Trends in Reading and Writing Research in Science and Mathematics Education

Larry D. YoreUniversity of Victoria

David PimmUniversity of Alberta

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Educational Reforms in North America: Canada & USA

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Cross-Curricular View of Current Reforms

Standards for the English Language Arts (NCTE/IRA) Principles and Standards for School Mathematics (NCTM) Science for All Americans (AAAS) National Science Education Standards (NRC) Curriculum Standards for Social Studies (NCSS) Technology for All Americans (ITEA) Western Canadian Protocol for Mathematics (Alberta,

British Columbia, other western provinces) Pan-Canadian Framework for Science (CMEC)

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Common Features Across the Disciplines (Ford, Yore, & Anthony, 1997)

Target GoalsAll StudentsContemporary Literacy

Pedagogical OrientationsConstructivismAuthentic Assessment

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Contemporary Literacy (Yore, 2000)

Abilities, Thinking, and Habits of Mind to Construct Disciplinary Understanding

Communications to Inform and PersuadeBig Ideas/Unifying Concepts

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Interacting Senses of Science Literacy: Cognitive Symbiosis?(Norris & Phillips, 2003)

Fundamental Sense Cognitive and Metacognitive

Abilities Critical Thinking Habits of Mind Scientific Language Arts Information and

Communication Technologies

Derived Sense Understanding of the Big

Ideas and Unifying Concepts Nature of Science

People’s attempt to search, describe, and explain patterns of events in nature

Scientific Inquiry Technological Design

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Symbiosis between Fundamental and Derived Senses

Learning How Impacts Using Language to LearnLearning to talk/argue and talking/arguing to learn

scienceLearning to read science and reading to learn

scienceLearning to write and writing to learn science

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Enhancing Science Literacy

Embedded Oral Interactions, Argument, Reading, and Writing Instruction in Science Inquiry (Yore, 2000; Yore, Bisanz, & Hand, 2003; Saul, 2004)

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Constructivism — Interactive and Constructive (Yore, 2001)

Theory about learning — not teaching — that assumes learners construct understanding from prior knowledge, sensory experiences, and social interactions

Prior knowledge may contain misconceptions that are difficult to change

Conceptual change approaches must challenge misconceptions and allow learners to construct a more understandable and powerful replacement concept

Numerous interpretations of constructivism Select an interpretation that matches the discipline and goals

— Learning Cycle

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Constructivist Approach:Science Co-op Learning Cycle (Shymansky, Yore, & Anderson, 2004)

Engage — Access, assess, and challenge learners’ prior knowledge

Explore — Allow opportunities for learners to investigate the target concepts with hands-on, visual, and language experiences

Consolidate — Scaffold the learners’ interpretations of the experiences and connect to the established understandings

Assess — Document learners’ ideas in all parts of the cycle to facilitate and evaluate learning

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Authentic Assessment(Yore, Williams, Shymansky, Chidsey, Henriques, & Craig, 1995)

Assess in the same context as teaching and learning Document the construction of understanding as well as

the recall of ideas Assess throughout instruction Use assessment techniques that match the target

outcomes and processes Assess to empower learning and to inform instruction

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Myths about Science (McComas, 1998)

Science evolves — hypotheses, theories, laws. Hypotheses are educated guesses. The scientific method is general and universal. Evidence accumulates to produce truths. Science and inquiry result in absolute proof. Science is procedural, not creative. Science can address all questions. Scientists are objective. Experimentation is the primary route to claims. All science is reviewed to ensure honesty.

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Modern View of Science

“There is a reality that we may know some day, and claims

about nature must be tested.”

(Yore, Hand, & Florence, 2004)

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Modern View of Science

Science knowledge is a temporary explanation that best fits the existing evidence, established knowledge, and current thinking.

Science knowledge claims develop with the aid of a hypothesis and data that are collected and that support or refute the hypothesis.

Science knowledge claims are open to repeated public evaluation.

The scientific method is not bound by a single set of steps — Problem, hypothesis, design experiment, collect data, analyze data, and draw conclusion.

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Science is like Doing a Crossword Puzzle.

