Module 5: Numeracy in the Middle Years

Chapter 1 Numeracy Defined

‘All teachers are teachers of numeracy.'

Numeracy is the study of numbers, measurement, time, chance and probability, using fractions, and using decimals (NDHSglasgow, 2014). Students need a solid grounding in mathematical concepts and procedures to be numerate (Department of Education and Early Childhood Development, 2009). This gives them “the ability to effectively use the mathematics required to meet the general demands of life at home and at work, and for participation in community and civic life” (National Literacy and Numeracy Week, 2008). Numeracy is used and studied across the curriculum in every subject, thus it is the responsibility of all teachers to teach their students numeracy skills to interpret information or to solve practical problems, and in making appropriate choices of what strategies they can use. Teachers and schooling are preparation for people’s lives after school and “regardless of their future careers, all young people need high levels of numeracy in order to participate effectively in Australian society and to be in control of their life and wellbeing” (Department of Education and Early Childhood Development, 2009).

Chapter 2 Numeracy and the Australian Curriculum

Notes on each of six numeracy elements from descriptions in the ACARA (2016) ‘Numeracy, Key Ideas’ web page:

1.       Estimating and calculating with whole numbers

-          understand and use numbers in context

-          estimate and calculate

-          use money.

2.       Recognising and using patterns and relationships

-          Ability to identify trends and predict patterns

-          Solving problems in context using this skill

3.       Using fractions, decimals, percentages, ratios and rates

-          Understanding of the meaning of fractions and decimals, and how they can be represented as percentages, ratios and rates

-          Understanding of real-life application of this knowledge

-          Ability to interpret proportional reasoning in context

-          Ability to apply proportional reasoning in context

4.       Using spatial reasoning

-          Making sense of the space around them

-          Visualise 2D shapes and 3D objects to solve problems in authentic contexts

-          Interpret maps and diagrams to solve problems in authentic contexts

5.       Interpreting statistical information

-          Familiarity with the way statistical information is represented

-          Interpret data displays to solve problems in authentic contexts

-          Interpret chance events to solve problems in authentic contexts

6.       Using measurement

-          Learn about measurement of length, area, volume, capacity, time and mass

-          estimate and measure with metric units

-          operate with clocks, calendars and timetables

Some ways in which I can develop numeracy for Grade 5 and 6 in:

The Arts

-          For “develop skills with media technologies to shape space, time, movement and lighting within images, sounds and text” (ACAMAM063), I could have the students create a short digital sequence using camera angles such as close-ups and medium close-ups to focus on character relationships, power or mood. This addresses “Recognising and using patterns and relationships”.

Health and Physical Education

-          For “manipulate and modify elements of effort, space, time, objects and people to perform movement sequences” (ACPMP065), I could have the students work with a partners to explore pushing and pulling movements and how these can be manipulated to perform counter-balances. This addresses “Recognising and using patterns and relationships”, “Using measurement” to estimate and measure with metric units, and “Using fractions, decimals, percentages, ratios and rates” to apply proportional reasoning.

Humanities and Social Sciences

-          I could have the students create a timeline of sequenced information about Australian history and people’s lives, events, developments and phenomena. Then I could have them Interpret the information displayed to identify, describe and compare distributions, patterns and trends, and to infer relationships and make predictions for the future (ACHASSI097). This addresses “Recognising and using patterns and relationships “, and “Using measurement” through operating with clocks, calendars and timetables.

Chapter 3 Numeracy in the curriculum

*Questions from Chapter 9 Numeracy in the curriculum (Siemon, Beswick, Brady, Clark, Faragher, & Warren, 2011, pp. 181 - 199)

1. How would you describe the relationships between mathematics and numeracy?

Numeracy is the ability to be able to decide when a mathematical strategy is needed to solve a problem in a real-life context, to be able to choose the best option for calculating, and then deciding on an action based on the result. A knowledge in mathematics is a necessary foundation of a numerate person.

2. List five reasons for why good numeracy skills are important.

-          To make good decisions in financial matters for your situation.

