The context rich realistic mathematics education and formal mathematical development of students

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The context rich realistic mathematics education and formal mathematical development of students

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Title: The context rich realistic mathematics education and formal mathematical development of students

1
The context rich realistic mathematics education
and formal mathematical development of students
2
The correlation between the context rich
realistic math education and the formal
mathematical development of fourth grade
secondary school students
3
The context rich realistic mathematics education
and formal mathematical development of
studentsThe correlation between the context
rich realistic education and the formal
mathematical development of fourth grade
secondary school students

Introduction Literature review MethodResul
tsConclusion and Discussion

IntroductionThe aim of the study is to examine
whether there is any relation by offering context
rich realistic mathematics education and the
formal mathematics development of students in the
fourth grade of secondary school. Problem
exploration- letter Lieve Maria- no time
problem but a content problem-Resonance group-
Research CITO primary school

Resonance group 20071. Take care for that the
developing of arithmetic and formula skills walks
as a red thread through the entire mathematics
education. 2. Split up all mathematics
subjects of the central written final exam (CE)
in two parts a part, without help (of a graphic
calculator and formula card), and a part with
help.3. Reconsider the role of contexts in the
mathematics education

Literature review
Learning theoriesRealistic mathematics
education

Levels of cognitive development
Piaget Bruner van Hiele
Tall

Realistic mathematics education
Treffers (1987)
Gravemeijer (2005) Drijvers (2006)

Realistic mathematics education
Drijvers (2006)
Algebraic Skills Basic
skills Symbol sense - Algebraic
arithmetic - Algebraic reasoning -
Procedural routine - Strategy skills
The two sides of algebraic skills

Method Research questions Type of
study Sample of the study Procedure, data
collection Variables and measures

Research questionsAre there significant
differences between performance of students on
Context Rich Realistic (Part 1 and 2) and Non
Context Rich Realistic Math Test, the
perception of mathematics in the Classroom
Environment and the Metacognitive skills in
terms of their school types?
The context rich realistic mathematics education
and formal mathematical development of
studentsThe correlation between the context
rich realistic education and the formal
mathematical development of fourth grade
secondary school students
13

Is there a significant correlation between the
Non Context Rich Realistic Math performance
and the Context Rich Realistic Math (Part 1 and
2) performances and the math achievement (Mark
math) and language skills (Mark Dutch
language)?

Is there a significant correlation between the
Non Context Rich Realistic Math performance
and the Context Rich Realistic Math (Part 1 and
2) performances and the perception of
mathematics Classroom Environmentand the
Metacognitive skills. A significant correlation
of the five instruments.

Sample of the study4th grade students of
secondary schools School type VMBO, HAVO and
VWOGender

Sample of the studyAge

Procedure and data collectionwww.onderzoekwis
kunde.nl
www.schoolenquete.nlwww.hyves.nl

The context rich realistic mathematics education
and formal mathematical development of
studentsThe correlation between the context
rich realistic education and the formal
mathematical development of fourth grade
secondary school students
18
Respondenten
The context rich realistic mathematics education
and formal mathematical development of
studentsThe correlation between the context
rich realistic education and the formal
mathematical development of fourth grade
secondary school students
19
Method/Textbook used by students
The context rich realistic mathematics education
and formal mathematical development of
studentsThe correlation between the context
rich realistic education and the formal
mathematical development of fourth grade
secondary school students
20

Variables and measures instruments
- Demographic data- Classroom Environment
Survey - Metacognition Inventory- Non Context
Rich Realistic Math Test- Context Rich Realistic
Math Test (Part 1 and 2)

Demographic dataSchool type GradeAgeGender
Used methodMath mark Dutch language mark

Classroom Environment survey (Taylor, Fraser
and White, 1994) Three subscalesPersonal
RelevanceMathematics Uncertainty
Attitude towards math

Classroom Environment survey For reliability
analysis Cronbachs Alpha coefficient is
calculated as 0,774Comparing

Metacognition Inventory - understanding of
the problem - planning and monitoring of the
problem solving process - elaboration and
control of the problem solution and answer
17 items Yes/No Crownbachs Alpha 0.531

Non Context Rich Realistic Math
TestMathematical Thinking test developed by
Lutfiyya (1998) Five dimensionsGeneralization
InductionDeductionUse of symbolsLogic thinking