“Picture a scientist as working on part of an enormous crossword puzzle: making an informed guess about some entry, checking and double-checking its fit with the clue and already-completed intersecting entries. ... Much of the crossword is blank, but many entries are already completed, some in almost-indelible ink, some in regular ink, some in pencil, some heavily, some faintly. Some are in English, some in Swahili, some in Flemish, some in Esperanto, etc. … Now and then a long entry, intersecting with numerous others.”

(Haack, 2003, pp. 93-94)

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Science as Argument(Osborne, Erduran, & Simon, 2004)

Elements of ArgumentationClaimsEvidenceWarrantsBackingsCounter-claimsQualificationsRebuttals

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Classic Pattern of Argumentation(Toulmin, 1958)

Evidence Claims

Warrants

Backings

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Example of a Classic Argument(Yore, et al., 2004)

Examination of SARSSARS patients Caused byand healthy people a virus

Warrant 1: A unique virus (corona) was isolated by UVic and UBC scientists.Warrant 2: SARS patients’ blood and body fluids contain the virus.Backing 1: Established knowledge about respiratory diseases.Backing 2: Influenza is caused by a virus, not bacteria.

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Extended Pattern of Argumentation(Toulmin, 1958)

Evidence Qualifiers and Claims Counter-claims

Warrants Rebuttal

Backings

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Example of an Extended Argument(Yore, et al., 2004)

Examination of:AIDS and HIV in HIVhealthy some causespatients people AIDS

HIV was found Peoplein all AIDS with weakpatients and some immunehealthy patients systems

Interactive-Constructive Model of Science Reading:Requisite Knowledge, Metacognition, and Strategies

Prior Domain andTopic Knowledge

Metacognitive Awarenessand Executive Control

Science ReadingStrategies

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Explicit Science Reading Instruction: Important Reading Strategies that Respond to Instruction (Yore, 2000)

Assessing Generating Questions Summarizing Inferring Monitoring Utilizing Text Structure

Reading and Reasoning Improving Memory Self-regulating Skimming, Elaborating,

Sequencing

Metacognition

Self-appraisal of Cognition

Self-management of Cognition

DeclarativeKnowledge

Planning

Evaluation

Regulation

ProceduralKnowledge

ConditionalKnowledge

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Metacognition (Yore, 2000)

Metacognitive Awareness/Self-appraisal of TaskDeclarative: WhatProcedural: HowConditional: When & Why

Executive Control/Self-management of TaskPlanning: Setting

purpose, etc.Evaluation: Monitoring

progressRegulation: Adjusting

effort and action

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Expert Science Reader: Index of Science Reading Awareness(Yore, Craig, & Maguire, 1998)

Science ReadingScience TextScience Reading Strategies

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Science Reading

Reading is interactive-constructiveMeaning Making, not Meaning TakingSelf-confidence and Self-efficacyShift Reading to Textual Demands

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Science Text

Words are labels for ideas and experienceText is somebody’s interpretationText represents the nature of science

Tentative claims about realityMay not actually represent realityContains a degree of uncertainty

Evaluates plausibility, accuracy, and connectedness of text

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Science Reading Strategies

Identify purpose, access prior knowledge, plan heuristic, and select strategies

Use knowledge-retrieval techniquesUse input techniques to access text-based

informationUse knowledge-constructing techniquesApply critical thinkingMonitor and regulate reading

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Writing in Science(Yore, 2000; Yore, Bisanz, & Hand, 2003)

Models: Knowledge Telling or Knowledge Building (Keys, 1999)

Genre (form & function)NarrativeDescription InstructionArgumentationExplanation Also see Unsworth, 2001

Effective Applications Involve a series of tasksRequire transformationEncourage revision

without repetitionCo-authoring as

enculturation into the science discourse community (Florence & Yore, 2004; Yore, Hand, & Florence, 2004)

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Narrative(Gallaghan, Knapp, & Noble, 1993; Aram & Powell, 2005)

Process: Sequencing people and events in time and space

Purpose: Entertain, tell a story, or recount personal or historical experiences

Structure (story grammar): Setting, characters, problem, actions, and resolution

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Description(Gallaghan, Knapp, & Noble, 1993; Aram & Powell, 2005)

Process: Classifying and describing things into taxonomies of meaning

Purpose: Documents the way something is or was

Structure: General class, qualities, parts and functions, and habits

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Instruction (Gallaghan, Knapp, & Noble, 1993; Aram & Powell, 2005)

Process: Logically ordering a sequence of actions or behaviors.

