New Pedagogies in Teaching & Learning

The purpose of the present study is to investigate whether making thinking visible through the use of thinking routines leads to deeper understanding in mathematics through rich classroom discourse. The thinking routines chosen in this study are See-Think-Wonder, What Makes You Say That and I Used to Think…, Now I Think… They are used to guide the students to explore, justify and self-regulate their mathematical thinking respectively. A classroom with rich discourse involves students building on prior knowledge to make connections to new concepts, articulating their ideas and using different representations to validate their thinking. We hypothesize that thinking routines will bring about rich classroom discourse, thus helping students to develop a deep understanding in mathematics. The study involved two Primary 4 classes and two teachers. Both groups were put through instructions over three months (5.5 hours each week) with a week of term break in the middle. The three thinking routines with a series of guiding questions were integrated into the lessons deliberately and purposefully. Through this process, students construct and co-construct new knowledge beyond mathematical procedures and computation. The teachers applied skilful questioning to engage students in exploring, justifying and reviewing their mathematical reasoning; and facilitated the development of new understanding. The results showed that students’ responses and engagement revealed evidence of deep learning in mathematical concepts for the identified topics. They gained deep understanding during rich classroom discourse when they thought through the concepts systematically with thinking structures, built on each other’s knowledge and communicated their mathematically reasoning. This forms part of the process of developing students’ critical and inventive thinking.

Primary mathematics students faced difficulties in using mathematical language  to  articulate conceptual understanding clearly  and to solve word problems in a systematic manner.  Teachers aimed to sharpen students’ mathematical thinking and to express mathematical   ideas precisely, concisely and logically — core skills as stated in the mathematics syllabus (MOE, 2013).
This presentation  features  a scaled-up study of teachers from two schools supporting  Primary   Four students in making their  mathematical thinking visible and audible through written and oral communication, mediated by technology. Aligned with the ICT Masterplan4 in Education, the study seeks to deepen subject mastery, develop  students’ competencies as self-directed learners and active contributors  to learning (MOE, 2014), and nurture confident problem solvers and skilled  effective communicators (ELIS, 2013).
Grounded in social constructivist underpinnings (Vygotsky, 1978) with learning as an active process through learner knowledge construction, teachers adopted screencasting  (Educause, 2006; Soto, 2014) technology to capture students’ word problem solving focused on Fractions and Decimals.  Drawing on Polya’s problem solving model (1957),  four classes of high progress and low progress students under their teachers’ guidance learned through ‘think alouds’ (Ericsson & Simon,1980; Martin & Wineburg, 2008; Olson et al.,1984) to make explicit the steps used in problem solving (Thurlow, Barrera & Liu, 2009) and the  underlying thinking behind the process.
This presentation showcases frameworks for scaffolding students’ verbalising their mathematical thinking and guiding students in their peer critique.  The study examined the impact of integrating screencasting in mathematics lessons  on teachers’ pedagogic practice and beliefs,  and students’ learning. Data sources included teachers’ instructional resources, students’ screencast recordings, students’ peer feedback, teachers’ reflections and students’ perspectives from focus group discussions.
Teacher-guided scaffolding enabled students to analyse mathematical problems, deconstruct task demands and articulate their problem solving systematically. Students sharpened their precision in mathematical language use and their analytical skills in problem solving. Their meaning negotiation, refinement of their peers’ use of mathematical language and sharpening of their mathematical thinking were exhibited to different degrees. Teachers benefitted from the shared learning experience in careful task planning to address  learner differences and needs, and supporting students in  mathematical problem solving. Pedagogical implications are discussed. 

The origin of lesson study in Japan can be traced back to the early Meiji era (1868 – 1912). The school has found the structure for lesson study to be useful and has embraced lesson study since 2011. The school has a framework for lesson study and also time is protected for teachers to plan the lesson. In 2017, the school incorporated Applied Learning Programme (ALP) into the academic subjects. Hence thinking skills were applied in mathematics since 2017. In this sharing, the impact of the thinking skill of analysing parts and whole (CPDD, 2012) will be discussed in the implementation of a lesson on the maths concepts of factors and multiples. The open ended approach by the pupils to use the thinking skill in solving a problem will be shared. The findings showed that the context contributed to the possibilities of multiple solutions. In addition, the mastery of the maths concepts on factors and multiples also contributed to the solving of the problem. More significant is the learning by the teachers in the process of planning and designing the lesson with an iterative approach that has benefitted both the teachers and the pupils. There are challenges in the implementation of lesson study and applying the thinking skills. Some of these past and present challenges will be shared with some suggested solutions.