Junior Panel ReportsJunior Panel Reports

What do we want

students to know and be able to

do?

Question 1

Consider the following problem…

There are 125 sheep and 5 dogs

in a flock. How old is theshepherd?

A transcript of a child solving this problem aloud...• reveals the kind of misinformed

conception of mathematics that many children hold: 125+5=130 ... this is too big, and 125-5=120 is still too big ... while 125/5=25. That works! I think the shepherd is 25 years old.

Katja invites 8 children to come to her Katja invites 8 children to come to her birthday party, which takes place in 4 birthday party, which takes place in 4

days. How old will Katja be on her days. How old will Katja be on her birthday?birthday?

KGrade 1

Grade 2Grade 3

Grade 4Grade 5

0

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20

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40

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60

Students Attempting a Solution

Radatz (1984) Untersuchungen zum Mathematikunterricht

Suspension of Sense Making

““The overwhelming tendency [of The overwhelming tendency [of students] was to ask themselves whether students] was to ask themselves whether to add, subtract, multiply, or divide to add, subtract, multiply, or divide rather than ask whether the problem rather than ask whether the problem made sense.made sense.

“…“…after a couple of years of experience after a couple of years of experience with traditional mathematics education, with traditional mathematics education, students approach word problems in a students approach word problems in a thoughtless and mechanical way, without thoughtless and mechanical way, without paying attention to the context and paying attention to the context and without any reference to their common without any reference to their common sense.”sense.”

Lieven Verschaffel, Brian Greer and Erik Corte Lieven Verschaffel, Brian Greer and Erik Corte (2000) (2000) Making Sense of Word ProblemsMaking Sense of Word Problems

“Many students develop proceduralfluency, but they often lack the deepconceptual understanding necessary tosolve new problems or make

connectionsbetween mathematical ideas.”

Teaching and Learning Mathematics p. 8

If the balloons popped the sound wouldn't be able to carry since everything would be too far away from the correct floor. A closed window would also prevent the sound from carrying, since most buildings tend to be well insulated. Since the whole operation depends upon a steady flow of electricity, a break in the middle of the wire would also cause problems. Of course, the fellow could shout but the human voice is not loud enough to carry that far. An additional problem is that a string could break on the instrument. Then there could be no accompaniment to the message. It is clear that the best situation would involve less distance. Then there would be fewer potential problems. With face to face contact, the least number of things could go wrong.

(Bransford and Johnson 1972, p. 719)

Consider the following…

Even though you recognize every word in this paragraph, you probably don't understand it.

The passage uses a schema that most people have not experienced or would even imagine experiencing, so when you read it you find nothing in your long-term memory that you can use to interact with the information in the passage. If you are given a schema for the passage, however, it is easy to understand.

Making MeaningMaking Meaning…

Four Roles of Literate Learners p.9, 64, 81

Comprehension Strategies, p.68

Strategically…

Question 2

•How will we know what they have learned?

First Steps: Reading Developmental Continuum

Supporting Differentiation

• Observant teacher• Assessment of prior knowledge• Developmental continuum• Inclusive learning environment• Student choice• Authentic materials and resources

Question 3

•How will I help them learn and respond if they are not learning?

Explicit Instruction

Zone of actual development

Zone of proximal development New zone of actual development

Explicit Instruction & Support

Comprehension Strategies, p.68

Strategically…

Gradual Release of Responsibility

Read Shared Guided Independent Aloud Reading Reading

Reading Responses Conversations

Student independence

Teacher responsibility

Explicit InstructionMeaningful, Engaging Tasks

Across the CurriculumAcross the School

Throughout the System

VideoVideo

What might it look like in the classroom?

Explicit Instruction

Read Aloud Shared Reading Guided Reading Independent ReadingModelled Writing Shared Writing Guided Writing Independent Writing

All teacher Joint Responsibility All Student

Most Support

Least Support

Zone of actual development

Zone of proximal development New zone of actual development

Explicit Instruction & Support