How to teach the metric system

Blendspace. (n.d.). MATH: POWERS OF 10 and EXPONENTS. Gebruikt op 19-01-2023. URL: <https://www.blendspace.com/lessons/R23YlI3L8W6yOQ/math-powers-of-10-and-exponents>

Preface

The following article is a translated summary of a study that was concluded over six months during the last year of my studies to become a teacher in chemistry. You will find the full document underneath. For obvious reasons, I took out the names of the students who were observed, the schools where the study was concluded, and the co-authors. Since it is difficult to translate an entire 190-page study, I left some images and appendixes unchanged. I hope it helps you in the same way it helped me gain insight into the learning behavior of students – in particular in the metric system.

didactic-research-how-to-teach-the-metric-system-anonymous-english-translation Download

Introduction

The study explores the persistent issues students face with the metric system, despite it being a fundamental part of primary education. It is observed that students across various educational levels struggle with metrics, particularly in measuring and geometry, as detailed in a 2019 Ministry of Education report and previous studies. These reports highlight that although there has been a slight improvement in arithmetic and mathematics at the end of primary school, the metric system remains challenging for many students. Problems are especially pronounced with tasks involving unit conversions, where only a small percentage of students perform well.

The study aims to address these challenges by designing an intervention to enhance students’ mastery of the metric system. The goal is to improve students’ understanding of area, volume, and unit conversions, focusing on less common prefixes and the ability to convert between small and large units. The intervention seeks to make metric units more meaningful and comprehensible, with a detailed plan to be outlined in subsequent chapters. This approach is intended to address the underlying issues and improve overall student performance in metric-related tasks.

Theory

The article outlines the core objectives and methodologies for teaching the metric system across primary and secondary education, highlighting challenges and didactic solutions.

Core Objectives: In primary education, the focus is on understanding numerical structures, solving geometric problems, and using various measurement units. Despite these goals, secondary education reveals gaps in students’ metric system comprehension, attributed to issues within the system itself rather than teaching methods. Secondary education aims to deepen students’ understanding of the metric system through more advanced mathematical and scientific applications.

Numbers and Measurement: Primary education emphasizes mastering the decimal system, which simplifies conversions by grouping quantities in powers of ten. Key learning aspects include efficient grouping, understanding positional value, and practical measurement skills using standard measures.

Methodology for Secondary Education: The action model progresses from concrete experiences to abstract concepts, guided by competency dimensions such as factual knowledge, application, reasoning, and metacognitive reflection. Secondary education aims to refine mathematical understanding, solution procedures, and application skills, assuming proficiency in basic operations from primary education.

Challenges: Students with math difficulties often struggle with number structures and basic operations. Practical simulations of metric system contexts can be challenging, and varied support models may cause confusion.

Didactic Solutions: Practical contexts, like counting and using money, help students grasp decimal grouping and place value. The HTE model is recommended for its focus on decimal positions and conversions. Self-discovery and directed questioning, coupled with differentiated practice and collaborative learning, enhance understanding. Group work fosters mutual support and responsibility, improving learning outcomes.

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In conclusion, addressing metric system teaching challenges requires a structured approach, integrating self-discovery, practical contexts, and consistent models to ensure students develop a robust understanding for academic and real-life applications.

Didactic design

The chapter on “Didactic Design” outlines the development of a lesson aimed at teaching students the metric system through an understanding of the decimal system. The design is rooted in principles such as self-discovery, directed questioning, and collaborative learning. The lesson is structured into five phases:

Beginning of the Lesson: Students are introduced to the lesson’s framework and the concept of Lesson Study without prior discussion of objectives to encourage self-discovery.
Counting Sticks: Students work in groups to count sticks in bundles of ten to simplify the process. This phase encourages a positive attitude towards mathematics and collaborative learning. Through directed questioning, students are guided to recognize the usefulness of bundling.
HTE Model: Students transition from counting sticks to understanding the HTE model, which represents numbers in terms of bundles and prefixes (kilo, hecto). This phase connects the practical task of counting to abstract mathematical concepts and the metric system.
Practice: Students work independently on worksheets of increasing complexity to reinforce their understanding. Differentiation ensures that advanced learners are also challenged.
Conclusion: The lesson ends with a “Think, Share, Exchange” exercise where students reflect on their learning, discuss in groups, and share insights with the class.

Expected student reactions include engagement, enthusiasm, and increasing confidence in applying the metric system.

Research questions

The research aims to enhance students’ understanding of the decimal and metric systems by improving their number sense. Despite extensive practice, many students still struggle with these concepts, often due to inadequate foundational knowledge. The hypothesis is that current teaching methods do not adequately address this gap. The lesson will transition from concrete to abstract concepts, using guided questioning and the HTE model to solidify understanding. Key research questions focus on how students learn through self-discovery, guided questioning, the Van Groenestijn action model, practice, differentiation, and collaborative learning. Observations, student responses, and interviews will be used to assess learning outcomes.

