Transcript Dia 1 - UGent

A wizard at mathematics as teacher? A study into
the knowledge of fractions of preservice primary
school teachers
H. Van Steenbrugge, M. Valcke, A. Desoete
Support committee:
‣ Prof. dr. A. Desoete (co-promotor, UGent)
‣ Prof. dr. K.P.E. Gravemeijer (ESOE)
‣ Prof. dr. J. Grégoire (UCL)
‣ Prof. dr. M. Valcke (promotor, UGent)
‣ Prof. dr. L. Verschaffel (KULeuven)
[email protected]
PME 34 – 18-23/7/2010
Belo Horizonte
Overview
•
Introduction
•
Current study
•
Methodology
•
Results
•
Conclusion
Introduction: fractions
•
Fractions: important though very difficult topic
• students’ performance results (NCES, 2000)
• Teachers (Van Steenbrugge, Valcke, & Desoete, 2010)
•
Important: percentages, decimals, and algebra (Lamon, 1999)
Introduction: elementary school students
•
Gap procedural – conceptual knowledge of fractions (Aksu, 1997;
Post, Cramer, Behr, Lesh & Harel, 1993)
•
Conceptual K: multiplicity of meanings (Kilpatrick, Swafford, &
Findell, 2001)
• 5 subconstructs
Introduction: elementary school students
Five subconstructs
• Part-whole:
•
Ratio: “John and Mary are making lemonade. Whose lemonade is going to be
sweatier, if the kids use the following recipes? John: 2 spoons of sugar for every 5
glasses of lemonade; Mary: 4 spoons of sugar for every 8 glasses of lemonade”
•
Operator: “By how many times should we increase 9 to get 15?”
•
Quotient: “Five cakes are equally divided among four friends. How much does
anyone get?”
Introduction: elementary school students
•
Measure: number and interval
• Number: “Write for every number in the left column, the corresponding
fraction in the right column.”
• Interval: “Locate 9/3 and 11/6 on the following number line”
Introduction: elementary school students
•
Students most successful on tasks about the part-whole sub
construct & In general they have too little knowledge of the other
sub constructs
•
Especially students’ knowledge on the sub construct measure
seems to be problematic
(Charalambous & Pitta-Pantazi, 2007; Clarke, et al., 2007;
Hannula, 2003).
The current study
•
Teachers’ knowledge of fractions??
‣ Scarce and limited (Newton, 2008)
•
Deep understanding of school mathematics by elementary school
teachers  educational practices & students’ learning (Borko, et
al., 1992; Hill, Rowan, & Ball, 2005; Ma, 1999)
•
How some procedures work & WHY these procedures work
(Newton, 2008)
The current study
•
Deep knowledge: preservice teachers and inservice teachers ??
(Tirosh, 2000; Zhou, Peverly, & Xin, 2006)
•
Serious concerns regarding the readiness of some student
teachers to teach mathematics to elementary school children
(Conference board of the mathematical sciences, 2001;
Verschaffel, Janssens, & Janssen, 2005)
The current study: research questions
•
To which extend do preservice teachers master the procedural
and conceptual knowledge of fractions
•
To which extent do preservice teachers master a deeper
knowledge concerning fractions?
Methodology
290 preservice teachers
• First year trainees: 184; Third year trainees: 106
• Male: 43; Female: 247
• General oriented secondary education: 197
• Practical oriented secondary education: 93
Instrument:
• Conceptual K: existing instruments (elementary school students)
• Procedural K: textbooks
Results: procedural – conceptual K
Grand mean: .80 (.11); PK: .86 (.15); CK: .79 (.12)
2*2*2*2 mixed ANOVA design:
• Gender: M > F
• Sec: GSE > PSE
• Type: PK > CK
• Gender*Type
• Gender*Type*Sec
Results: procedural – conceptual K
Gender*Type
• CK: M > F; PK: M = F
• F: P > C; M: P = C
Gender*Type*Sec
• GSE & PSE: CK: M > F; PK: M = F
• GSE & PSE: F: P > C; M: P = C
• CK: F(GSE) > F(PSE) ; M(GSE) = M(PSE)
• PK: F(GSE) = F(PSE) ; M(GSE) = M(PSE)
•
=> M>F on CK; PK>CK for F; GSE>PSE for F&CK
Results: conceptual K
2*2*2*2 mixed ANOVA design:
• Subconstruct
• RATIO > rest
• P-W > rest minus ratio
• OP > mi; = q; < ratio; p-w; mg
• Q > mi; = op; < ratio; p-w; mg
• MG > op; q; mi; < pw, ratio
• MI < rest
• Gender: M>F
• Sec: GSE>PSE
• Gender*Subconstruct: M>F except for Q
• Year: not significant
Results: Deep knowledge
2*2*2* ANOVA design:
5/6 – 1/4 = …; 2/6 + 1/3 = …; 5 : 1/2 = …; 2/5 x 3/5 = …; 3/4 : 5/8 = …
•
•
•
•
Mean: .42 (.20)  /2 !
Sec: GSE >PSE; p = .045
Gender*Year; p = .047
Year: …
Conclusion
•
Partial overlap results preservice teachers & elementary school
students
• Chicken – egg?
•
.80/1: ok?
•
Deep knowledge ...
•
Teacher education?
Some remarkable results ...
70%
•
Locate number 1:
63.10%
•
“Is there a fraction located between 1/8 and 1/9? If yes, give an example.”
52.07%
•
1.33 = ...
43.45%
•
“By how many times should we increase 9 to get 15?”
•
“Which of the following are numbers? Put a circle around them:
A 4 * 1.7 16 0.006 2/5 47.5 1/2 $ 1 4/5”
•
“Peter prepares 14 cakes. He divides these cakes equally between his 6 friends. How
much cake does each of them get?”
35.86%
35.52%