Transcript presentation slides

NOTICING
NUMERACY
NOW!
RESEARCH FUNDED BY THE NATIONAL SCIENCE FOUNDATION:
Transforming Undergraduate Education in STEM (TUES) Award # 1043667, 1043656, 1043831
About Us
Preservice Teacher Preparation Collaborative
Jonathan Thomas Northern Kentucky University
KY Center for Mathematics
[email protected]
Edna O. Schack
Morehead State University
[email protected]
Sara Eisenhardt
Northern Kentucky University
[email protected]
Molly H. Fisher
University of Kentucky
[email protected]
Margaret Yoder
Eastern Kentucky University
[email protected]
Janet Tassell
Western Kentucky University
[email protected]
Cindy Jong*
University of Kentucky
[email protected]
Todd Brown*
University of Louisville
[email protected]
Greg Gierhart*
Murray State University
[email protected]
* Comparison Implementers
INSTRUCTIONAL MODULE
Three interrelated skills of Professional Noticing
of children’s mathematical thinking:
• Attending to the children’s work
• Interpreting children’s work in context of
mathematics
• Deciding the appropriate next steps
Jacobs, V. A., Lamb, L. L. C., & Philipp, R. A. (2010). Professional Noticing of Children’s Mathematical
Thinking. Journal for Research in Mathematics Education, 41, 169-202.
STAGES OF EARLY ARITHMETIC LEARNING (SEAL)
Olive, J. (2001). Children's number sequences: An explanation of Steffe's constructs and an extrapolation to rational
numbers of arithmetic. The Mathematics Educator, 11, 4-9.
Steffe, L. (1992). Learning stages in the construction of the number sequence. In J. Bideaud, C. Meljac, & J. Fischer (Eds.),
Pathways to number: Children’s developing numerical abilities (pp. 83–88). Hillsdale: Lawrence Erlbaum.
Wright, R. J., Martland, J., & Stafford, A. (2000). Early numeracy: Assessment for teaching and intervention. London: Paul
Chapman Publications/Sage.
SEAL
LEARNING PROGRESSION OF EARLY QUANTITATIVE UNDERSTANDING
VIA EXAMINATION OF COUNTING SCHEMES
Stage 0:
Stage 1:
Stage 2:
Stage 3:
Stage 4:
Stage 5:
Emergent Counting Scheme
Perceptual Counting Scheme
Figurative Counting Scheme
Initial Number Sequence
Intermediate Number Sequence
Facile Number Sequence
PRIMARY RESEARCH QUESTION
To what extent can teacher educators
facilitate the development of Preservice
Elementary Teacher (PSET) professional
noticing (attending, interpreting, and
deciding) of children’s mathematics?
Video-Based Assessment Prompts
1.Please describe in detail what this child did in
response to this problem.
(Attending)
2.Please explain what you learned about this child’s
understanding of mathematics.
(Interpreting)
3.Pretend that you are the teacher of this child.
What problem or problems might you pose next?
Provide a rationale for your choice.
(Deciding)
ATTENDING BENCHMARKS
INTERPRETING BENCHMARKS
DECIDING BENCHMARKS
Preliminary Analysis Conducted at 3 Research Sites
Attending
University 0
University 1
University 2
All Participants
Interpreting
N
M
SD
M
SD
M
SD
Pre-Test
37
2.14
.79
1.59
.797
1.54
.61
Post-Test
37
2.43
.87
2.05
.84
2.22
.79
Pre-Test
23
2.39
.99
1.82
.89
2.04
.56
Post-Test
23
3.09
1.04
2.43
.73
2.70
.56
Pre-Test
34
2.38
1.10
1.76
.78
1.97
.67
Post-Test
34
3.00
1.10
2.15
.89
2.47
.75
Pre-Test
94
.96
1.82
2.43
.66
94
1.71
2.18
.81
Post-Test
2.29
2.80
1.03
Descriptive statistics of professional noticing measures by university
Attending
Interpreting
Deciding
Deciding
N
t
p
94
-3.986
<.001
94
-3.940
<.001
94
-6.485
<.001
Results of independent t-test comparing pre and post tests of all universities
.84
.74
the student blew through my last two tasks. I had her come up with a set of numbers that added
up to 13 and then again for 10. I asked her for three pairs of numbers each time, and she easily dictated
three sets each time. Lastly, I had drawn colored dots on index cards and flashed them to the student. She
correctly stated how many dots there were each time, even when I had used two different colors. She did a
great job.
Overall for this interview, I originally thought I was pitching it a little over the student’s proximal
zone of development by using both my own tasks and those from the 2nd and 3rd grade questionnaire since
she is only in 1st grade. However, I really think it was pitched at the right level. I got to see the student
pushed to the edge of her ability. In the end, the student confidently succeeded in all components of this
interview after doing things her own way.
The tasks and questions I presented in this interview were mostly to help me gain a better
understanding of the student’s addition and subtraction skills and her knowledge about place value and
number sequence. I loved the student’s answers for the screened addition and subtraction tasks. She has
some pretty advanced explanations for a 1st grader! Her reasoning demonstrates that she is able to chunk
multiple numbers in the same problem. After looking through the SEAL descriptions, her answers for
Preservice Elementary Teachers’
Professional Noticing in Clinical Contexts
these two problems combined with her answers for some of the other tasks, the
student was using thought processes that demonstrated knowledge from Stage 5Facile Number Sequence. A child in the facile number sequence stage might use
doubles to work out other facts which the student demonstrated when she thought
of 9+9 to find out 9+6. Also, a child in this stage might use knowledge of the inverse
relationship between addition and subtraction which the student did when figuring
out 14-3. A child at this stage can also count forwards and backwards by 2s, 10s, 5s, 3s, and 4s which the
student can do forwards. I am not sure if the student can count backwards by any of those intervals, but I
presume that she cannot do it automatically. She might be able to prove me wrong, but based off of what I
have observed, it would be a task that she could figure out if she had a long time, but it would not come
naturally.
Questions?