To know and use mathematics successfully, students need to develop the ability to receive and express mathematical ideas. When students learn to communicate mathematically, they are able to ask questions of one another, make conjectures, share ideas, clarify those ideas, suggest strategies, and explain their reasoning.
Counting and Representation are two of the key mathematical principles or “Big Ideas” in Number Sense and Numeration, and are closely linked together. Asking your students “how many” questions helps them to think about numbers and develop number sense. In order to answer “how many” questions, students often need to count. They usually answer with a number word (e.g., seven) or a symbol (e.g., 7). These number words and symbols are representations of a quantity that is determined by counting.
Parents play an important role in supporting student learning. Strong connections between home and school are needed to ensure that parents and teachers are working together to advance the mathematical development of children. These connections can be established through effective and varied communications with parents/guardians.
Having good number sense involves an understanding of the many relationships that exist among numbers. Number Relationships is one of the key mathematical principles or “Big Ideas” in Number Sense and Numeration. It is important to emphasize number relationships with your students to help them learn how numbers are interconnected and how numbers can be used in meaningful ways. Some examples of number relationships are comparison relationships and part-whole relationships.
Students with operational sense comprehend the operations of addition, subtraction, multiplication, and division. They recognize the relationships among these operations and use the operations effectively in real-life situations.
Problem solving is the process of applying prior knowledge, experience, skills, and understandings to new and unfamiliar situations in order to complete tasks, make decisions, or achieve goals. In the mathematics program, problem-solving situations can provide the meaningful and exciting experiences through which students learn concepts and skills.
Understanding quantity is pivotal to your students' ability to develop number sense. Students who possess a solid understanding of quantity will likely excel at estimating, comparing, and reasoning with numbers, and eventually, proportional reasoning – that is, using relationships between quantities, such as knowing that 1 dozen is 12, so 3 dozen is 36. And students who grasp quantities like five and ten go on to excel at place value, mathematical operations, and fractions.
To know and use mathematics successfully, students need to develop the ability to receive and express mathematical ideas. When students learn to communicate mathematically, they are able to ask questions of one another, make conjectures, share ideas, clarify those ideas, suggest strategies, and explain their reasoning.
Comprehending decimal numbers is an important development in students’ understanding of number. However, a deep understanding of decimal numbers can develop only when students have opportunities to represent decimal numbers and to relate them to whole numbers and fractions. Instruction that focuses on meaning, rather than on abstract rules, is the key to helping students understand decimal numbers and how they can be used in meaningful ways.
Learning about fractions extends students’ understanding of our numeration system. While whole numbers represent quantities of whole units, fractions signify parts of whole units or parts of sets. Although fractions are all around us, learning about fractions is difficult for some students. Instruction should emphasize the meaning of fractions before any abstract rules are introduced.
Parents play an important role in supporting student learning. Strong connections between home and school are needed to ensure that parents and teachers are working together to advance the mathematical development of children. These connections can be established through effective and varied communications with parents/guardians.
In this module, you will meet Dave, a Grade 6 teacher who is planning on teaching a lesson on Patterning and Algebra. In order to boost his students’ achievement levels, he decides to focus on: providing differentiated instruction to address all his students; engaging in problem-based teaching to make the subject more meaningful to the students; and getting coaching to improve his teaching skills.
In this module, you will meet Chris, a Grade 4 teacher who is planning on teaching a lesson on Measurement. In order to boost her students’ achievement levels, she decides to focus on: providing differentiated instruction to address all her students; engaging in problem-based teaching to make the subject more meaningful to the students; and getting coaching to improve his teaching skills.
Developing a strong understanding of multiplication and division in the junior years provides students with important tools for solving real-life problems and builds a strong foundation for proportional reasoning and algebraic thinking.
Problem solving is the process of applying prior knowledge, experience, skills, and understandings to new and unfamiliar situations in order to complete tasks, make decisions, or achieve goals. In the mathematics program, problem-solving situations can provide the meaningful and exciting experiences through which students learn concepts and skills.
