Lecture 3: Teaching Mathematics at the Primary Level (2024)

EDMA 2207 Teaching Mathematics at the Primary Level Semester 1 2024-2025 September 20, 2024 Wendy Griffith Primary School Mathematics MODULE 1 Components of the Primary Mathematics Curriculum LET’S TALK 5/8 of the children at a camp...

EDMA 2207 Teaching Mathematics at the Primary Level Semester 1 2024-2025 September 20, 2024 Wendy Griffith Primary School Mathematics MODULE 1 Components of the Primary Mathematics Curriculum LET’S TALK 5/8 of the children at a camp went hiking. The remaining 24 children went fishing. What is the total number of children at the camp?  REFLECTION “Teachers and teaching can make a significant difference to students’ learning outcomes in school Mathematics. Teachers have a powerful influence over what and how students learn. Through providing the appropriate learning environment in which content and pedagogy match the backgrounds, needs and interests of individual students, all students can learn Mathematics.” Jorgensen, Dole & Larkin (2020)  Mathematics Curriculum Mathematics Curriculum: Collection of knowledge that will be presented in the mathematics classroom. Supports high-quality learning, teaching and assessment. Recognizes mathematics education as a time of “being and becoming.” Thus, providing interesting, relevant and challenging experiences. Builds on knowledge, skills and dispositions children bring to the formal classroom. NCCA (2023) Teaching Mathematics Intellectual integrity of subject Students make CONTENT connections with Maths and other subjects and with the world. Creating inclusive & supporting environment PEDAGOGY Having high expectations of students TEACHERS’ Subject BELIEFS Students  Mathematics Curriculum NCTM Principles and Standards for School Mathematics NCTM (2000) Principles School Mathematics Content Process  Teaching Mathematics 1. CONTENT: Intellectual integrity of the subject Where deep learning and knowledge are paramount to learning experiences Students - Learn, apply and appreciate Mathematics - Make connections other subject areas and the world - Develop an understanding of the importance and relevance of Mathematics Jorgensen, Dole & Larkin (2020)  Components of Primary Mathematics Curriculum… Primary Mathematics Curriculum is organized by Content Areas (Strands) CONTENT: Number Concepts & Operations Algebra Measurement Geometry/Shape and Space Data Handling and Probability Jorgensen, Dole & Larkin (2020)  Components of Primary Mathematics Curriculum… Number Concepts & Operations: Pre-number work e.g. subitizing, counting, patterning (explore, extend & create), sorting etc. Place Value and Number System. Types of numbers- nominal, cardinal, ordinal. Four operations. Rational Numbers. Ratio and Proportion. Jorgensen, Dole & Larkin (2020)  Components of Primary Mathematics Curriculum… Algebra: Patterns - Types Sequences Geometry: 2D and 3D shapes Lines Lines of Symmetry Types of angles Jorgensen, Dole & Larkin (2020)  Components of Primary Mathematics Curriculum Measurement: Linear- estimate, measure & compare lengths (Non- Stand./Stand) (Perimeter and Area) Time –days, weeks, months, years, units of time, calendar, a.m. & p.m. Money – identify local coins, represent money, buy items. Jorgensen, Dole & Larkin (2020)  Components of Primary Mathematics Curriculum Measurement:… Mass – Concept, estimate, measure & compare, units (Non- Stand./Stand). Capacity- Concept, estimate, measure & compare, units (Non- Stand./Stand). Volume- Concept, estimate, measure & compare, units (Non- Stand./Stand). Data Handling: Collection of data Representing data – tally charts. Pictograph, Bar graph. Jorgensen, Dole & Larkin (2020)  Scope and Sequence of Primary Mathematics Attention should not only be paid to the Content and Process, but primary teachers should also consider Scope Sequence Scope: the breadth and depth of content and skills which are to be covered. Teachers must try to strike the right balance between these two. Sequence: the order in which concepts and skills are introduced and ordered during instruction.  Teaching Mathematics 2. PEDAGOGY: Developing supportive environments that caters to student diversity. Inclusive practices that values and build on knowledge students bring to the classroom Extend students’ confidence in using and applying Mathematics. Students Engage in deep learning about and through Mathematics Understand what teachers expect of them and the work they must do Teachers Need to value students and believe they can learn Mathematics  Teaching Mathematics “Good pedagogy is about high intellectual engagement and helping students to see and make connections; it is learner-centred, with each individual’s knowledge and culture valued and students feeling supported in their learning.” Reference: Queensland longitudinal reform study (2001) Mills & McGregor (2016)  Components of Primary Mathematics Curriculum Six Fundamental Principles For Excellence In Mathematics Education: 1. Equity 2. Curriculum 3. Learning 4. Teaching 5. Assessment 6. Technology NCTM (2020) P.S: PLEASE READ CHAPTER 1 TACHING MATHMEATICS in the 21ST CENTURY  NCTM SIX PRINCIPLES FOR SCHOOL MATHEMATICS Equity Excellence in Mathematics education requires equity—high expectations and strong support for all students. Curriculum A curriculum is more than a collection of activities; it must be coherent, focused on important Mathematics, and well articulated across the grades. Teaching Effective Mathematics teaching requires understanding what students know and need to learn and then challenging and supporting them to learn it well.  