This training video outlines four types of journals.

In the first session, we discussed the four journal types. Watch the video to hear us discuss each with an example. Take a lesson and write journal prompts for each of the four types.

For users of think! Mathematics, look at the example given in the Teaching Guide (TG) and say which type of journal the TG suggests. The basic idea of journal writing is simple – students articulating, explicating, communicating their mathematical thoughts on a regular (hence, journal) basis. Any teachers who want to do a self-directed study of journal writing are welcome to join us here. You may post questions in the comments section. These three videos provide the learners with basic information about journal writing and some inputs to provoke questions and catalyze action. Participants are encouraged to let their students write journals and learn to use the journal entries as assessment information and as a platform to stimulate engaged learning. Along the way, think about the benefits you have seen when students are asked to write journals and the attendant issues. You may share and discuss this with your group of colleagues or raise them here. How can we empower learners through journal writing? In this video, Dr Ban Har Yeap shares 4 types of journals that teachers can ask students to write.

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In this exploration, we’ll delve into the ‘before and after’ of Singapore’s math education – from its initial struggles to its remarkable triumph. We’ll unravel how the melding of these five influential thinkers’ ideas created an educational tapestry that improved test scores and transformed the nature of learning mathematics. Whether you’re an educator or a student, this story is a testament to the power of theory-informed practice and a source of inspiration for all who value the art and science of teaching.

Join us on this enlightening journey through Singapore’s math education revolution, a narrative that takes us from traditional approaches to innovative, world-leading strategies.

In the nascent days of its independence in the 1960s, Singapore, much like any young nation, faced the colossal task of building its educational infrastructure. The focus then was more on establishing schools and ensuring basic literacy and numeracy among its populace. Mathematics education, in these early days, followed a traditional, almost utilitarian approach. The emphasis was on rote learning and procedural proficiency – a reflection of the immediate need to equip students with fundamental skills.

As Singapore sought its place on the global stage, international benchmarks like the Programme for International Student Assessment (PISA) and the Trends in International Mathematics and Science Study (TIMSS) began to gain prominence. These assessments, focusing on practical and applied knowledge, revealed a stark contrast between Singapore’s traditional methodologies and the evolving global standards in math education. The results from the early years of these assessments served as a wake-up call, highlighting the need for a paradigm shift.

Classrooms in Singapore during this era were characterized by teacher-centered instruction, where the teacher was the primary source of knowledge, and students were passive recipients. The pedagogy centered around memorization and practice of standard procedures, with little emphasis on understanding or application. Math problems were largely context-free, focusing on numerical manipulation rather than real-world application.

As Singapore’s economy began to grow and diversify, the limitations of this approach became increasingly apparent. The need for a workforce capable of critical thinking and problem-solving in a rapidly modernizing world was at odds with the prevailing educational practices. Moreover, the one-size-fits-all approach failed to cater to the diverse learning needs of students, often leaving those who could not keep pace behind.

As Singapore grappled with the limitations of its traditional education system, a wave of reform began, deeply influenced by the work of several key educational theorists. These thinkers provided the theoretical bedrock upon which Singapore would build its new approach to mathematics education.

Jean Piaget’s theories on cognitive development played a pivotal role. Piaget proposed that children move through distinct stages of cognitive development, each with its own characteristics and limitations. This understanding led to a curriculum that was more developmentally appropriate, ensuring that mathematical concepts were taught in alignment with students’ cognitive stages.

Richard R. Skemp’s distinction between relational and instrumental understanding in mathematics had a profound impact. Skemp advocated for a deeper understanding of mathematical concepts, as opposed to mere procedural proficiency. This philosophy guided a shift in teaching methods, focusing more on understanding ‘why’ behind the ‘how’ in mathematical processes.

Lev Vygotsky’s social development theory, especially the Zone of Proximal Development (ZPD) concept, underscored the importance of collaborative learning. Vygotsky’s ideas led to an increased emphasis on group work and peer-to-peer learning in math classes, fostering a more interactive and supportive learning environment.

Jerome Bruner’s concept of scaffolding, where learners are provided with support structures to achieve higher levels of understanding, was instrumental in developing new teaching methodologies. Bruner’s emphasis on discovery learning, where students construct their own understanding, also influenced the design of math curricula.

Lastly, Zoltan Dienes’ principles of learning mathematics through play and exploration were reflected in the incorporation of manipulatives and hands-on activities in math lessons. This approach made math more engaging for students and reinforced their conceptual understanding.

These theoretical underpinnings necessitated a complete overhaul of the traditional mathematics curriculum. Teacher training programs were revamped to equip educators with the skills to implement these new pedagogical approaches. Textbooks and teaching materials were redesigned to align with the principles of these educational theorists, marking the beginning of a new era in Singapore’s math education.

