n oticing n umeracy n ow!
DESCRIPTION
N 3:. N OTICING N UMERACY N OW! . RESEARCH FUNDED BY THE NATIONAL SCIENCE FOUNDATION: Transforming Undergraduate Education in STEM (TUES) Award # 1043667, 1043656, 1043831. About Us. Preservice Teacher Preparation Collaborative. * Comparison Implementers. Instructional Module. - PowerPoint PPT PresentationTRANSCRIPT
NOTICING NUMERACYNOW!
N3
:
RESEARCH FUNDED BY THE NATIONAL SCIENCE FOUNDATION: Transforming Undergraduate Education in STEM (TUES) Award # 1043667, 1043656, 1043831
About UsPreservice Teacher Preparation
CollaborativeJonathan Thomas
Northern Kentucky UniversityKY Center for Mathematics
Edna O. Schack
Morehead State University
Sara Eisenhardt
Northern Kentucky University
Molly H. Fisher
University of Kentucky [email protected]
Margaret Yoder
Eastern Kentucky University
Janet Tassell Western Kentucky University
Cindy Jong* University of Kentucky [email protected] Todd Brown* University of Louisville [email protected] Gierhart*
Murray State University
* Comparison Implementers
Instructional Module
Attending to the children’s work
Interpreting children’s work in context of mathematics
Deciding appropriate next steps
Professional Noticing
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.
Pedagogies of PracticeDecomposition
of professional noticingRepresentations
video of early number sense diagnostic events
ApproximationsPSETs conduct diagnostic interview with child
Grossman, P. (2011). Framework for teaching practice: A brief history of an idea. Teachers College Record. 113, 12, 2836-2843.
Early NumeracyStages of Early Arithmetic Learning
• Learning Progression• Early Quantitative Understanding• Examination of Counting Schemes
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.
Early NumeracyStages of Early Arithmetic Learning Stage 0: Emergent Counting SchemeStage 1: Perceptual Counting SchemeStage 2: Figurative Counting SchemeStage 3: Initial Number SequenceStage 4: Intermediate Number Sequence
Stage 5: Facile Number Sequence
To what extent can teacher educators facilitate the development of Preservice Elementary Teacher (PSET) professional noticing (attending, interpreting, and deciding) of children’s mathematics?
PRIMARY RESEARCH QUESTION
Professional Noticing Assessment “I have seven little bears . . . But now I have too many shells. I have eleven shells. (Jon shows the eleven shells then covers them with his hand.) How many shells am I going to have left over?”
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)
Professional Noticing Prompts
Jacobs, V. A., Lamb, L. L. C., & Philipp, R. A. (2010)
Assessment Score LevelsAttending Interpreting DecidingLevel
4 Elaborate3 Salient Accurate
Appropriate & Connected 2 Limited Limited Adequate,
Disconnected1 Inaccurate Inaccurate
Inappropriate, No Rationale
Growth of PSET PN: Attending
“He knew that since the teacher said he had too many shells he had to do subtraction. He also knew that because the teacher said left over he had to do subtraction, or see what the difference was. The child understood key words and phrases and understood how to take away to get the right answer. He used the bigger number and took away using the smaller number and realized that 11-7=4.”
“In response to this problem this child first counted the bears and found that there were seven. From there he used his fingers and counted up from seven until he got to the number eleven. He had four fingers up so he said that that was his answer.”
POSTPRE
Growth of PSET PN: Interpreting
“It seemed that instead of subtracting seven from eleven he used the problem 7+?=11, and came up with four by counting from seven to eleven instead of from eleven to seven.”
“This child does not count on; he needed to count the bears from one in order to count the remainder of the shells. He uses his fingers to count when materials are unavailable to him. He understands associating one object with a number and adding a value with each corresponding object added.”
POSTPRE
Growth of PSET PN: Deciding
“I would pose more bears than shells. Or only have shells exposed, so he couldn't count the bears. How many shells must I take away to get 7 bears? Other ways of getting answer and using subtraction.”
“I would screen both of the counters. This requires the student to use a different type of counters (fingers) but he might run into trouble because he will be counting past 10. I[t] would be interesting to see how he got the answer.”