Non Context Rich Realistic Math
TestMathematical Thinking test developed by
Lutfiyya (1998) was adapted into Dutch by
Nazlicicek, Meijer and Karsten (2008)Pilotstudy
(Nazlicicek, 2008) a Crownbachs Alpha
0.778Used for each dimension 3 questions total
of 15 items Crownbachs Alpha 0.658

Example question(generalization)

Context Rich Realistic Math TestPart 1 Context
rich realistic tasks Part 2 More formal
mathematic tasks(procedural, process and use of
symbols) Part 1 seven items Part 2 eight
itemsReliability low Crownbachs Alpha 0.542

Context Rich Realistic Math Test
(Part1)Exercises chosen from used
methodsExample question Freek verdient netto
162 per week. Zijn netto maandloon berekent
hij met de formule                         13 x
weekloonmaandloon --------------------
                           3Hoeveel is het netto
maandloon van Freek?
696,-
700,-
702,-
714,-

Context Rich Realistic Math Test (Part
2)Example question
De functie f is gegeven door f(x) 5x - 12.
Bereken f(3)
2
3
4
5

Results Descriptive statistics of the total
scores of the instruments by school typeN, max
score, Mean and standard deviation

Descriptive statistics of school type and the
five dimensions of the Non Context Rich
Realistic Math Test

Results of One-way Anova Test of the total
score of Non Context Rich Realistic Math Test,
the Context Rich Realistic Math Test part 1 and
2, the Classroom Environment Test (PR , MU and
AM), and the Metacognition test.The group
means are significantly different for plt0.01

In conjunction with the One-way Anova is used
the Tukey's HSD test The mean difference is
significant at a 0.05 level

Research questionAre there significant
differences between performance of students on
Context Rich Realistic (Part 1 and 2) and Non
Context Rich Realistic Math Test, the
perception of mathematics in the Classroom
Environment and the Metacognitive skills in
terms of their school types?-

Results- HAVO and VWO students have a low mean
on the Classroom Environment Survey than VMBO
students- The dimension use of symbols has
low mean for each school type - On the Non
Context Rich Realistic Math Test VWO students
score a low mean on generalization- The HAVO
and VWO students means are not significant
different on the Context Rich Realistic Test
Part 1 and 2 and Metacognition Test - The VMBO
and VWO students means are not significant
different on the Classroom Environment Survey

Research question Is there a significant
correlation between the Non Context Rich
Realistic Math performance and the Context
Rich Realistic Math (Part 1 and 2) performances
and the math achievement (Mark math) and language
skills (Mark Dutch language) of the students in
the 4th grade of secondary school?

Pearson CorrelationSignificant at 0.01 level

Results- The correlation of the Non Context
Rich Realistic Math Test is higher with the
Context Rich Realistic Math Test Part 1 than Part
2- The correlation between the Context Rich
Realistic Math Test Part 1 and 2 is lower than
the correlation with the Non Context Rich
Realistic Math Test- No significant correlation
was found between students mathematics and
language achievement

Research question Is there a significant
correlation between the Non Context Rich
Realistic Math performance and the Context
Rich Realistic Math (Part 1 and 2) performances
and the perception of Classroom Environment and
the Metacognitive skills. A significant
correlation of the five instruments

Pearson CorrelationSignificant at 0.01 level

Results- the correlation is calculated for the
total score of each dimension and the
Metacognition Test has a significant correlation
at a 0,01 level (2- tailed) with the three
Mathematical tests- The Classroom Environment
Test has a negative correlationwith two of the
Math tests

Conclusion- The difference in math performance
of students by school type is clear- The
distinguishing of the three math tests is not so
clear- The use of symbols is by each school
type low - The perception of Classroom
Environment (attitude) of HAVO students is low
and equal by VMBO and VWO students - The three
math test and Metacognition are correlated - No
correlation between math and language achievement
with the three Math tests - Classroom
Environment correlated negative with the two of
the Math tests

Discussion- math education by methods and
instruction too context rich and realistic and
enough formal math development according to
school type- distinct math in horizontal,
processes and procedurals, vertical
mathematization- methods give too little
attention for how to use symbols- Classroom
Environment (attitude of students) measures what
we want

Suggestions- more respondents and a
longitudinal study to measure level raising of
the formal mathematic development - the
research instruments can be expand and
developed- the research extended with teachers
findings and ideas- method makers has to
realize that formal math development in the
first three grades has to take place more in each
school type