Mathematics_Introduction

Mathematics

Introduction

Mathematics is integral to every aspect of daily life. Skills can be used to solve problems related to time, sports, travel, money management, science, and art, to name a few. Mathematics is part of the story of human history and is particularly relevant to the British Columbian story. First Peoples in British Columbia, like Indigenous people around the world, used and continue to use mathematical knowledge and competencies to make sense of the world around them.

Mathematical values and habits of mind go beyond numbers and symbols: they help us connect, create, communicate, visualize, reason, and solve. Using mathematical thinking allows us to analyze novel and complex problems from a variety of perspectives, consider possible solutions, and evaluate the effectiveness of solutions. When developed early in life, these habits of mind generate confidence in our ability to solve everyday problems without doubt or fear of math.

Observing, learning, and engaging in mathematical thinking empowers us to make sense of our world. Exploring the logic of mathematics through puzzles and games can foster a constructive mathematical disposition and result in a self-motivated and confident learner with a unique mathematical perspective. Whether students choose to pursue deeper or broader study in mathematics, the new curriculum design ensures that they are able to pursue their individual interests and passions.

Features of the Mathematics curriculum

There is an eager expectation that the Mathematics curriculum will bridge the gap between students’ mathematics knowledge and their ability to apply it in a broad range of situations that they will encounter in everyday life. This connection is facilitated through fewer learning standards, a renewed focus on flexible teaching and learning, and an emphasis on building a strong foundation of mathematical understanding and skills.

Fewer learning standards

The curriculum has fewer learning standards, allowing teachers and students to spend more time on foundational skills and applying them to real-life situations. The curriculum is intentionally focused on “hands-on” experiential learning, using foundational skills to provide students with the opportunity to encounter math in a wide variety of experiences in everyday life. The goal of developing well-educated citizens is central to this feature of the curriculum.

Flexible teaching and learning

A renewed focus on flexible teaching and learning promotes confidence in teachers to choose the strategies, resources, and application best suited to the needs of students in the local setting (e.g., connecting mathematics to the local community and building a house for Habitat for Humanity). Mathematics should be viewed as an interdisciplinary set of skills.

A strong foundation of mathematical understanding and skills

As part of building a strong foundation of mathematical understanding and skills for every student, explicit financial components have been added to the curriculum, starting in Kindergarten. In addition, the Grades 10–12 draft curriculum ensures that, regardless of the pathway chosen by a student, there will be a common experience in Mathematics that includes financial literacy, mathematical reasoning, and probability/statistics.

Design of the Mathematics curriculum

The Mathematics curriculum has the same format as all other areas of learning. Four curriculum elements — the Big Ideas, Curricular Competencies, Content, and Elaborations — link the knowing, doing, and understanding of mathematics learning. Connecting mathematics knowledge with a hands-on approach to doing mathematics will lead to a deep understanding of mathematics concepts. Learn more information about this model.

Big Ideas

The Big Ideas of the Mathematics curriculum reveal the progression of related skills and concepts. For each area of mathematics — number, patterns and relations, spatial sense, and statistics and probability — important concepts are introduced in Kindergarten and evolve in both sophistication and degree of connection to the lives of students throughout the curriculum. The Big Ideas represent what students are expected to understand as a result of their learning.

To ensure a strong mathematical understanding, the Big Ideas are based on the powerful overriding themes of Mathematics that reflect the learning standards of each grade.

The five overriding themes are:

  1.  Number represents and describes quantity.
  2. Development of computational fluency requires a strong sense of number.
  3. We use patterns to represent identified regularities and to form generalizations.
  4. We can describe, measure, and compare spatial relationships.
  5. Analyzing data and chance enables us to compare and interpret.

The chart below shows the progression of learning from year to year.

Grade

Number:
Number represents and describes quantity.

Computational Fluency:
Development of computational fluency requires a strong sense of number.

Patterning:
We use patterns
to represent
identified regularities and to form generalizations.

Geometry and Measurement:
We can describe, measure, and compare spatial relationships.

Data and Probability:
Analyzing data and chance enables us to compare and interpret.

K

Numbers represent quantities that can be decomposed into smaller parts.

One-to-one correspondence and a sense of 5 and 10 are essential for fluency with numbers.

Repeating elements in patterns can be identified.

Objects have attributes that can be described, measured, and compared.

Familiar events can be described as likely or unlikely and compared.

1

Numbers to 20 represent quantities that can be decomposed into 10s and 1s.

Addition and subtraction with numbers to 10 can be modelled concretely, pictorially, and symbolically to develop computational fluency.

Repeating elements in patterns can be identified.

Objects and shapes have attributes that can be described, measured, and compared.

Concrete graphs help us to compare and interpret
data and show one-to-one correspondence.

2

Numbers to 100 represent quantities that can be decomposed into 10s and 1s.

Development of computational fluency in addition and subtraction with numbers to 100 requires an understanding of place value.

The regular change in increasing patterns can be identified and used to make generalizations.

Objects and shapes have attributes that can be described, measured, and compared.

Concrete items can be represented, compared, and interpreted pictorially in graphs.

3

Fractions are a type of number that can represent quantities.

Development of computational fluency in addition, subtraction, multiplication, and division of whole numbers requires flexible decomposing and composing. 

Regular increases and decreases in patterns can be identified and used to make generalizations.

Standard units are used to describe, measure, and compare attributes of objects’ shapes.

The likelihood of possible outcomes can be examined, compared, and interpreted.

4

Fractions and decimals are types of numbers that can represent quantities.

Development of computational fluency and multiplicative thinking requires analysis of patterns and relations in multiplication and division.

Regular changes in patterns can be identified and represented using tools and tables.

Polygons are closed shapes with similar attributes that can be described, measured, and compared.