POSTPRE
Results of ANOVA comparing pre and post assessments of all universities
Attending Interpreting Deciding
N M SD M SD M SDUniversity 0 Pre-Test 37 2.14 .79 1.59 .797 1.54 .61 Post-Test 37 2.43 .87 2.05 .84 2.22 .79University 1 Pre-Test 23 2.39 .99 1.82 .89 2.04 .56 Post-Test 23 3.09 1.04 2.43 .73 2.70 .56University 2 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 .75All Participants Pre-Test 94 2.29 .96 1.71 .81 1.82 .66 Post-Test 94 2.80 1.03 2.18 .84 2.43 .74Descriptive statistics of professional noticing measures by university
Scale N F (3,91) PPartial Eta Squared
Attending 1-4 94 16.800 < .001 .156
Interpreting 1-3 94 15.617 < .001 .146
Deciding 1-3 94 40.130 < .001 .306
Preliminary Analysis of Three Research Sites
Professional Noticing Measure Descriptive Statistics – All Sites
Attending
Interpreting
Deciding
N M SD M SD M SDScale 1-4 1-3 1-3Pre-assessment
94 2.29 .96 1.71 .81 1.82 .66
Post-assessment
94 2.80 1.03 2.18 .84 2.43 .74
ANOVA comparing pre and post
All Universities
Scale N
F(3,91) P
Partial Eta
Squared
Attending 1-4 94 16.800 <.001
.156
Interpreting
1-3 94 15.617 <.001
.146
Deciding
1-3 94 40.130 <.001
.306
Questions?
tinyurl.com/noticingnumeracynow
Attending Benchmarks“He counted from one up when counting all of the bears. He then counted the remaining shells on his fingers to get the answer 4.”
“Counted the bears individually then used his fingers to count up to 11.”
“Instead of subtracting 11-7, he counted to seven and then used his fingers to see how many more it took to get to 11.”
“The child subtracted in response to this question using his fingers as a manipulative. Starting with 11 & working backwards.”
ELABOR
ATE SALIENT
LIMITE
D INACCURA
TE
Attending Benchmarks“He counted from one up when counting all of the bears. He then counted the remaining shells on his fingers to get the answer 4.”
“Counted the bears individually then used his fingers to count up to 11.”
“Instead of subtracting 11-7, he counted to seven and then used his fingers to see how many more it took to get to 11.”
“The child subtracted in response to this question using his fingers as a manipulative. Starting with 11 & working backwards.”
4 32 1
“I learned that this child can add easier than subtract because instead of 7-11 he did 7+__=11. I also learned that he needs a representation of the numbers to solve the problem (the bears, his fingers, and shells).”
Interpreting Benchmarks
“This child understands a one-to-one correspondence with objects, he needs to touch the objects and he still uses his fingers to count on.”
ACCURAT
E
LIMITE
D INACCURA
TE
“I learned that the child is able to count on from a given number. He didn't have to go back and start at 1.”
“I learned that this child can add easier than subtract because instead of 7-11 he did 7+__=11. I also learned that he needs a representation of the numbers to solve the problem (the bears, his fingers, and shells).”
Interpreting Benchmarks
“This child understands a one-to-one correspondence with objects, he needs to touch the objects and he still uses his fingers to count on.”
32 1“I learned that the
child is able to count on from a given number. He didn't have to go back and start at 1.”
“I would ask the child to tell me why there were four shells leftover. This would tell us whether or not the child had an understanding of remainders. This will tell us if he has the concept of sharing equally, rather than giving the four shells to select bears.”
“I might say "How did you get this answer" to see how they explained their logic.”
“I believe that the next task should be a really small number subtracted by a very large number. Ex. 20-6. This problem would be harder to count on your hands and you could get a better understanding of his conceptual knowledge of the problem and addition itself.”
Deciding Benchmarks
CONNECTED
RATIONALE
DISCONNECTE
D RATIONALELITTLE OR NO
RATIONALE
Appropriate Decision with…
Adequate Decision with…
Inappropriate Decision with…
“I would ask the child to tell me why there were four shells leftover. This would tell us whether or not the child had an understanding of remainders. This will tell us if he has the concept of sharing equally, rather than giving the four shells to select bears.”
“I might say "How did you get this answer" to see how they explained their logic.”
“I believe that the next task should be a really small number subtracted by a very large number. Ex. 20-6. This problem would be harder to count on your hands and you could get a better understanding of his conceptual knowledge of the problem and addition itself.”
Deciding Benchmarks
APPROPRIATE
& CONNECTED
ADEQUATE,
DISCONNECTE
D INAPPROPRIA
TE,
DISCONNECTE
D
“I would ask the child to tell me why there were four shells leftover. This would tell us whether or not the child had an understanding of remainders. This will tell us if he has the concept of sharing equally, rather than giving the four shells to select bears.”
“I might say "How did you get this answer" to see how they explained their logic.”
“I believe that the next task should be a really small number subtracted by a very large number. Ex. 20-6. This problem would be harder to count on your hands and you could get a better understanding of his conceptual knowledge of the problem and addition itself.”
Deciding Benchmarks
32 1
PSET Professional Noticing in Clinical Context
Instructional Module