Exciting news! Maths Pathway has been selected from a group of amazing applicants to be part of the first HundrED Victorian Spotlight. We’re one of 10 innovative education products that will be part of a travelling showcase around Australia, during which HundrED will share the amazing results Maths Pathway partner schools are achieving. We hope the showcase will inspire more schools to join our community, and the revolution to improve maths education for all Australian students.
Who is HundrED?
HundrED is a not-for-profit organisation from Finland that aims to ‘seek and share innovations in education’ around the world. They want to improve education by promoting educational innovations that are pedagogically sound, and that are helping drive a revolution to bring education into the 21st Century.
In the first line of their manifesto, HundrEd points out that the purpose of education is to help every child flourish, which is something we identify strongly with here at Maths Pathway. We believe that every child has the right to an amazing maths education, and that having a good maths education opens a multitude of doors for students as they move through their lives.
HundrED Spotlights
This year HundrED are running two ‘Spotlights’, one focused on Sustainability (based in California), and one in Australia to showcase the amazing education innovations that are coming out of Victoria (in partnership with Education Changemakers). You can learn more about the spotlight, and HundrED at https://hundred.org/en
HundrED announced that Maths Pathway is included in the Innovation Spotlight last night, to a packed room at the Hundred Spotlight Summit as a part of the EduChange Festival. It was a great night, and great to see some of the other awesome education innovations coming out of Victoria!
If your school doesn’t currently use Maths Pathway, but you’re looking for a way to deliver truly differentiated mathematics education to your students from a provider with proven impact, check out our 2018 Impact Report to see data that shows the incredible outcomes our partner schools are achieving. Alternatively, book a chat or demo through our website so that we can show you what we have to offer! mathspathway.com
Our Learning team gets together regularly to deep dive into the pedagogy behind a particular model, problem, or interesting question that has been presented to the team. This might come from new research, teacher feedback, or just out of interest! In these blogs we’ll be summarising the topics that come up and giving you an insight into how our learning team makes decisions and the kinds of problems they work with on a daily basis!
A little while ago our Learning team sat down for one of their regular pedagogy digs. Michaela Epstein, Mabel Chen, and Ammar Aldaoud were present. The topic this time around? The ‘charge model’ for presenting positive and negative integers, which is used across three modules in the ACMNA280 content descriptor (“Compare, order, add, and subtract integers”). This topic came from a few teachers who emailed in asking about the reasoning behind using this model specifically.
What is the charge model?
The charge model is one of a number of models used in Maths Pathway modules to teach concepts relating to integers. It is used alongside other models like number lines, thermometers, and MAB blocks.
Doing a bit of research, we found a paper by Judith B Kohn (“A physical model for operations with integers”), which was the earliest mention of this model we could see in the literature. Kohn puts forward this model as a solution to the fact that all operations can’t be represented with the alternative models mentioned above.
The charge model is based on using coloured circles to represent positive and negative ‘charges’. These charges can be added up to represent different numbers.
Before being introduced to the ‘charges’ —a more abstract concept— students are introduced to the concept of dealing with both positive and negative values using the idea of gift cards and bills. This is to give the students something more concrete and familiar to work with before introducing the model.
If you have a bill for ten dollars, you have ‘-$10’. Whereas if you get a gift card for ten dollars you have ‘$10’:
Michaela (our Head of Learning) pointed out during this discussion that money is the first topic that has a reference to ‘negative’ numbers, as seen in accounting records from China dated to 200BCE!
Following this conceptual introduction using money, students are introduced to the idea of representing numbers as ‘charges’. This is similar in concept to ions in chemistry or similar.
For example, this represents a value of +5:
And this would represent a value of -4:
Following this, students are then introduced that a single positive charge and a single negative change cancel out to create a net charge of 0. This happens in the module ‘Balancing Positives and Negatives’, and is the main focus of this module.
Once students are comfortable with the idea that zero is made from positive and negative charges that ‘cancel out’, they can then use this system to model addition and subtraction with integers (supplemented with more ‘gift/bill’ examples):
Addition
Subtraction
The subtraction situation is quite interesting. To be able to do these subtractions, more charges need to be drawn.
As an example. for ⁻4-3, you start with 4 negative charges. You want to subtract 3 positive charges. Since there are no positive charges to start with you need to draw these into the picture. For every new positive charge that's drawn, a negative charge is also needed so that the overall value of the picture doesn't change. That is why we end up with more than 4 negative charges in the picture.
