodaustralia.org.au/nqsplp/wp-content/uploads/2012/05/EYLFPLP_E-Newsletter_No22.pdfeveryday

Image sourced from: http://www.earlychildhoodaustralia.org.au/nqsplp/wp-content/uploads/2012/05/EYLFPLP_E-Newsletter_No22.pdfKeep on talking!

Useful ReferencesAustralian Government Department of Education, Employment and Workplace Relations (2007)Early Childhood Literacy and Numeracy- building good practice, http://www.vcaa.vic.edu.au/documents/earlyyears/buildinggoodpractice.pdf (accessed August 26, 2014)

Early Childhood Australia (2011) Being Numerate: Early Years Learning Framework Professional Learning, Newsletter 22 http://www.earlychildhoodaustralia.org.au/nqsplp/wp-content/uploads/2012/05/EYLFPLP_E-Newsletter_No22.pdf (Accessed August 26, 2014)

Ontario Ministry of Education, Student Achievement Division, Capacity Building Series, Special edition 22, Maximizing Student Mathematical Learning in the Early Years (2011) http://www.edu.gov.on.ca/eng/literacynumeracy/inspire/research/cbs_maximize_math_learning.pdf (accessed August 26, 2014)

Ontario Ministry of Education, Student Achievement Division, Capacity Building Series, Special edition 21, Asking Effective Questions (July, 2011)

http://www.edu.gov.on.ca/eng/literacynumeracy/inspire/research/cbs_askingeffectivequestions.pdf

Building Mathematical Competencies in Early Childhood https://www.youtube.com/watch?v=iVFP-4iw_r4

https://www.youtube.com/watch?v=BMoF-hiH3J8https://www.youtube.com/watch?v=rsKNrnlfXt4&list=PLVVQEyDnsoWVRYxJSIO3RoET9R0P1gtcx&index=3https://www.youtube.com/watch?v=xssBJpOBecs&list=PLVVQEyDnsoWVRYxJSIO3RoET9R0P1gtcx&index=4

https://www.youtube.com/watch?v=WVfwBQe_IJE&list=PLVVQEyDnsoWVRYxJSIO3RoET9R0P1gtcx&index=5

https://www.youtube.com/watch?v=1IjesoJJTp0

http://nrich.maths.org/early-years Nrich early years site

Five Practices for Orchestrating Productive Mathematics Discussions (Smith & Stein) http://www.aamt.edu.au/Webshop/Newest-resources/Five-Practices