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Jo Boaler: ‘We need a revolution in how we think about maths’

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Jo Boaler: ‘We need a revolution in how we think about maths’

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Jo Boaler, professor of mathematics education at Stanford University, has big ambitions - she's on a mission to transform maths education.

She ends each email to the 60,000 people signed up to her www.youcubed.org website with "Vive la révolution" and it's not just a rhetorical flourish.

"It is revolutionary to change maths in this way," she says. "It is going to take a revolution for people to think [differently] about what the subject is."

She begins by pointing out that many children think that maths is a subject in which all the answers are right or wrong. And they are wrong. The misapprehension is understandable, though. Professor Boaler points out that the version of maths taught in many school classrooms is "narrow and impoverished", focused on coming up with the right answers quickly.

In her book Mathematical Mindsets, she argues that there should be less testing in maths, less worrying about failure, more use of visual representations and "manipulatives" (items such as blocks and cubes that students can handle) and more emphasis on group work to solve complex problems.

"We need to free our young people from the crippling idea that they must not fail, that they cannot mess up, that only some students can be good at maths and that success should be easy and not involve effort," her book concludes. She says that at its core, maths is about not simply getting a string of right answers but rather reasoning - that is, how you get to those answers.

Of course, there are right answers. And wrong ones. "You want kids to get things right of course, and you don't want them making mistakes all the time," Professor Boaler says. "But kids will make a mistake and think 'I'm not a maths person, I can't do this'. So if you tell them that when you are making mistakes and struggling this is when you are learning, this is a transformative message for them. They are allowed to make mistakes. It doesn't mean that's their goal."

Mathematical Mindsets has a foreword from Professor Boaler's Stanford colleague Carol Dweck, the psychologist who has inspired many teachers with her work on the importance of a "growth mindset" and encouraging children to believe that talent is not something you are born with but something you can work towards.

But is there a danger that the emphasis on growth mindsets means that rather than children being told they are just bad at maths, they are now told they have the wrong mindset? It's not the children who need to change, Professor Boaler replies: it's the teachers.

"You cannot just give a mindset intervention to kids and say 'OK you have a growth mindset now' and then give them the same teaching," she says. "It is not saying children need a different mindset. It's saying let's give children a different mindset by teaching in a different way."

Professor Boaler began teaching at Haverstock School in North London before moving into academia with a master's and PhD in mathematics education at King's College London. Her supervisor was Paul Black, renowned as the co-author with Dylan Wiliam of Inside the Black Box, the influential book on Assessment for Learning.

She became a professor at Stanford and after a three-year stint back in the UK as the Marie Curie professor of mathematics education at the University of Sussex, she returned to California.
Banning times tables
Professor Boaler's ideas are not without their critics. On a visit to England at the beginning of term, she said that in an ideal world she would ban times tables tests. It's not that times tables aren't worth learning, but the greater goal of maths education is more important, she argues. Therefore, perhaps we should seriously think about whether it is worth risking some children being turned off the subject, aged 8, for the sake of ensuring they can answer 7x6 under pressure, without hesitation.

The reaction to her comments was swift. Charlie Stripp, director of the National Centre for Excellence in the Teaching of Mathematics, said: "It is not the learning of times tables that is causing anxiety but rather it is lack of times table knowledge. It should be an educational entitlement that all children are helped to learn their times tables."

Professor Boaler emphasises that her views come from decades of academic work. "These are not just ideas," she says. "We have research data. We're in a time when other educators outside maths are pushing for more problem-solving, more applied thinking, less testing.

"I'm not the only one doing this: there are hundreds of people who are doing what I'm doing. I've attracted attention because I'm able to turn research into practice, to say, 'What is the implication of this for the classroom?' But I am just standing on the shoulders of others who have been computing the evidence for years upon years.

"It's a good time to move forward."
Jo Boaler is speaking at Bett 2016 on 21 January at 2.15pm This article first appeared in the 4 December edition of TES. Read more on your tablet or phone, or by downloading the TES Reader app for Android or iOS. Or pick it up at all good newsagents.

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Jo Boaler: 'We need a revolution in how we think about maths'

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Jo Boaler, professor of mathematics education at Stanford University, has big ambitions - she's on a mission to transform maths education. She ends each email to the 60,000 people signed up to her www.youcubed.org website with "Vive la révolution" and it's not just a rhetorical flourish.

