Discourse Activities-Improving Mathematical Language Acquisition National Partnerships Schools’ Forum Melbourne, February 2012 Michelle Bootes Euroa Secondary College

Literacy in Mathematics and Mathematical Literacy “... literacy in mathematics, that is, how students access mathematics through language, and with the role that language plays in mathematics teaching and learning.” [ p. 3 Meiers 2010] Mathematical Literacy (or numeracy) Is “an individual’s capacity to identify and understand the role mathematics plays in the world... to use and engage with mathematics in ways that meet the needs of the individual …” [ PISA, as cited in OECD, 2004, p.15]

COAG recommended: “That the language and literacies of mathematics be explicitly taught by all teachers of mathematics …” (National Numeracy Review Report, p34) Literacy instruction is also a necessary part of mathematics instruction (Draper 2002).

Project Title: Discourse Activities: Can They Improve Student Mathematical Vocabulary Learning? Research Question: What kind(s) of discourse strategies are associated with the best improvement in the mathematical language acquisition of low-achieving Year 7 students from low-SES backgrounds?

Definitions Low-Achieving (LA) is defined as those Year 7 students who scored below a VELS Level 4.0 in the On Demand Adaptive Number Testing in February “Discourse Activities” are learning activities which allow students to use dialogue and discussion as part of their learning [Zack and Graves (2001), Hufferd-Ackles, Fuson and Sherin (2004), Marino (2005), Kersaint (2007)].

Methodology  Vocabulary Pre and Post-Test (All Year 7 students)  Teacher Journal (All Year 7 teachers) Lesson Components:  Active Teaching  Imagined Representations  Purposeful Games and Puzzles  What if?  Fluency Tasks Nicholson (1989) considered it to be of great importance to diagnose whether or not key words are available to students and are properly understood. Discourse Activities 1 1. Sullivan, P. (2011) Creating Mathematics Lessons. Retrieved from EDF6421, Monash University Studies Online:

Activity 1: Essential Vocabulary Nicholson (1989) considered it to be of great importance to diagnose whether or not key words are available to students and are properly understood. Task 1: In pairs, write a list of essential key mathematical words that will be used in your next mathematics unit or topic. Task 2: Complete the Fraction Vocab sheet. Estimate the number of students who properly understand the words in the list. Cloze Activity Generator blank/

Results: Group Year 7 Groupout ofdenominator equivalent to improper fraction equal partsmixed numberreduced to proper fractionnumeratorfraction A-pre A-post B-pre B-post C-pre C-post D-pre D-post Percentage of Students With Correct Response In Each Group Low Achieving Students High Achieving Students Anomalies between pre and post-tests Fraction Vocabulary

Results: Pre and Post Vocabulary Tests

Results: Teacher Journals LA: Groups A and B HA: Groups C and D

Conclusions: 1.Suggests that “Purposeful Games and Puzzles” and “Imagined Representations” may lead to the best improvement in language acquisition for the low achieving groups. 2. “Active Teaching”-Traditional with little opportunity for discourse does not improve language learning, even for high achieving students. 3. It is of “great importance to diagnose whether or not key words are available to students and are properly understood” (Nicholson, 1989), and for teachers to select discourse strategies that will improve language acquisition.

Purposeful Games and Puzzles (PGPs) Possible Lesson Component/s Teacher Introduction Students Working Teacher Review Purposeful Games and Puzzles Explaining rules and demonstrating game:  Relationship cards  Race to...  DIY Experience  Loop Cards Student playing games in mixed groups, with like needs pairs evolving. Synthesis of student products and summary teaching. Sullivan, P. (2011b). Creating Mathematics Lessons. Retrieved from EDF6421, Monash University Studies Online:

Mathematical Games: Race to …………… (Brousseau, 1997) Race to 10, start at 0, adding 1 or 2. Race to 3, start at 0, adding ½ or ¼ Race to 1, start at 0, adding 0.1, 0.05 or 0.15 Race to 0, start at 100, taking away any number from 1 to 12 Race to 5x + 5y, start at 0, adding x, y or x + y Race to 128, start at 1, multiplying by 2, √2, 2√2 Sullivan, P. (2011). Creating Mathematics Lessons. Retrieved from EDF6421, Monash University Studies Online:

Activity 2: What might a “Race to … ” task look like for your unit or topic? Design a task and try this out on a partner. Each game can be extended to more conventional exercises utilising the particular skill that has been practiced. Students find it engaging to choose: The ways of working The type of examples The level of complexity.

Puzzles: Relationship Cards The following is an example of a mathematical puzzle, adapted from a suggestion by Swan (no date). The puzzle involves a set of term (or number) cards and operation cards (Relationship Cards), a subset of which could be: Activity 3: In teams, use the decks provided, choose the two operation cards that can be placed between the two term cards to represent the connection. Activity 4: Using the blank card sheet, develop another relationship puzzle.

Loop Cards: Whole Class Loops Answer Question Answer Question

Activity 5: Task 1: A loop card activity- some of the cards (green) can be found on your table. Task 2: Create your own loop card activity using the sheet provided.

Summing up Purposeful Games and Puzzles  Students have to evaluate a range of possible solutions  Self-correcting  Strategy enhances the search for mathematical connections  Focuses on conceptual understandings, strategic competence and productive dispositions  Student choice is used  Medium for prompting (by teacher) for communication  Low risk for students

Factors Influencing Student Response  Student Choice > Contributes to motivation  Productive Communication > There is more to discuss than the correct answer  Fosters collaboration and fun

Why is student communication so important? Strategies that generate discourse in the mathematics classroom give students the opportunity to explain their own mathematical thinking, and make significant contributions that can be questioned and built upon by other students. (Hufferd-Ackles, Fuson and Sherin 2004)

Discourse Activities  Several articles point to the importance of “student talk” in helping students to overcome language difficulties in mathematics (Aiken 1971).  Zack and Graves (2001) found that dialogue leads to learning because the participants talk about their work, things that confuse them and how the ideas of others help or do not help them to make mathematical meaning.  Learning the literacies of mathematics can be characterised as the use of oral or written language to make sense of mathematics and to communicate, solve problems and engage in discussions and decision making (Kersaint 2007).

Purpose of Discourse Activities Provides oral language (text) practice Students:  Compare texts  Share text  New text is formed  New language is acquired. This is language acquisition.