The transition from theory to practice marked a significant turning point in Singapore’s mathematics education. Classrooms transformed from places of passive learning to vibrant hubs of inquiry and exploration. The adoption of these new teaching methodologies was not just a change in technique but a cultural shift in the perception of mathematics education.

The effectiveness of these reforms was underscored by Singapore’s remarkable performance in the Programme for International Student Assessment (PISA) and the Trends in International Mathematics and Science Study (TIMSS). These international benchmarks provided concrete evidence of the positive impact of the reforms. Students from Singapore consistently ranked at the top or near the top in these assessments, showcasing the success of a more holistic and understanding-based approach to mathematics education.

In the new Singaporean math classroom, teachers became learning facilitators rather than mere knowledge dispensers. Interactive and collaborative activities became commonplace. Concepts were taught through real-world applications, making mathematics more relatable and less abstract. The focus shifted to problem-solving and critical thinking, encouraging students to understand the ‘why’ and ‘how’ of mathematics, not just the ‘what’.

The inclusion of differentiated learning strategies ensured that each student’s unique needs and learning pace were respected and catered to. Technology began playing a crucial role, integrating digital tools to provide personalized and interactive learning experiences. The continuous evolution of teaching methodologies showed Singapore’s commitment to staying at the forefront of educational innovation.

The transformation of Singapore’s mathematics education serves as a powerful case study on the effective application of educational theories in practice. It underscores the importance of continual assessment and adaptation in teaching methodologies. Looking ahead, Singapore continues to explore new frontiers in education, preparing its students not just for exams but for a lifetime of learning and problem-solving.

The story of Singapore’s journey in mathematics education is a compelling testament to the power of integrating theory into practice. It’s a narrative that began with traditional, rote-learning methods and evolved into an innovative, world-class educational system deeply rooted in the insights of Piaget, Skemp, Vygotsky, Bruner, and Dienes.

This transformation didn’t just elevate Singapore to the top of international rankings like PISA and TIMSS; it revolutionized the very nature of mathematics teaching and learning. The shift from a teacher-centric, memorization-based approach to one that emphasizes understanding, problem-solving, and collaborative learning exemplifies the profound impact that thoughtful, research-based educational reform can have.

For educators and students around the world, Singapore’s journey offers valuable lessons. It shows that embracing change, grounded in solid educational research, can lead to remarkable outcomes. It’s a reminder that education is an ever-evolving field where the willingness to adapt and innovate is key to success.

As we reflect on Singapore’s achievements in math education, it becomes clear that the journey is as important as the destination. It’s a journey that continues to inspire, challenge, and motivate educators and learners alike, reminding us that in the quest for educational excellence, learning never stops.

]]>Yet instruction looks remarkably different in classrooms abroad, particularly in countries lauded for their students’ high mathematics performance. Rather than jumping straight into direct instruction, teachers in these high-achieving nations like Singapore dedicate upwards of half the class period or more to collaborative problem-solving activities that allow students to reason through challenging questions, invent solution pathways, and grapple with key concepts before any formal teaching takes place. This “guided discovery” phase aims to first activate students’ critical thinking and taps into their innate curiosity, setting them up to deeply integrate the forthcoming lesson.

Singapore’s matched success in both teacher training and math achievement on prominent global assessments like PISA has drawn considerable international attention. Unlike the fragmented teacher prep landscape in America, Singapore ensures consistent rigor and messaging by funneling all of its teachers through the elite National Institute of Education (NIE) at Nanyang Technological University. There, educators master reach specific techniques for lesson planning and delivery tailored for Singaporean classrooms – most notably, the research-backed “Singapore Math” 3-Part Lesson.

Originally adapted from groundbreaking methodologies developed in Japan, Singapore’s signature 3 Part Lesson format marks a profound divergence from conventional math instruction. Meticulously structured to align with cognitive science on how students best acquire new skills, the immersive three-part framework serves as the backbone for mathematics education across all of Singapore’s highly effective schools. Each phase works synergistically to set students up for deep, enduring comprehension and competency. While seemingly simple in theory, skillfully leveraging each segment requires considerable expertise – hence Singapore’s systematic training for all up-and-coming math teachers.

Let’s explore what sets this tested teaching tradition apart:

Every Singapore Math lesson kicks off with an Anchor Task, an intriguing open-ended challenge that immediately hooks students’ interest while activating their prior knowledge. This thoughtfully constructed lead-off activity – mathematically rich yet readily accessible for learners of all levels – steers the subsequent learning and forms a cognitive reference point to build upon moving forward. Teachers leverage the Anchor Task to spur student collaboration, guide discovery of key ideas and procedures, and surface any gaps in understanding needing attention.