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Educators debate whether some math basics are 'a dead issue in the year 2016'

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Educators debate whether some math basics are 'a dead issue in the year 2016'

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When it comes to improving the math skills of Ontario students, the $60 million recently pledged by the province will likely just make matters worse, suggests University of Manitoba mathematics professor Robert Craigen.

"Guess what, you've just funded the ideas that are already causing the problems," he said.

In fact, says Craigen, when you look at the spending on math education per pupil across Canada, there's an inverse relationship - provinces spending the most are getting the worst results.

​ The problem, says Craigen and other critics of the math curriculum being used across the country, are teaching methods that de-emphasize learning the basic skills. Multiplication tables, long division, adding and subtracting big numbers and computing fractions - these fundamentals, critics say, are being minimized in the classrooms.

"There are even parents we are hearing from in Ontario saying 'I taught my child how to add down columns and the teacher sent a note home saying please stop teaching the old algorithms to the students because it's harming them,'" he said.

Instead, the focus has been placed on the so-called discovery or inquiry method of learning, where memorization is discouraged and the teacher is more of a guide to encourage students to try different ways to figure out problems, often using materials like blocks or drawing pictures.

"For 17 years, kids came to my class and watched me do mathematics," Al Overwijk, an Ottawa math teacher recently told CBC News. "But now I'm coming to work and watching them work and trying to help them and guide them."

Discovery method gone too far

While some measure of discovery is important in math, the use of the method in classrooms has gone too far, according to Anna Stokke, an associate professor of mathematics at the University of Winnipeg.

Stokke, who co-founded with Craigen the Western Initiative for Strengthening Education in Math, wrote a report last year for the C.D. Howe Institute titled What To Do About Canada's Declining Math Scores.

She noted that, according to one international study, Canadian students' math performance in all but two provinces declined between 2003 and 2012. And in several provinces, the percentage of students performing at the lowest levels in math significantly increased while the percentage of students performing at the highest levels significantly decreased.

The culprit, she said, was too much discovery method teaching. Her solution was to go back to the basics. She prescribed an 80/20 split - 80 per cent of the math class spent on direct learning and 20 per cent on discovery-based techniques.

"Teachers who wish to use discovery-based teaching techniques should consider doing so conservatively; the instructional balance should always favour direct instruction," she wrote.

However Marian Small, founder of the University of New Brunswick's Mathematics Education Centre, and an advocate of the discovery method, says if math scores are down, it's in part due to teachers who have not fully made the transition to the discovery method.

But it's also a reflection of the North American "I don't have time for anything, I don't want to be bored," culture, she says.

"Kids are less patient to do things that they used to do and that has nothing to do with curriculum. That has to do with how people are," says Small.

'Get out a calculator'

Small says that, while she too believes in teaching the basics, it's how children learn those basics that needs to be rethought.

"There used to be one way to do it and now we think there's more than one way," she said. "I think we have to decide what are the basics in the year 2016 as opposed to what were the basics a bunch of years ago."

Small, who prefers "problem-based" over the term discovery-based, says the method gives kids a problem and opportunities to figure it out for themselves before someone tells them how to do it.

"Whether a kid can do that long multiplication, I think that's a dead issue in the year 2016," she says.

"I do not think we need a lot of people who can multiply three, two-digit numbers or two, three-digit numbers because if you're going to do that, you get out a calculator."​​

But Craigen rejects Small's assertion.

That sort of skill "is an important benchmark in the development of an overall conception of how numbers and arithmetic work, in preparation for algebra, which is the gateway in high school to the higher mathematical disciplines they will see in college," he says.

"It's long been settled that the establishment of basic facts, in memory, and the development of automatic skills for the most basic tasks is really of fundamental importance in developing long-term skills."​

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Who needs long division? The debate over teaching math basics | CBC News

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When it comes to improving the math skills of Ontario students, the $60 million recently pledged by the province will likely just make matters worse, suggests University of Manitoba mathematics professor Robert Craigen. "Guess what, you've just funded the ideas that are already causing the problems," he said.

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Elementary school students will get 1 hour of mandatory math a day in September: province

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Elementary school students will get 1 hour of mandatory math a day in September: province

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The Ontario government is promising $60 million toward improving math education for elementary school students, a move that includes a new mandatory minimum of an hour of math class each day.

Education Minister Liz Sandals announced the plan for a "renewed math strategy" at a downtown Toronto elementary school Monday morning.

The 60-minute math minimum will apply to students in Grades 1 through to Grade 8 and is one of several new initiatives the province is promising.

