Schack, E. O.1, Fisher, M. H.2, Thomas, J. N.3, Eisenhardt, S.4

Preservice Teachers’ Noticing of Children’s Mathematical Thinking
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6 Schack, E. O. , Fisher, M. H. , Thomas, J. N. , Eisenhardt, S. , Tassell, J. , & Yoder, M.
Research Ques5ons •  To what extent can teacher educators facilitate the
development of Preservice Elementary Teacher (PSET)
professional noticing (attending, interpreting, and deciding)
of children’s mathematics?
•  To what extent does PSET professional noticing performance
correlate with PSET attitudes toward mathematics?
Professional No5cing Benchmark Development Professional No5cing Video Assessment Findings The research team reviewed the professional noticing
video clip and identified key response features for each of the
assessment prompts, beginning with attending. We examined
a sample set of PSET responses to identify emerging themes
(Glaser & Strauss, 1967). Coupling the key response features
with emerging themes suggested four distinct response levels.
We ranked our calibration data using the benchmarks.
A Kruskal-Wallis test determined there was no statistically significant difference between universities in the changes in
participant scores from pre- to post-test. Therefore, subsequent analysis was conducted on participants as a single group.
A Wilcoxon Signed Ranks Test was conducted for each of the three prompts to determine if statistically significant gains
were found for each component of professional noticing. The results of this test are in the table below. Statistically
significant increases were found in all three components with deciding having the strongest increase. Deciding lower preassessment scores provided more opportunity for growth (Schack, Fisher, Thomas, Eisenhardt, Tassell, & Yoder, accepted).
N3 Instruc5onal Module Theore5cal Framework Grossman et al. (2009) posed this framework for teaching •  Decomposition
•  Representation
•  Approximation
Professional No.cing Early Numeracy Steffe (1988) and others posed Stages of Early Arithme.c Learning Jacobs, Lamb, & Philipp (2010) defined as three interrelated skills •  Attending
•  Interpreting
•  Deciding
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Emergent
Perceptual
Figurative
Initial Number
Intermediate
Facile
The decomposition (Grossman, Compton, Igra, Ronfeldt,
Shahan, & Williamson, 2009) of the construct of professional
noticing into three interrelated skills—attending,
interpreting, and deciding—allowed for the skills to be
progressively nested throughout the module (Boerst, Sleep,
Ball, & Bass, 2011). Integrated with the nested development
of professional noticing, the Stages of Early Arithmetic
Learning gradually unfold through video clip representations
of practice (Grossman et al., 2009).
A pre- and post- professional noticing measure was a
brief video clip of a diagnostic interview in which a child is
presented with a comparison task. After viewing the video,
PSETs respond to three prompts, each related to one of the
components of professional noticing – attending,
interpreting, and deciding.
“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?”
The benchmarking process was replicated for interpreting
and deciding components which each resulted in three distinct
response levels. All data were ranked by two researchers with
discrepancies discussed for consensus. To improve inter-rater
reliability, the researchers ultimately developed benchmark
scoring flowcharts for each professional noticing component.
