Literacy in the mathematics classroomAaron Wilson
Why focus on literacy in Mathematics?Activating prior knowledgeText features and purposesVocabularyStrategies for translating word problems
Why focus on literacy in Mathematics?
Inquiry focusSince any teaching strategy works differently in different contexts for different students, effective pedagogy requires that teachers inquire into the impact of their teaching on their students. (NZC, p.35)
NZ CurriculumEach learning area has its own language. As students discover how to use them, they find they are able to think in different ways, access new areas of knowledge, and see their world from new perspectives(NZC, p.16)
NZ CurriculumStudents need specific help from subject area teachers as they learn:Specialist vocabularyHow to read and understand its textsHow to communicate knowledge and ideas in appropriate waysHow to listen and read critically, assessing the value of what they read and hear(NZC, p.16)
Shanahan & Shanahan (2008)
Cross-curricular literacyMany literacy messages fail to resonate with mathematics educators because they neglect, deemphasize, or misrepresent the nature and content of the discipline of mathematics.- Siebert and Draper (2008, p. 231).
Why focus on literacy in Mathematics?Assessments written in English will always be, to some extent, assessments of English (Abedi, 2004; Martiniello, 2007 Lower language proficiency tends to be associated with poorer mathematics performance (Cocking & Mestre, 1988; Wiest, 2003).
Why focus on literacy in Mathematics?Research indicates that students peform 10% to 30% worse on arithmetic word problems than on comparable problems presented in a numeric format (Abedi & Lord, 2001; Carpenter, Corbitt, Kepner Jr, Lindquist, & Reys, 1980,Neville-Barton & Barton, 2005).
Children were shown 5 birds and 3 worms and asked, How many more birds are there than worms? 17% of the nursery school children and 64% of the first graders correctly answered the question correctly. When the problem was rephrased as, Suppose the birds all race over and each one tries to get a worm! How many birds wont get a worm? 83% of the nursery school children and 100% of the first graders answered correctly (Hudson,1983).
Talking point:Students generally find it harder to solve a word problem than they would if the same problem was presented in a mathematical format.
The language of mathematicsMathematics has a unique linguistic register with special features that must be mastered by students of mathematics. A mathematics register is the variety of language oriented to mathematics activities comprising the meanings and uses of the various linguistic forms that appear in the context of these activities (Halliday,1975).
The language of mathematicsQuality teaching bridges students intuitive understandings and the mathematical understandings sanctioned by the world at large. Language plays a central role in building these bridges: it constructs meaning for students as they move towards modes of thinking and reasoning characterised by precision, brevity, and logical coherence (Marton & Tsui, 2004).
The language of mathematicsIn order to enculturate their students into the mathematics community, effective teachers share with their students the conventions and meanings associated with mathematical discourse, representation, and forms of argument (Cobb & Yackel, 1996; Wood, 2002).
ActivityRead the three NCEA texts and identify aspects of language your students might find challenging
2. Activating prior knowledge and building necessary background knowledge
Why activate prior knowledge?It is (relatively) simple to do and can pay big dividends Reading comprehension always involves making links between new and existing knowledgeStudents comprehension will be greater when they know in a broad way what the text is going to cover or be aboutStudents motivation to read is greater when they have a purpose for readingHelps teachers identify gaps or misunderstandings that might cause students problems.
Student attitudesTypes of textsReading ChallengesTeaching challengesTeacher attitudesReading in Mathematics
Identifying problemsAnalyse the NCEA texts and explain examples where students experience or lack of experience of the context might affect their understanding.Discuss what you could do as a teacher to prepare students for situation where they encounter unfamiliar contexts.
What are some features of mathematics word problems?Word problems are stylized representations of hypothetical experiences- not slices of everyday existence (Lave, 1992, p. 77). One of the most significant problems provided by many of the contexts used in mathematics classrooms occurs when students are required to engage partly as though a context in a task were real whilst simultaneously ignoring facts pertinent to the real life context (Boaler, 1994, p. 554).
Other issuesMeaney and Irwin (2005) found that Year 8 NZ students were far more successful at recognising the need to peel away the story shell of word problems.Students real world concerns sometimes get in the way of their mathematical problem solving, For example, when asked to describe, How much of the pizza is left? A year 4 student responded, All the herbs. !Lower socio-economic students were more likely to focus on the contextual issues of a problem at the expense of the mathematical focus, (Lubienski, 2000)
The mathematics or the context: What knowledge to activate?Solving word problems involves individuals analysing them in a specialised way to build a task- or content-specific mental representation that is most conducive to successful problem solution (Kintsch & Greeno, 1985). Effective reading of a word problem will involve identifying what type of problem it is so appropriate schema can be activated. Readers need to abstract the problem type (Paris, 2010).
Prior knowledge of word problemsIn terms of the 3 NCEA texts,What prior knowledge is it important for students to activate? i.e. knowledge of the context or mathematical knowledge or both?What likely gaps in experience might affect students reading?Can students real life experiences and understandings hinder rather than help their problem-solving? How can teachers prepare students to cope with a lack of knowledge about context?Are literacy mantras about activating prior knowledge useful (or even harmless) in a mathematics context?
Hypothesis: Students might find that their familiarity with a particular context is actually a barrier to solving a problem because they might apply everyday rather than mathematical solutions to the problem e.g. Id calculate the distance between those two points using a tape measure (rather than by applying a theorem).
Word problem problemsHypothesis: When some students encounter an unfamiliar context in a word problem they might react by not attempting the problem, or giving up too easily e.g. I couldnt solve it because Ive never played golf before.
Experience and knowledge of contextTeach predictable contexts & their associated vocabularyDevelop students strategies for coping with unpredictable contexts.
A wallerer is at the top of a vertical clanker. The top of the wallerer is 60m above the ground at the base of the clanker.Sione walks away from the base of the clanker along horizontal ground until he comes to a jumba.He measures the angle of elevation from the ground to the top of the wallerer as 69 degrees. He then walks in the same direction until the angle of elevation is 40 degrees and stops. How far from the jumba did Sione walk?
Predictable contexts (90151)
Price per unit
Tax on income PAYE
Tax (on interest)
Change in value
Reduce in value
Increase in value
3. Text features and purposesExpert readers read different text types in different ways because we know they have:Different featuresDifferent purposes
ActivityYou have 45 seconds to get as much important information from the news story as you can. Your time starts now.What are the main ideas?What types of knowledge did you draw on to locate this information so quickly?
HypothesisStudents will be better at reading word problems when they are explicitly taught about the purpose and text features of this genre.
Organisational featuresOrganisational features that may be useful for students to focus on in this context include:the name and description of the achievement standard they are attempting. For example, a word problem presented in a standard headed right angle triangles is likely to have variables that refer to the length of lines, degrees of angles and location of points (and relationship between them).words that are italicized, underlined or in bold as the author is probably signalling that these are importantHeadings, subheadings, labels (e.g. on rows, columns, axis)
Understanding the word problem genre or text type.To what extent do students understand that word problems:Are stylized representations of hypothetical experiences- not slices of everyday existence?Have unique features and purposes?Demand a special