Others include having up to three math lead teachers at all elementary schools, math support for students in Grade 6 through Grade 9 outside the school day and more opportunities for teachers to improve their math teaching skills through a dedicated math P.A. day.

Sandals says the renewed strategy is based on the latest research available and the province's previous efforts to improve literacy.

"While Ontario's math results are quite good compared to other jurisdictions, we know that we have more to do," said Sandals in a news release following the announcement.

Mathematics professor and educator John Mighton hopes that the increased funding and time in the classroom doesn't just go towards the same old teaching methods.

The founder of the international numeracy program JUMP Math and adjunct professor at the University of Toronto says newer, innovative teaching methods based on emerging research will help students improve at math.

"Districts, school boards and ministries have to start turning to that evidence and making sure what we're doing is aligned with very solid research," Mighton said in an interview.

"There's been a push towards discovery, to have kids figure things out and discover things, and that's a very positive thing. But the research is suggesting you need to balance that with a lot more guidance, practice."

In a 2012 study, Ontario students performed at the Canadian average in math, but EQAO testing scores for Grade 3 students and Grade 6 students went down four and seven per cent between testings in 2009 and 2013.

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Elementary school students will get 1 hour of mandatory math a day in September | CBC News

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The Ontario government is promising $60 million toward improving math education for elementary school students, a move that includes a new mandatory minimum of an hour of math class each day. Education Minister Liz Sandals announced the plan for a "renewed math strategy" at a downtown Toronto elementary school Monday morning.

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Decline of Canadian students’ math skills the fault of ‘discovery learning’: C.D. Howe Institute

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Decline of Canadian students’ math skills the fault of ‘discovery learning’: C.D. Howe Institute

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Canadian students' math skills have been on a decade-long decline because rote learning was replaced by discovery-based methods that promoted multiple strategies and estimations, according to a new report that calls for a return to tradition.

"You know what's the worst kind of instruction? The kind of instruction that makes kids feel stupid. And that's what a lot of that discovery stuff does; their working memory gets overloaded, they're confused. That's bad instruction," said Anna Stokke, an associate professor in the University of Winnipeg's department of mathematics and statistics, who wrote the C.D. Howe Institute report.

The report draws on results from national and provincial tests as well as an OECD assessment performed every three years in more than 60 countries that measures how well 15-year-olds can apply skills in reading, math and science to real life situations.

Canada fell out of the top 10 countries for math in 2012. The report notes that all but two Canadian provinces also saw "statistically significant" declines in their math scores, compared with their 2003 performances. Alberta, once a math leader, and Manitoba saw the steepest drops, while only Quebec held its ground. Saskatchewan declined slightly but not enough to be considered significant. Beyond that, the pool of students at the lowest achievement levels grew while those at the very top shrank.

'You know what's the worst kind of instruction? The kind of instruction that makes kids feel stupid. And that's what a lot of that discovery stuff does'

"You can look at it in terms of where do we rank et cetera, et cetera, but when we see that our students are doing worse, relative to 10 years ago, there's no excuse for that," said Stokke. She pointed out that even Sweden, whose 2012 drop in all subjects was so severe the OECD has warned the country must reform its school system, did not see as big a decline in its math scores as did Manitoba and Alberta.

The report puts a good deal of the blame on discovery or experimental learning approaches that encourage students to explore different ways to solve math problems instead of using a single standard algorithm and often promote concrete tools such as drawing pictures, or using blocks or tiles to represent math concepts. The idea is students will gain a deeper understanding of math and be better equipped to apply it to a variety of situations.

What really happens, though, says the report, is students' working memories get overwhelmed if they don't know their times tables and can't quickly put a standard algorithm to work to solve a more complex problem, both features of what's known as "direct instruction." Key operations, such as addition and subtraction of fractions, are overly delayed until the middle school years, just as students need that facility to tackle algebra.

'We all feel the urgency to correct the matter soon, before too many children are lost'

Such concepts should be introduced earlier, says the report. And while it stops short of throwing discovery learning out completely, it says the curriculum balance should be tilted in favour of direct instructional methods, recommending an 80/20 split as a rule of thumb.

"I'm fine with a bit of discovery learning ... [but] you want to make sure that you're getting the balance right, that most of the balance is going towards instructional techniques that are actually going to work," said Stokke.

A petition calling for a back-to-basics math curriculum in Alberta, started by Edmonton-area mother Nhung Tran-Davies, has gathered more than 17,000 signatures. It was presented to the previous Conservative government last year, with some limited success, but Ms. Tran-Davies hopes she won't have to start all over again with the province's new NDP government.

