The Research of Dr. Marian Small Disseminated through the following books : Good Questions - Great Ways to Differentiate Mathematics Instruction More Good Questions - Great Ways to Differentiate Mathematics Instruction And summarized in the following slides.
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The Research of Dr. Marian Small
Disseminated through the following books:
Good Questions - Great Ways to Differentiate Mathematics Instruction
More Good Questions - Great Ways to Differentiate Mathematics Instruction
And summarized in the following slides.
Equity does not mean that every student should receive identical instruction; instead it demands that reasonable and appropriate accommodations be made as needed to promote access and attainment for all students
(NCTM, 2000, p.12)
One way that we see the differences in students is through their responses to the mathematical questions and problems that are put to them. For example, consider the task below, which might be asked of 3rd-grade students:
In one cupboard, you have three shelves with five boxes on each shelf. There are three of those cupboards in the room. How many boxes are stored in all three cupboards?
How might students approach this task?
Liam immediately raises his hand and simply waits for the teacher to help him.
Angelita draws a picture of the cupboards, the shelves, and the boxes and counts each box.
Tara uses addition and writes 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5.
Dejohn uses addition and writes 5 + 5 + 5 = 15, then adds again, writing 15 + 15 + 15 = 45.
Rebecca uses a combination of multiplication and addition and writes 3 x 5 = 15, then 15 + 15 + 15 = 45.
To remove barriers to learning while still challenging each student to take risks and responsibility for learning
(Karp & Howell, 2004)
One approach to meeting each student’s
needs is to provide tasks within each student’s zone of proximal development and to ensure that each student in the class has the opportunity to make meaningful contribution to the class community of learners.
Zone of proximal development is a term used to describe the “distance between the actual development level as determined by independent problem solving and the level of potential development as determined through problem solving under adult guidance or in collaboration with more capable peers.”
(Vygotsky, 1978, p. 86)
In other words, working within a student’s zone of proximal development is to assist students in accessing new ideas that are close enough to what they already know to make the access feasible.
Questions framed in such as way that a variety of responses or approaches are possible
Sets of tasks, usually two or three, that are designed to meet the needs of students at different developmental levels but that get at the same idea and can be discussed simultaneously
The same question is put to the entire class but it is designed for differentiation of response based on each student’s understanding.
Open questions need just the right amount of ambiguity.
Any question too specific may target a narrow level of understanding.
For example, instead of asking students to find 25% of 48 . . .
Ask students to fill in values for the blanks to make this statement true:
72 is _____% of _____
1. The number 4 is a factor of two different numbers. What else might be true about both of the numbers?
2. An expression involving the variable k has the value 10 when k=4. What could the expression be?
3. The mean of a set of numbers is 8. What might the numbers be?
4. A shape has six sides and two 900 angles. What could it look like?
To create parallel tasks to address a particular Big Idea, it is important to first think about how students might differ developmentally in approaching that idea/concept.
Then the object is to develop similar enough contexts for the various options that common questions can be asked of the students as they reflect on their work.
For example, if the Big Idea is Measurement, a set of Parallel Tasks might be as simple as letting students chose whether they are comfortable with linear or area measurements:
Option 1 An object has a length of 30 cm. What might it be?
Option 2 An object has an area of 30 cm2. What might it be?
Common Follow-up questions could be:
To use and take advantage of the relationships between the operations in computational situations
Option 1 Show that the product of two numbers can sometimes be greater than the quotient and sometimes less
Option 2 Choose two numbers to make the following statement true:
quotient < difference < sum < product
Questions that could be asked of both groups include:
An experimental probability approaches a theoretical one when enough random samples are used.
Option 1 You roll two dice. Is it more likely that the sum is 8 or that the difference is 2?
Option 2 You roll two dice. You want an event that is only a bit less likely than rolling a difference of 2. What could it be?
Questions that could be asked of both groups include:
To use Dr. Small’s template for developing Open Questions and Parallel Tasks and find or develop at least four Open Questions and two Parallel Tasks from your first CMP2 unit.
We’ll then ask you to share your favorite Question/Task with the entire group.