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cpa representation of multiplications
Qualification Course

Multiplicative Reasoning

Training>Course Directory

1 day

Duration

6 credits

Earned

This course is designed for primary school teachers who wish to learn the essentials of teaching multiplicative reasoning to primary school pupils. It is intended for classroom teachers, maths leads and senior leaders. Participants are expected to be familiar with the materials covered in the 'Essentials of Teaching Maths Mastery' course. Therefore, it is strongly recommended that attendees complete that course before registering for this one.

Course Objectives

This professional development course for teachers aims to deliver the following outcomes:

  1. Develop a comprehensive understanding of how to teach and learn multiplicative reasoning within the broader context of the maths curriculum.
  2. Encourage a shift in educators' perspectives on teaching and learning multiplicative reasoning.
  3. Provide practical advice for lesson planning and enhancing lessons on multiplicative reasoning.
  4. Elevate educators to a high level of expertise in the subject of multiplicative reasoning.

Upon completion of this course, educators will possess thorough knowledge of teaching and learning multiplicative reasoning within primary education settings. By actively participating in real classroom scenarios—effectively stepping into their students' shoes—teachers will develop genuine empathy for the learning process.

This course aims to equip teachers with both the necessary content and the pedagogical knowledge to teach multiplicative reasoning effectively. As a result, pupils will gain a conceptual understanding of the topic, become fluent in applying multiplicative reasoning, and be able to use their knowledge to solve a wide range of familiar and unfamiliar problems.

Earn 6 credits

Course Content

  1. Different Usage of Numbers and Semantics Teach pupils to understand multiplicative reasoning through proportional reasoning models, using clear examples and visual aids. For instance, illustrate the difference between 'one-half of 8 apples' and '8 half-apples' with pictorial representations to demonstrate varied applications of fractions and concepts of ‘whole or changing wholes’.
  2. Concepts Necessary to Understand Multiplicative Reasoning Emphasise the foundational concepts such as equality, equivalence, and the diverse contexts in which numbers are used (cardinal, nominal, measures, ordinal). Incorporate real-life examples and manipulatives, and introduce tools like ratio mappings, two-way tables, double number lines, ratio tables, and comparative bar models. Explore the geometric reasoning and its positive relationship with multiplicative reasoning, highlighting that all circles are similar shapes with individual scalar products.
  3. Conventions Address common misconceptions about multiplicative reasoning, focusing on the roles of the numerator and denominator and identifying scale factors to show proportional reasoning. Use interactive activities and guided explorations to correct these misconceptions and reinforce correct conventions, enabling teachers to support their students’ understanding.
  4. Spiral Curriculum Introduce complex proportional reasoning concepts in small, incremental steps over a long period, revisiting and expanding on these ideas at higher levels of understanding through subsequent years. Provide examples of how these concepts can be layered and expanded upon to ensure a deepening of knowledge.
  5. Differentiating Instruction Tailor multiplicative reasoning lessons to meet the diverse needs of pupils, providing additional support for those struggling and extending challenges for more advanced learners. Offer examples of differentiated activities and strategies that cater to a range of learning styles and levels of comprehension.
  6. Assessment Develop and implement effective assessment strategies to gauge pupils' understanding of multiplicative reasoning. Highlight tools and methods that provide insights into how well students comprehend and can apply fraction concepts.
  7. Operations Teach operations within multiplicative reasoning (addition, subtraction, multiplication, division), including methods to handle decimals and mixed numbers, in ways that are understandable and engaging for pupils.
  8. Problem Solving and Investigations Engage pupils in problem-solving and investigative tasks involving multiplicative and proportional reasoning, using bar models, number lines, and other visual representations. Provide examples of problems that encourage pupils to apply their knowledge in various contexts of reasoning and analysis.
  9. Holistic Approach Apply these concepts in a variety of situations linking numbers, fractions, decimals, and percentages. Explore abstract contexts and extend proportional reasoning to algebra and geometry.

Who this is course intended for?

This course is intended for classroom teachers, maths leads, and senior leadership. It builds upon the foundational knowledge acquired in The Essentials of Teaching Maths Mastery course.

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