learning mathematics collaboratively : enhancing students mathematical understanding

8/12/2019 Learning Mathematics Collaboratively : Enhancing Students Mathematical Understanding

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Learning Mathematics CollaborativelyEnhancing Students Mathematical Understanding

Presented ByArfaseela AmiruddinKolej MARA Seremban

University of Warwick, United Kingdom Arfaseela/NARC2014/KMS



Contents

1. Background2. Objective and RQ3. Literature review4. Theoretical framework5. Methodology6. Findings and discussions7. Conclusion8. Implications of the study9. Future research

Arfaseela/NARC2014/KMS



Background

Discussions in a small group may encourage students to be explicitabout the ways they make new claims from previously establishedfacts and about the standards they use to identify whether anargument is acceptable (Weber et al. , 2008).

In Malaysia, research has been carried out since 1990 to investigatethe impact on students’ learning when they learn in collaborativesetting.

While many researchers have agreed that collaborative group workhas the potential to develop students' learning (O'Donnell, 2006;Webb & Palincsar, 1996), up till now there is still less researchinvolving factors that contribute to the development of students'understanding in mathematics.




OBJECTIVE AND RQ

• To investigate whether or not working in a collaborative groupsetting can help to develop students’ mathematical thinking.

• Particular interest in 3 aspects :i. What particular ways of engaging in collaborative

activity might helped promote the students’ mathematicalunderstanding?

ii. How did the students’ mathematical understandingemerge from their group work?

iii. How did the students’ collaboration in group influence thequality of the mathematical knowledge that constituted theirmathematical understanding .




Literature Review• McCrone’s (2005) view that discussions in collaborative group work

allow students to test ideas, to hear and incorporate the ideas ofothers, to consolidate their thinking by putting their ideas intowords , and hence, to build a deeper understanding of key concepts .

• Weber et al. (2009) contended that explaining to others canpromote learning as the explainer has the opportunity toreorganize and clarify material, to recognize misconceptions, to fillgaps in his/her own understanding, to internalize and acquire newstrategies and knowledge, and to develop new perspectives andunderstanding.

• Francisco’s (2012) study found that students rejected and acceptedsuggested ideas from group members as well as showing that theycould build a convincing explanation where it can help to promote

students’ mathematical understanding. Arfaseela/NARC2014/KMS



Theoretical Framework

• Help to identify the particular ways of engaging in collaborativeactivity.

Socio-Cultural Theory

• Acknowledge students’ learning and understanding as it emergesand evolves in moment-to-moment interactions

Improvisational Theory

• Determines the validity of students’ ideas.

Argumentation Theory



Methodology• Dadds and Hart (2001).

• Studies the researcher's own professional practice.• Improving his/her practice for the benefit of others.

PractitionerResearch

• aged between nineteen and twenty years• purposely selected as the samples

• from a homogenous backgroundSamples

• Students were divided into 4 groups.• There were five students in each group consisting

of both genders.Group Setting

• The socio-mathematical norms study shows that the teacher playsa central role in creating the quality of the mathematicalclassroom environment.

• Promote students to explain issues.• Encouraging students’ mathematical thinking.

Teacher’sIntervention



• Based on proof involving Trigonometry.• Support students to explore why things work in

mathematics and bring together their agreementsand disagreements in meaningful ways.• Providing students with a concrete basis for

conceptual understanding.

Tasks

• Each session lasted approximately one and halfhours.

• Audio-taped using Sony digital audio recorder.

Audio

Recording• Audio recording was listened to several times.• Part 1 : Improvisational Theory was used to

analyse the students’ interactions around themathematical ideas.

• Code-words : Potential pathway; etiquette;collective; agreed upon.

Data Analysis

• Part 2 : Toulmin's (1969) model.• Focus : Claim; data; warrantData Analysis




Findings and Discussion

1. Attitudes to collaborative group work:

Interesting, fun and helped to increase their understanding ofmathematics’ concepts.

Maximize mathematical knowledge – when they needed to justifyand explain their ideas.

Fatin, "Solving a task in a group made me remember everything;

most important, my mathematical concepts became stronger. Iremember a lot because besides proving the task to myself, I alsohave to defend my ideas by explaining and justifying them toothers. It makes you to go over it at least twice and helps you toremember it easily."




The repeated transformation from thought to expression and viceversa helped to produce a better understanding of the task.

Explanation and justification of students’ ideas will invite them tobe explicit about their implicit knowledge.

Risk-takers and becoming more confident in explaining ideas and justifying their arguments.




2. Rejecting and accepting each others’ suggestions:

Lack of explanations or inability to explain in detail the ideas.

Lack understanding of the concept.

Discarded others student’s solution after he/she was able toexplain the relevance of his/her own solution.




3. Students working together on the same idea:

Students collectively worked jointly together to evaluate asuggested idea.

Each group member took up each other’s ideas for reasoning,collectively developing and improving their ideas into agreed-uponways of reasoning.

The group was able to interweave fragments of each other’s ideas,

by allowing them to share an individual’s idea rather than taking itas shared idea to emerge from their coactions.

Coaction – acting with the ideas and actions of others in a mutual, joint way




4. Students’ arguments and convincing explanation :

Arguments in group discussion allowed students to respond with afurther explanation or justification of their ideas, especially whentheir ideas were challenged by another student.

They asked questions and raised challenges when they did notunderstand a particular statement.

Students build their knowledge, particularly the things they prove,directly and immediately upon their old knowledge.

It can be suggested that students’ argumentation can be developedwhen they convince others of the truth of their ideas.




5. Teacher’s intervention :

Students sometimes need the teacher to intervene in theirdiscussion, especially when they get stuck with a problem.

Two types of teacher’s intervention should be considered;i. interventions focused on the interaction between students

(process help)

ii. Interventions focused on the mathematical content of the tasks(product help)




Conclusion

Six benefits have been identified :

Students making implicit knowledge explicit;

Students learning through active interaction;Students developing conceptual understanding;Students becoming risk-takers, developing fluency with

and an ability to recall formulas;Students’ actions becoming normative.




Collaborative activity can promote students’ mathematicalunderstanding by creating opportunities for them to critically re-examine their mathematical reasoning and build new, moresophisticated forms of reasoning from the hints or ideas of others.

Encourage students to investigate the validity of their claims abouta particular situation and/or ideas.

The students solved the tasks in an interactive problem-solvingsetting and produced valid explanations and justifications for theirideas.




Implications of the study

Teachers should not distance themselves from students' groupdiscussions, because the teacher is the expert in the classroom.

Teachers perhaps need to remember they are not the only'resource' to exclusively teach the content of a subject or topic inmathematics.

Teachers should also express ways to interpret and engage in

mathematics activity which may help to promote students'mathematical learning.




Future Research

Teacher's intervention is needed because students often find itdifficult to communicate with each other and might reinforcerather than challenge each other's mathematical misconceptions.

It is worth studying types of help and intervention the teachersmight offer when engaging with students' group activity.

Other theories should also be considered as a framework

depending on the purpose of the study.




TH NK YOU


learning mathematics collaboratively : enhancing students mathematical understanding

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