Methodology

The methodology for analyzing the lesson using the Lesson Study method involves a structured approach to understand student learning and improve teaching practices.

Design-Based Research: The research begins with identifying a teaching problem related to the metric system and conducting thorough research, including test analyses, interviews, and literature reviews. A conceptual framework is developed to guide the design of an intervention lesson. This lesson plan includes detailed phases, teacher activities, expected student responses, and evaluation methods. Observation forms are created for different student types to monitor progress and adapt teaching strategies.

Selection of Students: Three types of students—struggling, average, and strong—are observed to ensure the lesson meets diverse needs. Backup students are also selected. Observations focus on whether the lesson challenges students, engages them, and achieves the learning objectives.

Data Collection: Observations concentrate on student thinking processes, not just correct answers, to identify misconceptions and problem-solving strategies. Post-lesson interviews with example students provide feedback on their learning experience, including their understanding of the lesson content and perceived difficulty.

Analysis: After the lesson, a debriefing session reviews student behavior and responses, assessing if lesson objectives were met and if predictions were accurate. Results from observations, student work, and interviews inform revisions to improve the lesson. This iterative process ensures the lesson effectively supports student learning.

Results

The chapter presents findings from Lessons 1 and 2, detailing observations, worksheets, student feedback, and necessary adjustments.

Lesson 1:
Observations: Student A (weak) worked independently but struggled with the worksheet and HTE model. Student B (average) engaged well but had difficulty with complex questions. Student C (strong) excelled, understanding and applying concepts effectively.
Worksheet Performance: Student A made numerous errors and did not effectively use the HTE model. Student B showed a solid understanding but struggled with calculations involving prefixes. Student C completed the worksheet accurately and quickly, indicating a strong grasp of the material.
DDU (Direct Dialogue and Understanding): Students were enthusiastic but had trouble articulating their learning. The teacher clarified objectives, improving comprehension.
Interviews: Student A found the lesson enjoyable but wanted more active participation. Student B appreciated the HTE model and the lesson’s educational value. Student C felt he could have performed well without the lesson but valued the differentiation.

Lesson 2:
Observations: Student A struggled initially but improved by adopting bundling strategies. Student B actively participated and performed well on the worksheet. Student C, while engaged, did not use the model correctly but answered most questions correctly.
DDU: Students were more engaged but still struggled to articulate their learning outcomes.
Interviews: Student A felt the lesson was beneficial but suggested clearer model explanations. Student B enjoyed the lesson and found the model useful. Student C felt the lesson lacked challenge and preferred working independently.

Conclusions: Both lessons were generally successful, with students showing enthusiasm and understanding. Adjustments for future lessons include collecting sticks before class explanations, improving students’ articulation of learning goals, and ensuring advanced students use the model to better assess understanding.

Conclusion

The chapter evaluates how students learn in different instructional scenarios and provides a comprehensive conclusion.

Discovery Learning: Allowing students to discover on their own, such as through counting sticks in groups, engaged all students. They experimented with various strategies and found bundling beneficial, reflecting Mulder’s (2020) findings on self-discovery.

Collaborative Learning: Collaboration showed mixed results. Advanced students quickly adopted bundling, influencing others, but there was limited evidence of collective strategy development. This aligns with Ebbens & Ettekoven’s (2016) idea of mutual dependence but shows some limitations in group strategy formulation.

Guiding Questions: Guiding questions effectively prompted students to devise strategies and understand concepts, especially for struggling and average learners. This approach, supported by Geerts & Van Kralingen (2020), helped students arrive at solutions without direct answers from the teacher.

Van Groenestijn Action Model: Applying this model facilitated a successful transition from concrete to abstract thinking. Adjustments in Lesson 2 improved students’ ability to use the model, benefiting especially struggling students. This approach aligns with Van Groenestijn, Van Dijken, and Janson’s (2012) model.

Discussion

The research involved two lessons with different student groups: one from a progressive school and the other from a traditional institution, with varying class years and student levels. The study did not use baseline measurements, relying instead on qualitative methods, which may limit precise progress evaluation. Combining self-discovery with collaborative learning proved challenging, as students seldom developed joint strategies. The DDU (Description, Discussion, Understanding) method showed students struggled to articulate their learning, suggesting it is more suitable for a series of lessons rather than a single one. Feedback revealed discrepancies between students’ self-assessment and actual understanding. Future research should explore the value of bridging decimal and metric systems for advanced students and consider adjusting lesson phases to maintain focus and engagement.

Reflection

Reflection on inquiry-based action highlights my growth in investigative skills, feedback integration, and collaboration. Initially, my team and I focused on understanding each other and setting agreements, which improved our project efficiency compared to previous experiences. Effective use of tools like Teams and OneNote enhanced organization and communication. Our collaboration evolved from independent work to closer teamwork, leveraging individual strengths for greater productivity. I learned valuable lessons in clarity from a colleague and appreciated diverse perspectives, although reaching consensus was sometimes challenging. My LIO year in chemistry enriched my ability to structure and connect project components, benefiting both my teaching and research skills.

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