While superficially straightforward, crafting just the right Anchor Task involves considerable intentionality. Teachers aim to pose problems tied to current curriculum goals yet rife with entry points to unleash the class’s existing capabilities. Allowing pupils to freely strategize and grapple with these engaging prompts for an extended period before formally introducing structured techniques ultimately sets the stage for enhanced comprehension once core lesson concepts are presented afterwards. Probing student solutions generated during the Anchor Task later enables educators to neatly bridge emerging ideas into targeted instruction.

Once students have deeply explored the initial challenge and developed preliminary problem-solving approaches, the teacher shifts gears into carefully scaffolded explanations, modeling target skills, and verification of comprehension. This strategic instruction doesn’t supplant students’ nascent ideas but rather builds purposefully on dawning understandings surfaced during the Anchor Task. helped solidify emerging comprehension through Guided Practice. Here, the teacher circulates to confirm correct grasp of lesson techniques, remedy lingering confusion, and provide just-in-time support tailoring guidance to individuals’ needs – essential formative assessment informing next steps. Singapore Math classrooms buzz with productive activity rather than passively absorbing information. Even when directing students through mathematical procedures, teachers use interactive questioning and hands-on learning aids to keep their audience discussion. engaged.

After confirming students have acquired the intended skills through supported practice and reinforcement, the teacher will then assign independent work to allow pupils to apply their freshly honed knowledge without aid. This is often assigned as homework but may occur in classrooms with time to spare. Either way, the preceding Anchor Task and Guided Practice equip students to productively practice independently, driving home concepts secured through collaborative experimentation and targeted remediation. Since caregivers often assist kids in math homework help, Singapore Math teachers take care to confirm pupil readiness before releasing problems for home practice. Without that assurance of capability, unfinished work or parent frustration may result.

In Singapore, this signature 3 Part Lesson blueprint sets the pace for active, high-yield mathematics instruction across all schools.ANCHOR students’ interest, GUIDE them toward core understandings, then RELEASE them to demonstrate self-reliant skill application – and the formula works! Beyond impressive test results like Singapore’s top PISA math ranking, close inspection of its classrooms reveals confident problem-solvers, not passive receptacles of information. But this success does not arise by accident or luck. Rigorous, uniform teacher training ensures correct implementation of student-centered methods proven to unlock mathematical insight. Paired with a rigorous national curriculum and high expectations for universal math literacy, Singapore’s commitment to the 3 Part Lesson fuels mathematics achievement among all its youth. And with abundant data validating this instructional mainstay, education leaders worldwide eye Singapore’s model hoping to spark similar outcomes back home.

Research Spotlight: The Power of the Anchor Task

Educational studies consistently validate placing rich, collaborative problem-solving activities at the heart of math instruction through vehicles like Singapore’s signature Anchor Tasks. Rather than rushing to model procedures, math lessons globally shown to foster heightened student outcomes dedicate substantial time upfront to student-centered exploration.

– Activating prior knowledge solidifies new connections

– Grappling with challenges sparks innate curiosity

– Peer discourse strengthens conceptual ties

– Relating concepts to tangible scenarios aids retention

In Singapore, these key drivers motivate the prominent Anchor Task phase launching every math lesson. Beyond superior assessment performance like topping PISA’s math rankings, Singaporean students exhibit creative mathematical thinking, flexible problem-solving, and confidence tackling unfamiliar questions. Anchor Tasks help instill these transferable skills from an early age.

When designing Anchor Tasks to unveil student thinking and set the stage for targeted instruction, teachers should ensure activities exhibit traits like:

– Tie to current learning goals while allowing space for multiple solution avenues

– Promote productive struggle and peer discourse

– Accessible for a diversity of ability levels

– Rich enough to support extensive visualization, manipulation and exploration

– Relatable to students’ lives and interests to boost engagement

Additionally, keep the endgame in mind – tasks should surface preconceptions to address and solidify nascent understandings to leverage moving forward. Avoid overly simplified exercises or those supporting a sole solution pathway. Promote collaboration, not isolation.

– Represent fractions with a classroom model – Have pairs of students use themselves, manipulatives or drawings to demonstrate examples of 1/4, 1/3 and other basic fractions divided into equal parts. Then have them switch models with peers to evaluate other approaches.

– Plan a class garden with model representations – Provide graph paper and measuring tools for teams to draft possible garden dimensions capable of yielding set vegetable totals, foregrounding multiplicative thinking.

– Find lines of best fit – Have students determine lines approximating real-world data you provide (e.g. height vs age), using multiple approaches like visual estimation, point plotting, physical tools like sticks and strings, or equations. Compare ending models.

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