Guided reading is the bridge between shared reading and independent reading. It allows teachers to help students make the transition from teacher modelling to student independence. In guided reading, the teacher scaffolds the learning of a small group of students as they apply strategies previously taught during read-alouds and shared reading to an unfamiliar, but carefully selected, text. This text is within the students' instructional range and provides reasonable challenges for learning. The teacher supports the students as they talk, read, and think their way through a text using effective reading strategies.
Independent reading is the final instructional approach presented in a scaffolded, comprehensive reading program. This approach builds on the explicit teaching of strategies and skills that has occurred during read-alouds, shared reading, and guided reading lessons. During an independent reading lesson, the teacher provides minimal support to readers: hence, students read independently.
Running records are assessment tools originally created by Marie Clay, a developmental psychologist and world-wide authority on early reading. Running records help teachers assess a student's oral reading proficiency objectively, reliably, efficiently, and at times that are convenient. The records are usually administered during the early stages of literacy development, before students become proficient silent readers. In special circumstances, they may be appropriate for use with older students who experience significant reading difficulties.
Shared reading is an interactive approach to the teaching of reading. Students are able to develop new skills in a safe and encouraging environment, and can consolidate skills they have already been taught. In shared reading, all students must be able to see the print and accompanying pictures so that the teacher can share with the students the responsibility for reading.
Junior students learn best when actively involved in their learning. Cooperative learning activities enhance academic learning by encouraging students to work together in different ways and helping build social skills in a safe environment. Students develop their ability to share information through listening and speaking, while assuming individual and group accountability.
Junior students learn best when actively involved in their learning. Literature Circles provide rich opportunities for students with common interests to read and discuss a wide range of texts, express personal opinions, and build vital group skills in a safe environment. In doing so, students find deeper meaning in a text and have the opportunity to present their ideas through oral and written responses.
Junior students learn best when actively involved in their learning. Today's junior students are comfortable with technology and use a wide range of electronic and online communication devices to send and receive information. Teachers must purposefully integrate technology into all aspects of classroom teaching and learning to help junior students critically assess, filter, and interpret the information they are receiving and develop the skills they need to use technology confidently and appropriately in the classroom and beyond.
All forms of media contain messages for an intended audience and purpose. To help junior students make sense of the multi-media culture they live in, they need critical thinking skills to analyse, and planning and production skills to create a variety of media texts. This module provides teachers with the background information and frameworks to effectively integrate media literacy across the curriculum.
Shared reading is an integral part of a comprehensive literacy program. It is an instructional approach that can be used with a whole class or with a small group. During shared reading, the teacher explicitly teaches proficient reading behaviours through modelling and think-alouds and begins to share with students the responsibility for reading.
Writer’s Workshop is a daily period of time committed to the process of writing. It begins with whole class explicit teaching (mini-lesson), followed by time in which students either write or participate in peer or teacher conferencing. The teacher provides support through small group guided lessons and/or individual or small group conferencing. Writer’s Workshop usually ends with time for students to share and/or reflect.
MODULE FOR PARENTS
The goal of this module is to provide you with a quick overview of the numeracy and literacy modules found on the eworkshop.on.ca site. You will find over 40 video clips that allow you to take a peek into the classroom to better understand what your children are currently learning in school. Try some of the interactive games, books, and activities at home with your children! They are designed to help strengthen the connection between your home and the classroom.
Problem Solving Template for creating an action plan for setting and implementing goals related to problem solving. Let Me Try>Developing an action plan>Developing your plan
Problem Solving First example of a teacher’s action plan for implementing problem solving in his/her math program. Let Me Try>Developing an action plan>Developing your plan
Problem Solving Second example of a teacher’s action plan for implementing problem solving in his/her math program. Let Me Try>Developing an action plan>Developing your plan
Problem Solving Poster cards for reminding students of different problem-solving strategies. Let Me Try>Your role in promoting problem solving>Teach problem-solving strategies
Problem Solving Transcript of testimonials from teachers who have integrated problem solving into their math programs. Let Me Try>Developing an action plan