To that end, she is holding a forum for the public and government officials this Friday evening in Edmonton to talk about how to advance reforms and hopes new education minister David Eggen will attend.

"We all feel the urgency to correct the matter soon, before too many children are lost," she said.

Stokke's report also suggests elementary school teachers in training should be required to take two semester-long courses at university in math with the aim of deepening their grasp of the concepts they will be teaching. Provinces should also consider making elementary teachers-to-be write a test in that same content before they're licensed.

Those are good ideas, said Ann Kajander, an associate professor in math education at Thunder Bay, Ont.'s Lakehead University. But she strongly criticized the research basis for recommendations against discovery-based learning techniques.

"How can we have a report that makes significant recommendations in mathematics education when absolutely none of the major mathematics education journals ... are included in the reference list?" she said. "As a researcher, that's absurd."

The report however does cite published research in science, psychology and neuroscience.

National Post

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Decline of Canadian students' math skills the fault of 'discovery learning': C.D. Howe Institute

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Canadian students' math skills have been on a decade-long decline because rote learning was replaced by discovery-based methods that promoted multiple strategies and estimations, according to a new report that calls for a return to tradition. "You know what's the worst kind of instruction? The kind of instruction that makes kids feel stupid.

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Robbie,Nikolai and Ada

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Painting the classroom 613
By:Adam,Nikholai and Robbie
The dimensions
wall a= 8.20m wall b door= 2.11x1.00=2.11 25.5-2.11=23.39m squared
wall b= 8.50m wall d windows= 1.10+2.36=3.46x2=6.92m
squared 25.5-6.92=18.58m squared
wall c= 8.20m
wall d= 8.50m the area of wall a and c=25.86m squared
23.39+18.58=41.97 25.86x2=51.72 51.72+41.97=93.69m squared
height=2.73m
length=8.50m
width=8.20m Adam
The amount of paint needed
We require approximately 21 liters or 6 gallons of paint. We need 6 1 gallon cans of paint to paint the entire classroom.
The details of the paint
paint colour= Blackberry Wine
nontoxic(No VOC)
shine=eggshell
BEHR premium plus 1-gallon paint

Final cost
Each 1-gallon can will equal $25.96
25.96x6=155.76 for 6 gallons of paint
155.76x12=$1869.12 for all the grade 6 classrooms
6x12=72 we will need to get 72 cans of paint to paint all the grade 6 classrooms (approximately)
Questions?
Anything else you want to know about this paint?

eggshell shine
Conclusion
Nikholai
Robbie
Robbie
Nikholai

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Painting the classroom 613By:Adam,Nikholai and Robbie The dimensionswall a= 8.20m wall b door= 2.11x1.00=2.11 25.5-2.11=23.39m squared wall b= 8.50m wall d windows= 1.10+2.36=3.46x2=6.92msquared 25.5-6.92=18.58m squaredwall c= 8.20m wall d= 8.50m the area of wall a and c=25.86m squared 23.39+18.58=41.97 25.86x2=51.72 51.72+41.97=93.69m squaredheight=2.73mlength=8.50mwidth=8.20m AdamThe amount of paint neededWe require approximately 21 liters or 6 gallons of paint.

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State University of New York at Oswego

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The Journal of Authentic Learning (ISSN 1558-7320) is a peer-reviewed, online journal, published by the Department of Curriculum and Instruction at the State University of New York at Oswego, which provides a forum for dissemination of original ideas in research, practice, or theory of authentic learning and teaching.

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Authentic Learning: Perspectives from Contemporary Educators

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Authentic Learning: Perspectives from Contemporary Educators

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The Four Characteristics of Authentic Learning

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The Four Characteristics of Authentic Learning

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Educational Research Newsletter and Webinars

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Authentic learning is a relatively new term that describes learning through applying knowledge in real-life contexts and situations. In a recent article in the Journal of Authentic Learning, Audrey Rule of the State University of New York (SUNY) at Oswego tries to answer the question she is most often asked: What do you mean by authentic learning?

Four components are repeatedly found in authentic learning, reports Rule, who did a content analysis of 45 journal articles that faculty members in the School of Education at SUNY-Oswego submitted as examples of authentic learning in their disciplines.

"Although the term authentic learning is broad and has not been applied to a specific instructional model, these four components are found repeatedly, suggesting that they are an integral part of authentic learning experiences," Rule writes.