-          In different classes in school it is necessary to develop different aspects of numeracy, such as in Geography, we need to have an understanding of geological history when learning about tectonics and geomorphology.

-          Using spatial reasoning is important for interpreting maps and diagrams, and using scales and legends, in authentic contexts (such as finding your way somewhere with a map).

-          Because in everyday life we need to make choices and use numeracy to solve practical problems, such as in cooking, or going out for dinner if you don’t want to cook. There are decisions to make in terms of money, time, temperature, location and how to get there etc. 

-          In all professions, employees are required to be numerate to different degrees for making choices and solving practical problems in the workplace.

3. What are the key behaviours that are essential to being numerate?

-          A grounding in mathematical concepts and skills from across the discipline (numerical, spatial, graphical, statistical and algebraic)

-          mathematical thinking and strategies

-          general thinking skills

-          grounded appreciation of context

4. What factors do teachers need to consider when planning for the numeracy opportunities that arise across the curriculum?

-          Time

-          Units of work they will be teaching

-          Particular cohort and individuals in class

-          If there is a whole school strategy in place

-          Different teaching strategies

-          Planning for authentic situations within lessons that will allow students to make choices of what numeracy strategy they need to use to solve problems. Planning for real-world connections

-          Working collaboratively with the other teachers so everyone’s on the same page and can develop a holistic picture of each students’ level of understanding, using this knowledge to take advantage of learning opportunities.

5. What does the term ‘critical numeracy’ mean to you?

“To be empowered through knowledge of mathematics as numerate citizens, able to apply this knowledge critically in societal and political contexts” (Victoria State Government, Department of Education and Early Childhood Development, 2009, p. 10).

When someone is proficient in numeracy they can use their knowledge to think critically and question claims which are made without proper justification. These skills and knowledge allow a person to make decisions and construct a position about an issue based on the results they get from practical problem solving.

7.       How can a teacher encourage their students to take a critical numeracy perspective across the learning areas?

By developing activities and assessments where numeracy skills are necessary, which are authentic with real life connections, and for which they must construct a position and react in response to their findings.

Chapter 4 Strategies for teaching numeracy in the middle years

Five strategies I will use for teaching numeracy to middle years students:

1.       I will inform them what the learning purpose for the lesson is so they are aware of what it is they are supposed to know to be successful

2.       I will make real-life connections with the problems they need to solve, so that they also know why they are learning

3.       I will support them to use their prior knowledge and learnings they have made in the area of numeracy, to work out problems using the same or similar numeracy strategies in different contexts

4.       I will use a lesson structure that begins with a numeracy warm-up, then break them up into smaller groups so I can differentiate my teaching to particular learning styles, then get the students to come back together to reflect on their learning

5.       I will often use collaborative and peer learning in my classes.

References

ACARA. (2016). Numeracy: Key ideas. Retrieved from http://www.australiancurriculum.edu.au/generalcapabilities/numeracy/introduction/key-ideas

Department of Education and Early Childhood Development. (2009). Numeracy in practice: teaching, learning and using mathematics. Retrieved from https://www.eduweb.vic.gov.au/edulibrary/public/publ/research/nws/numeracy_in_practice_paper_no_18.pdf

National Literacy and Numeracy Week. (2008). Critical numeracy in context [Video file]. Retrieved from http://www.nlnw.nsw.edu.au/videos08/critical_numeracy/index.html

NDHSglasgow. (2014, September 28). Numeracy Across the Curriculum [Video file]. Retrieved from https://www.youtube.com/watch?v=7Uo8t7mp9qI

Siemon, D.E., Beswick, K., Brady, K., Clark, J., Faragher, R., & Warren, E. (2011). Teaching Mathematics: Foundations to Middle Years. South Melbourne, Vic: Oxford University Press.

Victoria State Government, Department of Education and Early Childhood Development. (2009). Numeracy in practice: teaching, learning and using mathematics. Retrieved from https://www.eduweb.vic.gov.au/edulibrary/public/publ/research/nws/numeracy_in_practice_paper_no_18.pdf