Siyaphumelela Conference 2017, The Wanders Club, Johannesburg!


Carnegie Foundation Math Pathways Workshop 27 June 2017

Andre Freedman, Capital Community College, Connecticut

Bernadine Chuck Fong, Carnegie Math Pathways

Andre Freedman and Bernadine Chuck Fong

Workshop goals:

  • Learn about the design, goals, implementations of Carnegie Math Pathways
  • Experience Pathways lessons
  • Engage in design tasks to improve student success in maths and college
  • Engage in conversations about professional learning to address issues and concerns that are specific to local contexts

Staff had to learn new ways to teaching maths, there had to be ‘buy in’ for it to be successful. This is a great challenge.

How to radically transform outcomes for all mathematics students?

  • aim to get more student to complete maths courses and degrees
  • persistence (students don’t easily give up when challenged)
  • quality of learning (e.g. students can explain what a function is years after taking a maths course)
  • identities of learning (students see themselves as someone who can do maths).

Make maths a Gateway not a Gatekeeper, particularly to careers outside of calculus-requiring STEM courses.


  • Acceleration: Rather not have 3 developmental courses (pre-algebra, algebra 1, 2) before taking the required course
  • Problem-centered curriculum
  • Student-focused, collaborative pedagogy
  • ‘Productive Persistence’ interventions / practices to give students belief that they can succeed
  • Language and literacy supports
  • Train faculty so they can feel comfortable about the new approach
  • Use networking to support staff to get running and sustain change
  • Keep cohort together for 2 semesters in classes of 30 – 40, or as one institution did teach the 2 semesters in one term (quarter of a year) with about 5 hours a day and one other course -success rate was very high at 78%.

Statway and Quantway courses have served 20 000 students in 60 institutions across America since 2011.

Graph of success of students who took Statway, comparing students doing traditional sequence of 3 developmental courses vs Statway: Triple the success in half the time.

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Statway and Quantway are credit bearing courses, mostly for students who are not on the road to calculus, doing non-STEM courses, e.g. nursing, law, disciplines that mostly need statistics not calculus. Compared to the normal 3 semesters they complete 2 semesters. Content was left out after a big consultation process. Do law students need 1 year of algebra that they do not use in their degree or career? The aim is achieve a deep level of statistics by teaching in a different way, giving students an experience that will be more meaningful.

Example of questions:

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Active learning in class, mostly group activities, but students may leave class with misconceptions so the online component of the course provides individual learning and consolidation.

Many students are not learning maths by being in classes.

3 critical learning opportunities (Do my courses facilitate these?)

  1. Productive struggle: want students to have a difficult time in class and come to see struggle as good and leading to deeper learning. Many students want to have maths told to them all the time.
  2. Explicit connections across topics and modules
  3. Deliberate practice supported by out of class activities: online, projects.


We had 20 minutes to work on a Quantway activity on citizenship. Information is given to students when they need it, e.g. for a question that requires a written answer they are reminded that good writing practice includes writing your answer so that it makes sense when read alone. Maths definitions are given where needed too.

The role of a lecturer changes to a coach rather than explaining how to do every problem. It is very difficult for lecturers to take on this new role, they are pushed out of their comfort zone of delivering a lecture. A strategy to stop yourself talking is to drink a bottle of water after you have handed out the problems so you can’t talk!

Doing a change to this style of teaching cannot be done by a single staff member, there needs to be support from a cohort.

[I wonder how to motivate students to honestly work through the struggles  – what will be the assessment in the course? Andre later said the assessment tasks are similar to the classwork exercises but open-ended questions have fairly narrow answers. The assessments are not designed for productive struggle.]

Productive Persistence is about students’ tenacity. How can we shift students’ mindsets of mathematics, and of them as doers of mathematics?

Driver Diagrams

A driver diagram is a tool for mapping out the solution to a problem.

Start with an aim, a goal.

Then identify primary drivers, what need to occur for the goal to be reached.

Then identify secondary drivers, activities that must be done to achieve the primary drivers.

Then develop change ideas, what will role players do to support the drivers and the aim.


Our group worked on the aim: How to help students to overcome the belief that maths is difficult.

Primary drivers:

  1. Students should experience success in mathematics.
  2. Students must know where their knowledge gaps are that could be holding them back from solving problems.

Secondary drivers

  1. Give scaffolded, complex problems.
  2. A pre-activity diagnostic tool testing specific skills and knowledge prior to an activity to identify knowledge gaps and prior knowledge.

(1 and 2) Games that develop skills and knowledge in the forthcoming activities.

Change ideas

Students must feel that they are allowed to fail on the path to learning.

[See handout]


Persistence is not the issue – many take the same course 3, 4, 5 times! We want productive persistence.

Think of the cause and effect relationship of one activity to another. Maybe consider the probability of each activity impacting the aim.

Research has shown that a sense of not belonging, stereotype threat (believing that others believe you can’t do maths), self-believing you can’t do maths negatively affects performance.

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Start strong

Community building activities – ice-breakers, sharing personal details. (That’s why it’s helpful to have a cohort stay together.)

Growth mindset activity e.g. all mathematicians struggle,

Constract signing –  sign a contract to agree to helping group members to succeed in the course

Stay Strong

Student communication routines – e.g. students text a missing student, very different from a non-group setup where students feel no-one will notice if they miss class.

Mindset activity – You can grow your brain – students write a short essay / motivational letter to a friend saying what they learnt about how the brain works. If a student is struggling in, say, week 6, bring them into your class and pull out their essay / letter and see if they have lost sight of the view they wrote about.

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There are online mini-courses for lecturers teaching in the Pathways.


Radical transformation requires

  • Will for collective action
  • Seeing the system – your course in relation to other courses and the university as a whole
  • Mobilizing across the system to take action across the system.




I was very glad I attended. If you would like to ask me about the Pathways project, particularly the psycho-social and pedagogical changes that would be valuable for all maths courses you can email me at

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