NCTM SIX PRINCIPLES FOR SCHOOL MATHEMATICS Learning Students must learn Mathematics with understanding, actively building new knowledge from experience and previous knowledge. Assessment Assessment should support the learning of important Mathematics and furnish useful information to both teachers and students. Technology Technology is essential in teaching and learning Mathematics; it influences the Mathematics that is taught and enhances students’ learning.  Components of Primary Mathematics Curriculum PROCESS STANDARDS: Problem Solving Reasoning and Proof Representation Communication Connections NCTM (2020) P.S: PLEASE READ CHAPTER 1 TEACHING MATHMEATICS in the 21ST CENTURY  The Power Of Teachers’ Beliefs… “Teachers who believe that some students, due to their backgrounds or behaviours, are unable to learn mathematics will ultimately create learning environments that construct the expected outcomes.” “In good teaching, teachers must be mindful of the influence of their beliefs about teaching and learning Mathematics, and the power this has upon the learning outcomes of their students." Jorgensen, Dole & Larkin (2020)  The Power Of Teachers’ Beliefs… “One of the most important influences on learning was the teacher’s belief that ALL students could learn Mathematics.” Ashew et.al (1997) “In good teaching, teachers must be mindful of the influence of their beliefs about teaching and learning Mathematics nd about the influence these have on their students’ learning outcomes.” Jorgensen, Dole & Larkin (2020)  Solve the following Problem Nathan is 3 years old. Kyle is 4 times Nathan's age and Joshua is 10 times Nathan's age. How many years will it take for Kyle to be twice Nathan’s age and half Joshua’s age?  Principles of COUNTING  STABLE ORDER  1-1 CORRESPONDENCE  CARDINALITY  CONSERVATION  ORDER OF IRRELEVENCE  ABSTRACTION  HIERACHICAL INCLUSION  MOVEMENT IS MAGNITUDE  UNITIZING  Additive Reasoning Big Ideas: Additive reasoning includes various mathematical skills, concepts, and abilities that contribute to number sense. Additive reasoning is built on concepts of early number, including part–whole relationships, commutativity, and the inverse relationship between addition and subtraction. Additive reasoning both depends upon, and contributes to, the development of base-ten number understanding. Ebby, C. Hulbert, T and Broadhead, R. (2021).  Additive Reasoning Additive reasoning involves knowing when to use addition and subtraction in a variety of situations, choosing flexibly among different models and strategies, using reasoning to explain and justify one’s approach, having a variety of strategies and algorithms for multidigit addition and subtraction, and knowing if an answer or result is reasonable. Ebby, C. Hulbert, T and Broadhead, R. (2021).  Additive Reasoning Additive reasoning is one of the crucial components of mathematical competence and is built on conceptual understanding of number and part–whole relationships. As students learn to work with larger quantities, additive reasoning also involves understanding of the base-ten number system and relative magnitude. The part–whole relationship between two quantities involves understanding both the commutative property and the inverse relationship between addition and subtraction. Ebby, C. Hulbert, T and Broadhead, R. (2021).  Additive Reasoning Commutative Property of Addition A quantity can be broken up into two or more quantities. The order in which numbers are added does not matter. Instruction: Model with concrete situations. Develop part-whole understanding.  Additive Reasoning Inverse Relationship Between Addition and Subtraction Based on the Part- Whole relationship Taking away one part from the whole leaves the other part. Instruction: Model with concrete situations. Develop part-whole understanding. Four related relationships exist. Understanding relationships should be the central focus. Example: Fact Families 3+4=7 7–4=3 4+3=7 7–3=4  Additive Reasoning Connecting Additive Reasoning and Base –Ten Understanding Concepts of Additive Reasoning must be in place to develop an understanding of the Base Ten system. Base Ten system is composed of place value parts of varying unit sized that combine to make the whole. Example: a. 25 = 20 + 5 OR 5 + 20 b. 25 = 2 Tens and 5 Ones  Additive Reasoning Connecting Additive Reasoning and Base –Ten Understanding Based on the Part- Whole relationship Taking away one part from the whole leaves the other part. Instruction: Model with concrete situations. Develop part-whole understanding. Four related relationships exist. Understanding relationships should be the central focus. Example: Fact Families 3+4=7 7–4=3 4+3=7 7–3=4  WEEK 3 CLASS ACTIVITY In your groups of five which you have formed, kindly complete this following group activity. Carefully examine the Barbados ECE Mathematics syllabus and a Mathematics curriculum from another Caribbean or International country. 1. Compare the components of each document. E.g. Rational, Background, Goals, Format, Process Standards. Content etc.) 2. Select a grade/class level and a topic. Compare the scope and sequence of the two countries. 3. Summarise your findings in no more than one page of font 12. 4. Email your summary by Monday, 23rd September 2024. The group leader must email the document which should contain the names and ID# of each member.  Next Week MODULE 2: Issues in Teaching and Learning Mathematics in Primary Schools. Theoretical Foundations Read Chapter 2:Theories of Learning Mathematics Jorgensen, Dole & Larkin (2020)