So why teach it this way?
Some of the feedback that sparked this pedagogy dig was teachers asking why we use this model in particular for teaching these concepts. The focus of the discussion was on what the pros and cons are.
The Learning team mentioned a number of benefits in their discussion of the model:
Drawbacks the team pointed out:
Where to from here?
The team also discussed the idea of updating this module in the future to introduce students to the difference between an unary and binary operator. Because this model makes the difference between a negative value and a subtraction so explicit, it could be a good way to help students understand this difference more explicitly as well.
For the moment, the ‘Subtracting Integers’ does show this difference in the way that the minus symbol (-) and negative symbol (⁻) are formatted, but it’s not explicit. This change has been added to the Learning team’s backlog of content changes, for a future update.
What do you think?
Have you come across the charge model yourself in your practice?
B Corp media contact: Callie Rojewski, B Lab; crojewski@bcorporation.net; 610-293-0299 ext. 218
Today, Maths Pathway was recognised as being among the companies creating the most positive overall impact on its customers based on an independent, comprehensive assessment administered by the nonprofit B Lab. Honourees are featured on B the Change, the digital Medium publication produced by B Lab, at bthechange.com/bestfortheworld.
Maths Pathway is honoured in the Best For Customers list, which includes businesses that earned a Customer score in the top 10 percent of more than 2,400 Certified B Corporations on the B Impact Assessment. The full assessment measures a company's impact on its workers, community, customers and environment. To certify as B Corporations, companies like Maths Pathway must complete the full assessment and have their answers verified by B Lab.
The Customer portion of the B Impact Assessment measures the impact a company has on its customers by focusing on whether a company sells products or services that promote public benefit and if those products/services are targeted toward serving underserved populations. The section also measures whether a company’s product or service is designed to solve a social or environmental issue (improving health, preserving environment, creating economic opportunity for individuals or communities, promoting the arts/sciences, or increasing the flow of capital to purpose-driven enterprises). Honorees scoring in the top 10 percent set a gold standard for the high impact that business as a force for good can make on consumers around the world. Maths Pathway made the list thanks to exceptional practices that give teachers the tools, time and professional development to help them achieve the greatest possible impact in their classrooms.
Maths Pathway is a social enterprise that has built an effective framework for scaling excellence in mathematics education. A recently published report showed that students in Maths Pathway partner schools learn mathematics at more than double the rate of students in classrooms that don’t use their model.
Maths Pathway envisions a world where every student’s learning experience is captivating, valuable and enables them to reach their full potential. In pursuit of this goal Maths Pathway is creating – and working with schools to implement – a groundbreaking mathematics Learning and Teaching Model.
With the rise of anger at a system that feels rigged, people are hungry for companies like Maths Pathway, who are changing the system by building businesses that seek to create the greatest positive impact,” says Jay Coen Gilbert, co-founder of B Lab. “Best For The World is the only list of businesses that uses comprehensive, comparable, third-party-validated data about a company’s social and environmental performance. As consumers, talent and investors increasingly demand transparent, values-aligned businesses to buy from, work at and invest in, companies will need to not just the best in the world but the best for the world, and not just to be nice but to be the most successful.
Close to 1,000 Certified B Corporations were named 2018 Best for the World Honourees, including: Patagonia; King Arthur Flour Company; Green Mountain Power; and the United Kingdom’s Charity Bank. Fifty-two countries are represented, including Denmark, India, South Africa and Taiwan. The selection criteria for Best For The World honourees are available at https://bit.ly/2IgAzF5.
Today there are more than 2,400 Certified B Corporations across more than 150 industries and 50 countries, unified by one common goal: to redefine success in business. Any company can measure and manage social and environmental performance at http://bimpactassessment.net.
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B Lab is a nonprofit organisation that serves a global movement of people using business as a force for good. Its vision is that one day all companies compete not only to be the best in the world, but the best for the world and society will enjoy prosperity for all for the long term.
B Lab drives this systemic change by: 1) building a community of Certified B Corporations to make it easier for all of us to tell the difference between “good companies” and good marketing; 2) passing benefit corporation legislation to give business leaders the freedom to create value for society as well as shareholders; 3) helping businesses measure, compare and improve their social and environmental performance with the free B Impact Assessment; 4) driving capital to impact investments through use of its B Analytics and GIIRS Ratings platform.
For more information, visit http://www.bcorporation.net