Purpose: State procedure of how something is done through a series of ordered steps or actions.

Structure: Goal, materials, ordered steps, and summary statement.

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Argument(Gallaghan, Knapp, & Noble, 1993; Aram & Powell, 2005)

Process: Persuading listeners or readers to accept a logical ordering of propositions

Purpose: Promote a particular point of view, claim, or solution

Structure: Thesis/position statement, series of claims, rebuttals and evidence, and summary or reiteration of thesis/position statement

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Explanation (Gallaghan, Knapp, & Noble, 1993; Aram & Powell, 2005)

Process: Sequencing phenomena/events in temporal or causal patterns

Purpose: Explain how something works, the processes involved, or the cause-effect relationship justified by a theoretical model or canonical knowledge

Structure: General statement, time-series steps, linked processes, cause-effect or problem-solution

Prior Domain andTopic Knowledge

Metacognitive Awarenessand Executive Control

Science WritingStrategies

Knowledge-Building Model of Science Writing

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Writing Genre (Unsworth, 2001; Yore, 2000)

Genre Purpose Outcome AudienceNarrative Recording Attitudes Self and

emotions others and ideas

Description Documentation Basic Other of events knowledge

Explanation Causality Cause-effect Others relationships

Instruction Directions Procedural Others knowledge

Argumentation Persuasion Patterns Others of argument

Research Trends in Reading and Writing in Mathematics Classrooms

David Pimm

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Focus of Research on Reading

Finding quite different sorts of text to offer students to read

Exploring situated ways for them to engage productively with such texts within a mathematics classroom (Borasi & Siegel, 2000)

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Focus of Research on Writing

Identifying features of different written genresLocating different plausible purposes for the

writingExploring different audiences for such writing

(Phillips, 2002)

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Elements of Reading and Writing Research

Form (genre) Audience Purpose Content Voice

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Form (genre)

Mathematics draws on certain forms whose features students need to become aware of

Examples include: Instructions (algorithm), word problems, geometric diagrams, investigative write-ups, etcetera

Research questions: Explicit teaching of features vs. immersion? Do students get to practice and become fluent with these forms and, if so, in what circumstances?

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Audience

Genuine audience in terms of need and access to knowledge

Questions of insider/outsider audience with respect to what is being communicated

Availability of author, negotiation of textResearch question: How to design tasks

involving a variety of audiences?

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Content

Writing mathematics vs. writing about mathematics (‘para-mathematical’ writing)

Research question: How is the content shaped by the related form, purpose, and audience? How does particular content shape these?

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Voice

Not just a question of first/third person, active or passive voice, but also what Bakhtin calls ‘addressivity’ — text that takes into account needs of the reader

Research question: How does a student develop an own mathematical voice (spoken/written)? What influences it?

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Task 1: Message Situation: In pairs, one

student makes (from pattern blocks) or draws a shape unseen by the other.

Challenge: Either orally or in writing, create a sequence of instructions to allow the partner to reconstruct the figure without any assistance from the shape creator.

Pedagogic Intent: To increase student awareness of

different features of speech and writing, to attune them to potential ambiguity, and to develop their sense of the need for orientation of the reader/hearer.

To draw attention to the fact that a drawing is made in time; but once made, the description to allow it to be re-made does not have to follow the original construction.

To have them respond to a need to develop a technical vocabulary to aid communication.

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Task 2: A Cut Proof

Situation: The order of the sentence statements in this proof have got scrambled and the first word(s) of each sentence cut off and placed in a pile.

Question/Challenge: Can you discover the original, correct order to restore the proof? How did you work on this task?

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Proposition

“Prime numbers are more than any assigned multitude of prime

numbers.”

