Trends in Reading and Writing Research in Science and Mathematics Education

1
Trends in Reading and Writing Research in Science
and Mathematics Education

• Larry D. Yore
• University of Victoria
• David Pimm
• University of Alberta

2
Educational Reforms in North America Canada USA
3
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)

4
Common Features Across the Disciplines (Ford,
Yore, Anthony, 1997)

• Target Goals
• All Students
• Contemporary Literacy
• Pedagogical Orientations
• Constructivism
• Authentic Assessment

5
Contemporary Literacy (Yore, 2000)

• Abilities, Thinking, and Habits of Mind to
  Construct Disciplinary Understanding
• Communications to Inform and Persuade
• Big Ideas/Unifying Concepts

6
Interacting Senses of Science Literacy Cognitive
Symbiosis?(Norris Phillips, 2003)

• Derived Sense
• Understanding of the Big Ideas and Unifying
  Concepts
• Nature of Science
• Peoples attempt to search, describe, and explain
  patterns of events in nature
• Scientific Inquiry
• Technological Design

• Fundamental Sense
• Cognitive and Metacognitive Abilities
• Critical Thinking
• Habits of Mind
• Scientific Language Arts
• Information and Communication Technologies

7
Symbiosis between Fundamental and Derived Senses

• Learning How Impacts Using Language to Learn
• Learning to talk/argue and talking/arguing to
  learn science
• Learning to read science and reading to learn
  science
• Learning to write and writing to learn science

8
Enhancing Science Literacy

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

9
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

10
Constructivist ApproachScience 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

11
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

12
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.

13
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)

14
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.

15
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)

16
Science as Argument(Osborne, Erduran, Simon,
2004)

• Elements of Argumentation
• Claims
• Evidence
• Warrants
• Backings
• Counter-claims
• Qualifications
• Rebuttals

17
Classic Pattern of Argumentation(Toulmin, 1958)

• Evidence Claims
• Warrants
• Backings

18
Example of a Classic Argument(Yore, et al., 2004)

• Examination of SARS
• SARS patients Caused by
• and 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.

19
Extended Pattern of Argumentation(Toulmin, 1958)

• Evidence Qualifiers and Claims
• Counter-claims
• Warrants Rebuttal
• Backings

20
Example of an Extended Argument(Yore, et al.,
2004)

• Examination of
• AIDS and HIV in HIV
• healthy some causes
• patients people AIDS
• HIV was found People
• in all AIDS with weak
• patients and some immune
• healthy patients systems

21

Interactive-Constructive Model of
Science ReadingRequisite Knowledge,
Metacognition, and Strategies
Prior Domain and Topic Knowledge
Metacognitive Awareness and Executive Control
Science Reading Strategies
22
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

23
Metacognition
Self-appraisal of Cognition
Self-management of Cognition
Declarative Knowledge
Planning
Procedural Knowledge
Evaluation
Conditional Knowledge
Regulation
24
Metacognition (Yore, 2000)

• Metacognitive Awareness/Self-appraisal of Task
• Declarative What
• Procedural How
• Conditional When Why

• Executive Control/Self-management of Task
• Planning Setting purpose, etc.
• Evaluation Monitoring progress
• Regulation Adjusting effort and action

25
Expert Science Reader Index of Science Reading
Awareness(Yore, Craig, Maguire, 1998)

• Science Reading
• Science Text
• Science Reading Strategies

26
Science Reading

• Reading is interactive-constructive
• Meaning Making, not Meaning Taking
• Self-confidence and Self-efficacy
• Shift Reading to Textual Demands

27
Science Text

• Words are labels for ideas and experience
• Text is somebodys interpretation
• Text represents the nature of science
• Tentative claims about reality
• May not actually represent reality
• Contains a degree of uncertainty
• Evaluates plausibility, accuracy, and
  connectedness of text

28
Science Reading Strategies

• Identify purpose, access prior knowledge, plan
  heuristic, and select strategies
• Use knowledge-retrieval techniques
• Use input techniques to access text-based
  information
• Use knowledge-constructing techniques
• Apply critical thinking
• Monitor and regulate reading

29
Writing in Science(Yore, 2000 Yore, Bisanz,
Hand, 2003)

• Models Knowledge Telling or Knowledge Building
  (Keys, 1999)
• Genre (form function)
• Narrative
• Description
• Instruction
• Argumentation
• Explanation
• Also see Unsworth, 2001

• Effective Applications
• Involve a series of tasks
• Require transformation
• Encourage revision without repetition
• Co-authoring as enculturation into the science
  discourse community (Florence Yore, 2004 Yore,
  Hand, Florence, 2004)

30
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

31
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

32
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.

33
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

34
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

35
Prior Domain and Topic Knowledge
Metacognitive Awareness and Executive Control
Science Writing Strategies
Knowledge-Building Model of Science Writing
36
Writing Genre (Unsworth, 2001 Yore, 2000)

• Genre Purpose Outcome Audience
• Narrative 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

37
Research Trends in Reading and Writing in
Mathematics Classrooms

• David Pimm

38
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)

39
Focus of Research on Writing

• Identifying features of different written genres
• Locating different plausible purposes for the
  writing
• Exploring different audiences for such writing
  (Phillips, 2002)

40
Elements of Reading and Writing Research

• Form (genre)
• Audience
• Purpose
• Content
• Voice

41
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?

42
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 text
• Research question How to design tasks involving
  a variety of audiences?

43
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?

44
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?

45
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.

46
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?

47
Proposition

• Prime numbers are more than any assigned
  multitude of prime numbers.
• (Euclid IX. Prop 20)

48
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.

49
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.

50
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
  anothers mathematical writing and thinking at a
  distance.

51
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.

52
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.

53
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 districts 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.

54
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.

55
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.

56
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.

57
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.

58
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.

59
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.

60
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., ONeill, J. (1998). Mathematics
  and narrative. Language and Education 12(3),
  210-221.