The four themes supporting authentic learning are:

1. An activity that involves real-world problems and that mimics the work of professionals; the activity involves presentation of findings to audiences beyond the classroom.
2. Use of open-ended inquiry, thinking skills and metacognition.
3. Students engage in discourse and social learning in a community of learners.
4. Students direct their own learning in project work.

Real-world problems

One component of authentic learning is that it targets a real problem and that students' engagement holds the possibility of having an impact outside the classroom, Rule says. "This audience beyond the classroom changes the problem from an 'exercise' to something more important, allowing students to become emotional stakeholders in the problem," she writes.

In science, for example, this may be accomplished when students collect water quality data from local streams. Model lessons that address authentic learning in social studies could include students' analysis of primary documents related to the Pledge of Allegiance. In developing literacy, reading resources could be connected to real life with bus schedules, maps, diaries and interviews with people.

Inquiry and thinking skills

For authentic learning, students must exercise higher levels of thinking, according to this analysis. For example, science teaching should reflect the scientific process of knowledge construction. Learning in mathematics should occur through discovery, inquiry and induction. Instead of math problems that require that students merely apply a known procedure, authentic mathematical tasks require solvers to use different representations in their solutions and to work with realistic and complex mathematical data. In art education, students can use thinking skills to deconstruct visual and textual information in media ads.

Discourse in a community of learners

A community of learners can be a group of learners working together to unravel a problem or refer to the community setting in which the project is based. Science investigations should link students to scientists through data sharing, critiquing, and direct communication. Multiculturalism can be brought to the classroom by exploring numbers in other languages, symbols of ancient societies and games of skill and chance from around the world.

Student-directed learning

For authentic learning, problems must have a personal frame of reference and be open-ended, according to this article. "This cannot happen without student choice in defining the problem and selecting the path of its solution," Rule writes. In the field of health promotion and wellness, for example, educators provide information so that individuals may make informed choices.

Choice also occurs when students make their own interpretations of literature and art. "Research related to effective instructional practice emphasizes the need for greater personalization and individualization of instruction because learning is an individual experience," the article states. Instruction can be personalized by allowing the learner to choose from the rich variety of pathways.

Apprenticeships also provide important opportunities for students to interact with the wider community and reflect upon their experiences, the article states. The author invites readers to examine their reading and learning situations to identify more ways that authentic learning is implemented.

" Editorial: The Components of Authentic Learning" by Audrey Rule, Journal of Authentic Learning Volume 3, Number 1, August 2006, Pp. 1-10.
Published in ERN January 2007 Volume 20 Number 1

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The four characteristics of 'authentic learning'

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Authentic learning is a relatively new term that describes learning through applying knowledge in real-life contexts and situations. In a recent article in the Journal of Authentic Learning, Audrey Rule of the State University of New York (SUNY) at Oswego tries to answer the question she is most often asked: What do you mean by authentic learning?

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Copyright 2018, Jon Mueller. Professor of Psychology, North Central College, Naperville, IL. Comments, questions or suggestions about this website should be sent to the author, Jon Mueller, at jfmueller@noctrl.edu.

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examples: authentic tasks: middle school: mathematics (Authentic Assessment Toolbox)

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Copyright 2018, Jon Mueller. Professor of Psychology, North Central College, Naperville, IL. Comments, questions or suggestions about this website should be sent to the author, Jon Mueller, at jfmueller@noctrl.edu.

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Victoria State Government

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The main point of an authentic task is to encourage students to find ways of solving rich mathematical tasks themselves. Different ways of solving a task reveal qualitatively different knowledge and skill sets, and these can be evaluated in terms of the Learning and Assessment Framework for Multiplicative Thinking (LAF)

To use the authentic tasks with your students:

How the authentic tasks were developed

Authentic tasks in the Scaffolding Numeracy in the Middle Years (SNMY) project were developed at a school level by teachers and students.

Teachers and students researched possible problems, community issues or tasks that needed to be addressed and chose one of these to develop as an authentic task. The tasks chosen gave students opportunities to demonstrate many of the key ideas and strategies identified in the LAF.

How to define an authentic task

In general, an authentic task is one which:

is purposeful and engaging

models how people solve real problems in work and/or communities

puts knowledge to work

potentially demonstrates what students know and can do

supports multiple representations and solution strategies

offers opportunities for meaningful learning and higher order cognitive thinking

results in some product, presentation or outcome as a result of the deliberations of the group and/or individual.