Attending Benchmark Scoring Flowchart
Does the response contain addi.onal accurate evidence? Examples: 1. Child began the count at 1 2. Child counted by 1’s 3. Child flashes a “7 finger paWern” prior to ini.a.ng the count Does the response contain the two salient features? 1. The child counted the available bears/
objects (7) 2. The child counted (con.nued) using his fingers 4. Child constructs/glances at finger paWern at the conclusion of the count 5. Child did not need to recount his finger paWern at the conclusion of the count Was there opera.onal presump.on and/or PSET presump.on? (i.e. reference of addi.on or subtrac.on) Was there opera.onal presump.on and/or PSET presump.on? (i.e. reference of addi.on or subtrac.on) Yes No Yes Score 2 Score 4 Score 2 No Score 3 Does the response contain addi.onal accurate evidence? Examples: Does the response have at least one salient feature? *If there is incorrect evidence, then Score 1 1. Child began the count at 1 2. Child counted by 1’s 3. Child flashes a “7 finger paWern” prior to ini.a.ng the count 4. Child constructs/glances at finger paWern at the conclusion of the count 5. Child did not need to recount his finger paWern at the conclusion of the count Was there opera.onal Presump.on? (i.e. reference of addi.on or subtrac.on) Was there opera.onal Presump.on? (i.e. reference of addi.on or subtrac.on Yes Score 1 Score 2 www.PosterPresentations.com
N 94 94 94 z -­‐3.559 -­‐3.682 -­‐5.255 P <.001 <.001 <.001 Sample PSET Responses Evidencing Growth in Professional No5cing Brittany: Attending
“He knew that since the teacher said he had too many shells he had to do subtrac.on. He also knew that because the teacher said lem over he had to do subtrac.on, 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 un.l he got to the number eleven. He had four fingers up so he said that that was his answer.” Bri>any’s focus shiBed from an operaDonal presumpDon to factual evidence that provide context for making informed interpretaDons and decisions. Kiara: Deciding
Corey: Interpreting
“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 associa.ng one object with a number and adding a value with each Corey’s post response moved beyond descripDon corresponding object to interpretaDon about the added.” “It seemed that instead of subtrac.ng seven from eleven he used the problem 7+?=11, and came up with four by coun.ng from seven to eleven instead of from eleven to seven.” significance of the student’s acDons in the context of the mathemaDcs. “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 gesng answer and using subtrac.on.” Kiara’s post response was based both in the student’s strategy and the early numeracy learning progression, elements absent in her iniDal response. “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 coun.ng pas 10. I[t] would be interes.ng to see how he got the answer.” Score 1 No Score 2 Score 1 Project Personnel Contacts & Affilia5ons [email protected], Morehead State University
2 [email protected], University of Kentucky
3 [email protected], Northern Kentucky University &
Kentucky Center for Mathematics
4 [email protected], Northern Kentucky University
5 [email protected], Western Kentucky University
6 [email protected], Eastern Kentucky University
AVtudes Toward Mathema5cs Preliminary Findings The Attitudes Toward Mathematics Inventory (Tapia, & Marsh, 2004) was administered pre- and post-instructional
module. Initial descriptive statistics indicate a positive attitude change on all four factors of the inventory. Further
statistical tests will be run to determine significance and correlation to the video assessment findings.
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RESEARCH POSTER PRESENTATION DESIGN © 2012
Scale 1-­‐4 1-­‐3 1-­‐3 In summary, findings at three sites suggest the efficacy of a researcher-developed module aimed at promoting
professional noticing capacities among PSETs in the area of early number and operation. The development of such
capacities among aspiring teachers at multiple sites bodes well for scaled establishment of responsive teaching practices
within teacher preparation programs.
“The child counted up using “The child subtracted in his fingers from seven to get response to this ques.on to the number eleven.” using his fingers as a manipula.ve. Star.ng with 11 & working backwards.” No Professional No5cing Video Assessment Component AWending Interpre.ng Deciding “He counted from one up “Counted the bears when coun.ng all of the individually then used his bears. He then counted the fingers to count up to 11.” remaining shells on his fingers to get the answer 4.” Three areas of study provide the founda.on for the instruc.onal module: Pedagogies of Prac.ce Results of Wilcoxon Signed Ranks test comparing pre-­‐ and post-­‐assessments of all universi5es Sample Attending Responses at each Benchmark
Yes 3
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Noticing Numeracy Now:
Factor Enjoyment Mo.va.on Self-­‐Confidence Value Total Descrip5ve results comparing pre-­‐ and post-­‐assessments of all universi5es Pre-­‐assessment Post-­‐Assessment N Maximum Possible Mean Std Dev Mean Std Dev Average Change 77 50 35.1 9.27 36.7 9.11 1.64 77 25 16.3 4.15 16.8 4.26 0.55 77 75 52.8 15.21 54.6 14.48 1.74 77 50 44.1 4.45 44.5 4.51 0.40 77 200 148.2 29.80 152.6 29.36 4.32 RESEARCH FUNDED BY THE NATIONAL SCIENCE FOUNDATION: Transforming Undergraduate Educa.on in STEM (TUES) Award # 1043667, 1043656, 1043831