(Euclid IX. Prop 20)

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Scrambled Euclid Choose beginning words from the following list:

Then, First, Let, For, I say that, Now, Next, But, Therefore, And

1. …it also measures EF.2. …G is not the same with any of the numbers A, B, C.3. …it be prime; then the prime numbers A, B, C, EF have been found which are more

than A, B, C.4. …it be measured by the prime number G.5. …G is not the same with any one of the numbers A, B, C.6. …the prime numbers A, B, C, G have been found which are more than the assigned

multitude of A, B, C.7. …if possible, let it be so.8. …the least number measured by A, B, C be taken, and let it be DE. Let the unit DF

be added to DE.9. …EF not be prime; therefore it is measured by some prime number.10.…G, being a number, will measure the remainder, the unit DF; which is absurd.11.…by hypothesis it is prime.12.…A, B, C measure DE; therefore G also will measure DE.13.…EF is either prime or not.14.…A, B, C be the assigned prime numbers. I say that there are more prime numbers

than A, B, C.

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Why bother?

Pedagogic Intent:To allow students to struggle with a task involving a text

containing an unfamiliar style of mathematical presentation (so it draws on the history of mathematics).

To become aware of how much of the structure of a proof is contained in the first words of each sentence.

To see how the order of the sentences matters.To come up with a way of structuring a proof that conveys its

structure better.

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Task 3: Mathematical Pen-Pal Writing

Situation: Students from the same class are individually paired with a teacher education student in a class at a nearby university.

Challenge: To write a series of ‘friendly’ letters (a genre even young students are familiar with) back and forth; each letter to contain a mathematical problem for the other and their response to previous problems contained in letters.

Pedagogic Purpose: To expose students to a

genuine and interested mathematical audience outside of the classroom.

To have them experience the challenge of writing and explaining their mathematics and mathematical thinking at a distance.

To have students experience reading/interpreting another’s mathematical writing and thinking at a distance.

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References for Science and Language

Aram, R., & Powell, D. (2005). Genre in trade books. Presentation at the AETS meeting, Colorado Springs, CO.

Ford, C. L. (1998). Educating preservice teachers to teach for an evaluative view of knowledge and critical thinking in elementary social studies. Unpublished Ph.D Dissertation, University of Victoria, Victoria, BC, Canada.

Ford, C. L., Yore, L. D., & Anthony, R. J. (1997). Reforms, visions, and standards: A cross-curricular view from an elementary school perspective. Resources in Education (ERIC), ED406168.

Gallaghan, M., Knapp, P., & Noble, G. (1993). Genre in practice. In B. Cope & M. Kalantzis (Eds.), The powers of literacy: A genre approach to teaching writing (pp. 179-202), Pittsburgh, PA: University of Pittsburgh Press.

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Science References (continued)

Haack, S. (2003). Defending science within reason: Between scientism and cynicism. Amherst, NY: Prometheus Books.

McComas, W. F. (1998). The principal elements of the nature of science: Dispelling the myths. In W. F. McComas (Ed.), The nature of science in science education: Rationale and strategies. Dordrecht, NL: Kluwer.

Norris, S. P., & Phillips, L. M. (2003). How literacy in its fundamental sense is central to scientific literacy. Science Education, 87, 224-240.

Novak, J. D., & Gowin, B. D. (1984). Learning how to learn. Cambridge, UK: Cambridge University Press.

Osborne, J., Erduran, S., & Simon, S. (2004). Enhancing the quality of argumentation in school science, Journal of Research in Science Teaching, 41, 994-1020.

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Science References (continued)

Saul, E. W. (Ed.) (2004). Crossing borders in literacy and science instruction. Newark, DE: International Reading Association/National Science Teachers Association.

Shymansky, J. A., Yore, L. D., & Anderson, J. O. (2004). Impact of a school district’s science reform effort on the achievement and attitudes of third- and fourth-grade students. Journal of Research in Science Teaching, 41, 771-790.

Toulmin, S. (1958). The uses of argument. Cambridge, UK: Cambridge University Press.

Unsworth, L. (2001). Teaching multiliteracies across the curriculum. Philadelphia, PA: Open University Press.

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Science References (continued)

Yore, L. D. (2000). Enhancing science literacy for all students with embedded reading instruction and writing-to-learn activities. Journal of Deaf Studies and Deaf Education, 5(1), 105-122.

Yore, L. D. (2001). What is meant by constructivist science teaching and will the science education community stay the course for meaningful reform? Electronic Journal of Science Education, 5(4). Online journal: http://unr.edu/homepage/crowther/ejse.

Yore, L. D., Bisanz, G. L., & Hand, B. M. (2003). Examining the literacy component of science literacy: 25 years of language arts and science research. International Journal of Science Education, 25, 689-725.