Purposeful and engaging
Students, teachers and the community should see some real value in working on the task - that is, they want to solve it and see that it is worth the time spent on it.
Models how people solve real problems
The task should involve meetings or other activities that involve negotiation, planning, action, reporting, evaluating and exploring of alternatives.
Puts knowledge to work
The task should draw on a range of knowledge, skills and strategies from different areas of the mathematics and school curriculum more generally as well as what is known about the local environment.
Demonstrates what students know and can do
All learners should be enabled to make a start or contribute in some way. However the task should also challenge most learners at some level.
Supports multiple representations and solution strategies
For example, diagrams, stories, graphs, tables, symbolic expressions, written arguments, explanations and/or justifications can demonstrate multiple options.
Offers opportunities for meaningful learning and higher order cognitive thinking
For example, the task should allow for:

'aha' moments

the development of an extended range of problem solving strategies and/or skills

the construction and evaluation of conjectures, rules and/or generalisations.

Results in some product, presentation or outcome
Ultimately, there should be something tangible that can be 'pointed to' as a result of the deliberations of the group and/or individual.

Guidelines for development

Teachers developing authentic tasks for their students should:

research the problem

discuss the ideas

review and share

document

implement

refine and modify.

Research the problem
At the school level, research possible problems, community issues and tasks. Involve students, parents and community leaders.
Discuss the ideas
Discuss task ideas, brainstorm possibilities for demonstrating the mathematics identified at your level of the framework. Specify and document how this knowledge might be demonstrated.
Review and share
Review task ideas and share possibilities. List the specific mathematical ideas and strategies that might be demonstrated at each zone of the Learning Assessment Framework in the process of doing the task. Decide what evidence of student learning will be collected.
Document
Document the task and consider scoring rubrics to support classroom implementation and the subsequent evaluation of students' work.
Implement
Implement the task to evaluate the extent to which student numeracy learning has been impacted. During the implementation of the task, note as many observations as possible (yellow 'stickies' are a good way of doing this). Once the task has been completed collect evidence of student work.
Refine and modify
Once student work has been assessed, bring work samples and discuss. Brainstorm modifications to task and/or rubrics as necessary. Refine the task and/or rubrics on the basis of the discussion and feedback.

General examples

The following descriptions are general examples of authentic tasks. Authentic tasks that specifically give students opportunities to demonstrate many of the key ideas and strategies identified in the LAF can be downloaded below.
Developing an Emergency Plan
What is the best emergency plan for the school and the local community and how do we know that this is the best plan? This might involve consideration of the issues and options involved (eg, deciding which is the best place to assemble and why), planning, communicating, evaluating if the plan works, and preparing a report with diagrams etc.
After School Care
A community wanted to determine the viability of setting up an after school care program. To attract a government subsidy to support the scheme, they needed to develop a business plan. Decide what is needed, consult with relevant people, collect and analyse relevant data and prepare a draft business plan.
Rubbish problem
A school identified both a health and a financial problem with the rubbish removal - too much rubbish was being generated, not all of it was placed in bins and sometimes it could not be collected because of weather conditions. They decided to reduce the amount of rubbish by recycling as much as they could. What sort of containers would be needed and would this initial expense be worth it in the longer-term?
Football trip
A community wanted to send a junior football team to compete in a regional competition for a week. What might this involve and how could it be supported? Devise a fund-raising plan to support this activity.
Council submission
A local developer wanted to build units on a vacant block of land next to the school. The block provided a safe passage for many of the native animals that travel regularly between the creek and the adjacent National Park. To convince the Council that the development should not go ahead, it has been suggested that the school needs to prepare an Environmental Impact Report.
School transport
The subsidy for school buses has been reduced. How can bus routes, timetables etc be organised to ensure that current service levels are maintained?

Download sample SNMY tasks

The following authentic tasks were developed at a school level by teachers and students as part of the Scaffolding Numeracy in the Middle Years (SNMY) project:

More information

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Scaffolding Numeracy in the Middle Years: Authentic Tasks

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The main point of an authentic task is to encourage students to find ways of solving rich mathematical tasks themselves. Different ways of solving a task reveal qualitatively different knowledge and skill sets, and these can be evaluated in terms of the Learning and Assessment Framework for Multiplicative Thinking (LAF) To use the authentic tasks with your students: Authentic tasks in the Scaffolding Numeracy in the Middle Years (SNMY) project were developed at a school level by teachers and students.