Transcript Document 7128293

Trends in Reading and Writing
Research in Science and
Mathematics Education
Larry D. Yore
University of Victoria
David Pimm
University of Alberta
Educational Reforms in North
America: Canada & USA
2
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)
3
Common Features Across the
Disciplines (Ford, Yore, & Anthony, 1997)
Target Goals
All Students
Contemporary Literacy
Pedagogical Orientations
Constructivism
Authentic Assessment
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Contemporary Literacy (Yore, 2000)
Abilities, Thinking, and Habits of Mind to
Construct Disciplinary Understanding
Communications to Inform and Persuade
Big Ideas/Unifying Concepts
5
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 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
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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
10
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 Argumentation
Claims
Evidence
Warrants
Backings
Counter-claims
Qualifications
Rebuttals
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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
SARS patients
and healthy people
SARS
Caused by
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
Counter-claims
Warrants
Claims
Rebuttal
Backings
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Example of an Extended Argument
(Yore, et al., 2004)
Examination of:
AIDS and
healthy
patients
HIV was found
in all AIDS
patients and some
healthy patients
HIV in
some
people
HIV
causes
AIDS
People
with weak
immune
systems
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Prior Domain and
Topic Knowledge
Metacognitive Awareness
and Executive Control
Science Reading
Strategies
Interactive-Constructive Model of Science Reading:
Requisite Knowledge, Metacognition, and Strategies
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
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Metacognition
Self-appraisal
of Cognition
Self-management of
Cognition
Declarative
Knowledge
Planning
Procedural
Knowledge
Evaluation
Conditional
Knowledge
Regulation
Metacognition (Yore, 2000)
 Metacognitive
Awareness/Selfappraisal of Task
 Declarative: What
 Procedural: How
 Conditional: When & Why
 Executive Control/Selfmanagement of Task
 Planning: Setting
purpose, etc.
 Evaluation: Monitoring
progress
 Regulation: Adjusting
effort and action
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Expert Science Reader: Index of
Science Reading Awareness
(Yore, Craig, & Maguire, 1998)
Science Reading
Science Text
Science Reading Strategies
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Science Reading
Reading is interactive-constructive
Meaning Making, not Meaning Taking
Self-confidence and Self-efficacy
Shift Reading to Textual Demands
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Science Text
Words are labels for ideas and experience
Text is somebody’s 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
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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
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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)
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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
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Prior Domain and
Topic Knowledge
Metacognitive Awareness
and Executive Control
Science Writing
Strategies
Knowledge-Building Model of Science Writing
Writing Genre (Unsworth, 2001; Yore, 2000)
Genre
Narrative
Purpose
Outcome
Recording
Attitudes
emotions
and ideas
Description
Documentation Basic
of events
knowledge
Explanation
Causality
Cause-effect
relationships
Instruction
Directions
Procedural
knowledge
Argumentation Persuasion
Patterns
of argument
Audience
Self and
others
Other
Others
Others
Others
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Research Trends in Reading
and Writing in Mathematics
Classrooms
David Pimm
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 genres
Locating different plausible purposes for the
writing
Exploring different audiences for such writing
(Phillips, 2002)
39
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 text
Research 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)
47
Scrambled Euclid

1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
Choose beginning words from the following list:
Then, First, Let, For, I say that, Now, Next, But, Therefore, And
…it also measures EF.
…G is not the same with any of the numbers A, B, C.
…it be prime; then the prime numbers A, B, C, EF have been found which are more than A,
B, C.
…it be measured by the prime number G.
…G is not the same with any one of the numbers A, B, C.
…the prime numbers A, B, C, G have been found which are more than the assigned
multitude of A, B, C.
…if possible, let it be so.
…the least number measured by A, B, C be taken, and let it be DE. Let the unit DF be added
to DE.
…EF not be prime; therefore it is measured by some prime number.
…G, being a number, will measure the remainder, the unit DF; which is absurd.
…by hypothesis it is prime.
…A, B, C measure DE; therefore G also will measure DE.
…EF is either prime or not.
…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.
51
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.
52
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.
53
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.
54
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, 347352.
 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.
55
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.
56
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. 371409. Dordrecht, NL: Kluwer Academic Publishers.
57
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.
58
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.
59
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.
60