Analyzing and interpreting experiments in data probability develops an understanding of chance.

5

Numbers describe quantities that can be represented by equivalent fractions.

Computational fluency and flexibility with numbers extend to operations with larger (multi-digit) numbers.

Identified regularities in number patterns can be expressed in tables.

Closed shapes have area and perimeter that can be described, measured, and compared.

Data represented in graphs can be used to show many-to-one correspondence.

6

Mixed numbers and decimal numbers represent quantities that can be decomposed into parts and wholes.

Computational fluency and flexibility with numbers extend to operations with whole numbers and decimals.

Linear relations can be identified and represented using expressions with variables and line graphs and can be used to form generalizations.

Properties of objects and shapes can be described, measured, and compared using volume, area, perimeter, and angles.

Data from the results of an experiment can be used to predict the theoretical probability of an event and to compare and interpret.

7

Decimals, fractions, and percents are used to represent and describe parts and wholes of numbers.

Computational fluency and flexibility with numbers extend to operations with integers and decimals.

Linear relations can be represented in many connected ways to identify regularities and make generalizations.

The constant ratio between the circumference and diameter of circles can be used to describe, measure, and compare spatial relationships.

Data from circle graphs can be used to illustrate proportion and to compare and interpret.

8

Number represents, describes, and compares the quantities of ratios, rates, and percents.

Computational fluency and flexibility extend to operations with fractions.

Discrete linear relationships can be represented in many connected ways and used to identify and make generalizations.

The relationship between surface area and volume of 3D objects can be used to describe, measure, and compare spatial relationships.

Analyzing data by determining averages is one way to make sense of large data sets and enables us to compare and interpret.

9

The principles and processes underlying operations with numbers apply equally to algebraic situations and can be described and analyzed.

Computational fluency and flexibility with numbers extend to operations with rational numbers.

Continuous linear relationships can be identified and represented in many connected ways to identify regularities and make generalizations.

Similar shapes have proportional relationships that can be described, measured, and compared.

Analyzing the validity, reliability, and representation of data enables us to compare
and interpret.

Curricular Competencies

The Core Competencies — Thinking, Communication, and Personal and Social — are embedded in the Curricular Competencies. The Curricular Competencies introduced in Kindergarten have been expanded based on a developmental continuum throughout the grades focused on what students can do with mathematics.

Content

The Content is concept-based and reflects what students should know. It identifies the concepts or topics that students will learn about at each grade level. The Content acts as both a supporting structure intended to assist students in demonstrating the Curricular Competencies and a foundational element leading students to the Big Ideas.

Elaborations

There are Elaborations (included as hyperlinks) for many of the learning standards in the Mathematics curriculum. The Elaborations take the form of explanations, definitions, and clarifications. They provide additional information and support for both teachers and students and can serve as potential places to begin teaching and learning. Examples of Elaborations for a progression of Content learning statements are shown below.

 

K

5

8

Content

number concepts to 10

number concepts to 1 000 000

perfect squares and cubes

Elaborations

  • number concepts:
    • counting:
      • one-to-one correspondence
      • conservation
      • cardinality
      • stable order counting
      • sequencing 1 – 10
      • linking sets to numerals
      • subitizing
    • counting collections using local materials
    • counting to 10 in more than one language, including the local First Peoples language or languages

 

  • number concepts:
    • counting:
      • multiples
      • flexible counting strategies
      • whole number benchmarks
    • numbers to 1 000 000 can be arranged and recognized
      • comparing and ordering numbers
      • estimating large quantities
    • place value
      • 100 000s, 10 000s, 1000s, 100s, 10s and 1s
      • understand the relationship of digit places and their valueto 1 000 000
      • First Peoples use unique counting systems (e.g., Tsimshian use of three counting systems, for animals, people and things; Tlingit counting for the naming of numbers:
        10 = two hands, 20 = one person)
  • Perfect squares and cubes:
    • using colour tiles, pictures, or multi-link cubes
    • building the number or using prime factorization

 

Important considerations

Inquiry in Mathematics

The Mathematics curriculum continues to support the application of foundational math skills to problem solving. It is important for students to be able to approach problem solving with confidence. A problem-solving model provides students with the necessary skills to read a problem, choose from a variety of appropriate strategies, apply a strategy to solve the problem, and then reflect on the efficiency and accuracy of the strategy to explain the answer.

First Peoples perspectives

The Ministry of Education is dedicated to ensuring that the cultures and contributions of First Peoples in British Columbia are reflected in all provincial curricula. The First Peoples Principles of Learning consider important contexts and aspects of teaching and learning, such as the connection to place, the power of story, respect for Elders’ knowledge, and the need for a strong identity of self. It is important for teachers to use these principles to guide the incorporation of First Peoples mathematical content and knowledge in meaningful ways.

Local and traditional First Peoples knowledge contributes to our understanding of place. First Peoples knowledge is holistic and is embodied in experiential ways of learning, including the oral tradition. As First Peoples communities are diverse in terms of language, culture, and available resources, each community will have its own unique protocol for sharing local knowledge and expertise with the school system. For examples of teaching mathematics in a First Peoples context, see the First Nations Education Steering Committee website: http://www.fnesc.ca/resources/math-first-peoples/.

Mathematical habits of mind

Extensive research indicates that for students to develop mathematical habits of mind they must encounter and interact in intentional learning settings. Classroom design combined with active participation strategies will enhance student learning, increase achievement, and factor in the development of the well-educated citizen.

Students who have developed mathematics habits of mind exhibit expertise in:

  • persevering and using mathematics to solve problems in everyday life
  • recognizing there are multiple ways to solve a problem
  • demonstrating respect for diversity in approaches to solving problems
  • choosing and using appropriate strategies and tools
  • pursuing accuracy in problem solving1

 


 

Last updated: July 19, 2016