AFL in Mathematics

Mathematical communication in ICT-based lessons

Abstract

Teachers in the modern day classroom constantly grapple with many issues. One that for decades has been regarded as a serious issue is that of how intended learning outcomes impacts the learning that actually takes place within children (Wiliam, 2014). The great pedagogical debate between behaviourism and constructivism has its foundations on this. The call for changed teaching practices and philosophies for improved students' learning has sparked significant changes in the approach towards education within schools. Teachers are keen to employ a myriad of effective pedagogical strategies and have for long, studied the effects of assessment for learning on students' learning.


A group of teachers in Ang Mo Kio Primary School embarked on a journey to explore how AfL can be enhanced by technology to help students improve in their mastery of Mathematical language and reasoning. Guided by the beliefs that Afl practices improve students learning as well as our understanding of TPACK, our teachers designed and implemented learning interventions that transformed classroom learning from teacher-led to student-led. A wide range of ICT tools like Google sites and Linoit supported our programme.

Literature Review

Assesment for learning


Several researchers concur on the importance of Assessment for Learning (AFL) in the classroom. They conclude that employment of techniques of AFL point to substantial improvement in students' learning (Black & Wiliam, 1998; Leahy, Lyon, Thompson & Wiliam, 2005). Proponents of AFL advocate changes in teachers' approach to pedagogy in the classroom, giving more autonomy to students through self-directed learning and allowing them to be sources of learning for each other in the classroom (Koch & Shulamith, 1991).


Mathematical Communication


Research in cognitive psychology have revealed the positive relationship between cognitive discourse and improved learning in Mathematics (Sfard & Kieran, 2001). Kramaski & Zemira (2003) concur in their studies, highlighting that opportunities for metacognition develop students who attain higher levels of learning in mathematics and abilities to explain mathematical ideas beyond just procedural descriptions. This suggests the necessity of group-activities in learning to provide students with platforms to be engaged in mathematical discourse involving posing of questions, elaboration of answers and providing of peer feedback. To cater to the needs of students with poorer communication skills, learning activities need to be carefully planned to optimize opportunities for all students to be engaged.


ICT in education


Tin's (2005) review of research suggested a positive relationship between the use of ICT in lessons and students' attainment of Mathematical skills. Students who were more exposed to ICT in lessons generally outperformed their counterparts who experienced lesser interaction with ICT. The researcher further highlighted that the effects of ICT were most significant when ICT was fully integrated into the teaching of the subject. Findings too revealed that the use of ICT along with alternative teaching strategies benefited a wider range of students than in traditional learning environment. This directly emphasizes the importance of practitioners' understanding of technological pedagogical content knowledge (TPACK).


Practitioners' knowledge of TPACK is the knowledge of how ICT can be utilised to enhance teachers' delivery and students' acquisition of subject knowledge. Building on the works of Shulman (1987), Koehler and Mishra (2009) developed a framework to describe TPACK as seen in the figure below.

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Research Focus

To understand the relationship between collaborative learning using ICT platform and students' mathematical reasoning and communication.

Research Question


How does opportunities for mathematical thinking in the learning process build students’ mathematical reasoning and communication skills?

Methodology

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Lesson Design and Implementation

Introduction to ICT Tools and their Affordances


Social Learning Wall (MConline)


Social Learning Wall is a virtual platform that is implemented inside the Learning Management System (LMS). The wall provides an easily accessible platform for students to engage in collaborative discussion and information sharing. This helps students engage more deeply in classroom discussions previously dominated by verbal communication. The Social Learning Wall was used for classroom discussions during the lesson on 'Introduction of Decimals'. Teachers posed questions for discussion in wall posts and students responded in groups.


Screencast-O-Matic


This is an online application that allows users to record on-screen activity while communicating. This application was used during the lessons on Addition & Subtraction of Decimals. Students had to record their procedure of adding and subtracting decimals using number lines or place value charts. In these recordings, students had to explain their procedures using appropriate mathematical language with the help of key-words provided.


Linoit


Linoit is an online discussion platform where users communicate their ideas through 'stickies'. Stickies can be shifted and categorized according to similarity of ideas. This platform was used when students were engaged in the lesson on 'comparing of decimals'. Students had to explain their understanding of the relationship of place and value of digits in decimals. Teachers facilitated the discussions by grouping the stickies and allowing students to view and provide peer feedback.


Google Form


Google forms are online platforms that provide easy organization of ideas and thoughts generated through survey-styled questionnaires. Teachers prepare questions either in the form of open-ended ones or those with multiple choices. Once students have keyed in their answers, all answers are channeled into a single google spread-sheet. This allows for a one-stop access of students' learning. These forms were mainly used in the lessons on 'Area'.


Google Site


Google Site is an online platform that allows the consolidation of various online information generated from many users at a go. Sites were created by teachers to gather all prepared lesson resources and those generated by students during their various discussions using the many online tools embedded within the sites. The Google sites were used for both topics.


Learning Outcomes

Decimals

By the end of the topic, pupils should be able to

-use number line to add 1­place decimals by counting on;

-use place value chart to add 1­place decimals without re­grouping;

-use number line to subtract 1­place/2­places decimals with re­naming;

-use place value chart to subtract 1­place/2­places decimals with re­naming;

Discussions (Teachers' Learning and Insights)



  1. The ICT classroom caters to the needs of 21st century ICT-savvy learners; the interactive aspect that ICT lessons bring improves students' learning.
  2. ICT tools provided students with more motivation and ownership over their own learning. ICT tools increase students' engagement in lessons.
  3. Teachers gained an insight into integrating ICT purposefully and meaningfully into lessons.
  4. Teachers gained a higher level of competency in handling AfL information and data and used them to adapt subsequent lessons to meet students' learning needs.
  5. Students were able to provide constructive feedback to their peers and this was facilitated by the ICT tools that allowed students' work artefacts to be collected and made easily accessible to students.
  6. Students were better able to achieve lesson objectives, particularly in their usage of appropriate Mathematical language through the use of ICT tools. They were more aware of their ideas and how to phrase their subsequent answers.
  7. Students must be thoroughly briefed on clear expectations and rules to prevent cyberwellness issues in the classroom.

References

Koch, A., Shulamith, G. E. (1991). Improvement of reading comprehension of physics texts by students' question formulation. International Journal of Science Education. 13, 473-485.


Koehler, M. J., & Mishra, P. (2009). What is technological pedagogical content knowledge? Contemporary Issues in Technology and Teacher Education. 9(1), 60-70.


Kramarski, B. & Mevarech, Z. R. (2003). Enhancing mathematical reasoning in the classroom: The effects of Cooperative learning and metacognitive training. American Educational Research Journal. 40(1), 281-310.


Leahy, S., Lyon, C., Thompson, M. & Wiliam, D. (2005). Classroom assessment: Minute by minute, day by day. Educational Leadership. 63(3), 19-24.


Sfard, A. & Kieran, C. (2001). Cognition as communication: Rethinking learning-by-talking through multi-faceted analysis of students' mathematical interactions. Mind, Culture And Activity, 8(1), 42-76.


Tin, S. E. (2005). The impact of ICT on learning : A review of research. International Education Journal. 6(5), 635-650.