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Science References (continued) Yore, L. D., Craig, M. T., & Maguire, T. O. (1998). Index of science reading

awareness: An interactive-constructive model, test verification, and grades 4-8 results. Journal of Research in Science Teaching. 35(1), 27-51.

Yore, L. D., Hand, B. M., & Florence, M. K. (2004). Scientists’ views of science, models of writing, and science writing practice. Journal of Research in Science Teaching, 41, 338-369.

Yore, L. D., Hand, B., Goldman, S. R., Hildebrand, G. M., Osborne, J. F., Treagust, D. F., & Wallace, C. S. (2004). New directions in language and science education research. Reading Research Quarterly, 39, 347-352.

Yore, L. D., Williams, R. L., Shymansky, J. A., Chidsey, J. L., Henriques, L., & Craig, M. T. (1995). Refocussing science assessment: Informing learners, teachers, and other stakeholders. B.C. Catalyst, 38(4), 3-9.

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References for Mathematics and Language

Borasi, R., & Siegel, M. (2000). Reading counts: Expanding the role of reading in mathematics classrooms. New York: Teachers College Press.

Pimm, D. (1987). Speaking mathematically: Communication in mathematics classroom. London: Routledge & Kegan Paul.

Rowland, T. (2000). The pragmatics of mathematics education: Vagueness in mathematical discourse. London: Falmer Press.

Shuard, H., & Rothery, A. (Eds.). (1984). Children reading mathematics. London: John Murray.

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Further References Chapman, A. (2002). Language practices in school mathematics: A

social semiotic perspective. Perth, WA: Edwin Mellen Press. Gerofsky, S. (1999a). Genre analysis as a way of understanding

pedagogy in mathematics education. For the Learning of Mathematics, 19(3), 36-46.

Gerofsky, S. (1999b). The word problem as genre in mathematics education. Unpublished Ph.D. thesis, Burnaby, BC, Canada, Simon Fraser University.

Gerofsky, S. (2003). A man left Albuquerque heading east. New York: Peter Lang.

Love, E., & Pimm, D. (1996). “This is so”: A text on texts. In A. Bishop, et al. (Eds.) International handbook of mathematics education, pp. 371-409. Dordrecht, NL: Kluwer Academic Publishers.

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Further References (continued)

Morgan, C. (1996). The language of mathematics: Towards a critical analysis of mathematics texts. For the Learning of Mathematics 16(3), 2-10.

Morgan, C. (1998). Writing mathematically: The discourse of investigation. London: Falmer Press.

Netz, R. (1998). Greek mathematical diagrams: Their use and their meaning. For the Learning of Mathematics 18(3), 33-39.

Netz, R. (1999). The shaping of deduction in Greek mathematics: A study in cognitive history. Cambridge: Cambridge University Press.

Phillips, E. (2002). Classroom explorations of mathematical writing with nine- and ten-year-olds. Unpublished Ph.D. dissertation, Milton Keynes, Bucks, The Open University.

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Further References (continued)

Pimm, D. (1984). Who is “we”? Mathematics Teaching 107, 39-42. Pimm, D. (1987). Speaking mathematically: Communication in

mathematics classrooms. London: Routledge & Kegan Paul. Pimm, D., & Wagner, D. (2003). Investigation, mathematics education

and genre: An essay review of Candia Morgan's writing mathematically: The discourse of investigation. Educational Studies in Mathematics 50(2), 159-178.

Rowland, T. (1992). Pointing with pronouns. For the Learning of Mathematics, 12(2), 44-48.

Rowland, T. (1995a). Vagueness in mathematics talk. Unpublished Ph.D. thesis, Milton Keynes, Bucks, Open University.

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Further References (continued)

Rowland, T. (1995b). Hedges in mathematics talk: Linguistic pointers to uncertainty. Educational Studies in Mathematics 29(4), 327-353.

Rowland, T. (1999). Pronouns in mathematics talk: Power, vagueness and generalisation. For the Learning of Mathematics 19(2), 19-26.

Rowland, T. (2000). The pragmatics of mathematics education: Vagueness in mathematical discourse. London: Falmer Press.

Solomon, Y., & O’Neill, J. (1998). Mathematics and narrative. Language and Education 12(3), 210-221.