Number Talks in High School - STEP Conference
Number Talks in High School - STEP Conference
Number Talks in High School - STEP Conference
Agenda
Number
How
Talk
Dilemmas
Make sense of problems and persevere in solving them. Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.
proficient studentsconsider analogous problems and try special cases and simpler forms of the original problem in order to gain insight into its solution.
In order to take advantage of new opportunities and to meet the challenges of tomorrow, todays students need flexible approaches for defining and solving problems.
reasoning entailsattending to the meaning of quantitiesand flexibly using different properties of operations and objects.
Students ages 7-12 in two groups: above average ability & below average ability Gave them three different types of simple addition problems 4 different ways of solving the problems:
The lower ability group was doing a different kind of math!! Highlights the importance of exposing students to many different kinds of strategies for working with numbers.
Richard Skemp (1976) wrote about two different types of math understanding
Algorithm = a process or set of rules to be followed in calculations or other problemsolving situations, esp. by a computer Students memorize algorithms, or rules without understanding them and then often forget or mix up the many different rules When the problem doesnt exactly fit a rule, students do not know how to solve it
Skemp writes, the more complete a pupils schema, the greater his feeling of confidence in his own ability to find new ways of getting there without outside help Students can create an overview of problems and develop creative ways to solve them
Attend to precision
Mathematically
proficient students try to communicate precisely to others. Principles and Standards. Heibert
NCTM
study
(1993)
classrooms received alternate instruction (fewer problems, more discussion of methods and strategies)
Place Value
Instructed Computation Story Problem New Computation
8
4 1 8
22%
35% 38% 3%
25%
31% 56% 4%
21%
41% 53% 6%
27%
32% 43% 3%
71%
70% 90% 25%
69%
80% 97% 29%
Place Value
Instructed Computation Story Problem New Computation
7
13 3 5
37%
72% 45% 38%
24%
71% 44% 39%
36%
76% 60% 39%
53%
83% 79% 54%
60%
88% 76% 59%
86%
88% 93% 63%
Allowing students to talk about their solution methods leads to better understanding and therefore better results The data reported in this study suggest that, in mathematics classrooms, certain kinds of instructional tasks and discourse encourage more productive ways of thinking.
justify their conclusions, communicate them to others, and respond to the arguments of others.
Teacher probed students explanations to uncover details or further thinking about their problem-solving strategies
Classroom Whole-Class Small-Group A 23 36 B 25 25 C 92 77 D 71 50
Student Explaining in Small Groups Classroom Group gave correct/com plete explanation A 16 B 33 C 72 D 56
Student Achievement
Classroom
Written Assessment Interview
A
17 13
B
30 24
C
47 37
D
45 44
Analysis:
Teacher practices of questioning led to more student explanation and greater percentage of correct answers By asking students to explain their methods for solving problems and refraining from evaluating students answers, teachers helped create expectations and obligations for students to publicly display their thinking
Students afraid to share their thinking Maintaining number talks in high school students think its childish How much should a facilitator push? Traditional algorithm Receiving support from other faculty or parents doing number talks alone may be difficult Choosing a problem that is at the right level Supporting English Learners or students with special needs Timing Disjoint between number talk and lesson Status issues Introducing number talks in a way that is meaningful to high schoolers
We will focus on
Students afraid to share their thinking Maintaining number talks in high school students think its childish How much should a facilitator push? Traditional algorithm Receiving support from other faculty or parents doing number talks alone may be difficult Choosing a problem at the right level Supporting English Learners or students with special needs Timing Disjoint between number talk and lesson Status issues Introducing number talks in a way that is meaningful to high school students
2. Traditional Algorithm
Questions?