Dr. Janette Bobis is a mathematics educator and researcher in the Faculty of Education and Social Work at the University of Sydney. She teaches in the areas of primary and early childhood mathematics education and curriculum studies at the undergraduate and graduate levels. Her teaching, research and publications focus on two interrelated areas: (a)*teacher learning* in mathematics education, particularly knowledge, beliefs and practices of primary and middle years teachers; and (b)*student learning*, predominantly concerned with their motivation and engagement in mathematics and their understanding of estimation and mental computation strategies.

After completing her bachelor’s degree, Janette taught in a range of primary schools for eight years. She has previously lectured in early-childhood education, computer education, primary-mathematics education and general curriculum studies at the University of Western Sydney, University of Technology and Macquarie University.

Janette is recipient of several research and teaching awards, including a *Thompson Research Fellowship* (2013), a national *Practical ImplicationsAward* (2007) for her research on teacher pre-service education, an *Early Career Researcher Award* (1992), a *Commonwealth Prograduate Award*(1990), a national *Citation for Outstanding Contributions to Student Learning* (2007), a Vice Chancellor award for *Outstanding Teaching* (2009) and a *Faculty Excellence in Teaching Award*(2002).

Janette has held a number of senior administrative roles throughout her career, including Associate Dean Research in the Faculty of Education and Social Work,Associate Dean Postgraduate Programs,Director of the Master of Teaching program and Postgraduate Research Student Coordinator.

Colleagues who would like to meet Professor Bobis should contact Cathy Bruce (cathybruce@trentu.ca, ext 7500).

** **

**Events**

Public Lecture by Dr. Bobis

**Motivation, Engagement and Understanding in Mathematics: Insights from Research in Australia and Implications for Practice**

Moderated by: Dr. Cathy Bruce

Hosted by: The School of Education and Professional Learning

April 23, 2014 5pm

Wenjack Theatre

Light refreshments will be served.

Discussant for Research Lesson

**Spatial approaches to measurement with children ages 4-7**

Math for Young Children research project

Kitchener, Ontario

April 30, 2014

By invitation only.

]]>Here are a few things I have learned in examining the PISA data more closely:

1. Canada’s 15 year old students ranked 13 of 65 participating OECD countries. 9 countries performed better than Canada. Several were in our grouping of ‘same’ level. The decline is statistically significant.

A few average or low-performing countries improved over time, but among high-performing countries, only Macao-China, Poland, and Germany improved in mathematics over the past four PISA cycles. As with Canada, in the Netherlands, Finland, and Belgium there was a decrease in average achievement, while the other countries maintained their scores.

2. 92.0% of students across the OECD and 96.4% of students in Canada can complete basic skills questions including the ability to:

• answer questions involving familiar contexts where all relevant information is present and the questions are clearly defined.

• identify information and carry out routine procedures according to direct instructions and explicit situations.

• perform actions that are almost always obvious and follow immediately from the given stimuli.

3. 3% of students across the OECD and 4.3% in Canada were able to achieve the highest level of problem-based questions including the ability to:

• conceptualize, generalize and use information based on their investigations and modelling of complex problem situations, use their knowledge in relatively non-standard contexts.

• link different information sources and representations and move flexibly among them.

• demonstrate advanced mathematical thinking and reasoning and apply this insight and understanding͕ along with a mastery of symbolic and formal mathematical operations and relationships to develop new approaches and strategies for addressing novel situations.

• reflect on their actions and formulate and precisely communicate their actions and reflections regarding their findings, interpretations and arguments͕ as well as explain why they were applied to the original situation.

4. 15 year old Canadian Males are outperforming females in mathematics (by 10-17 points)

- females are outperforming males in reading (by 21-35 points)
- no significant gender difference in science

Here is a graph provided by CMEC (Council of Ministers of Education) on gender disaggregated data:

Whether we believe the PISA tests are important or not, these data raise some interesting dilemmas and questions.

For example, if our students are doing so well with basic skills questions in PISA and on EQAO – see comments by CEO of EQAO here: http://www.theglobeandmail.com/news/national/education/making-a-profit-on-apples/article16856546/

…then why oh why do we want to focus MORE on the “basics”? In a society where we always seem to be picking a side, this math debate is ripe for oversimplification.

I believe problem solving and fluency with basic procedures go HAND IN HAND and the separation of the two is actually part of our oversimplification of the challenges of high quality teaching and learning of mathematics ideas. Consider the following two questions:

The question on the left involves adding four two-digit numbers. I might even be able to answer the question without a clear understanding of what perimeter is. The question on the right involves adding at LEAST three sets of four digit numbers, and it requires a demonstrated understanding of perimeter. AND let’s just hazard a guess that it is slightly more engaging than the addition task on the left. When we are solving more complex problems, we are also practicing and applying procedures.

We need to move beyond quick answers and ask hard questions. What do we mean by “back to basics”? Why do approaches to math teaching and learning such as focusing on procedural skills get pitted against a focus on mathematical problem solving? How do we incorporate BOTH? – Do we really need to sacrifice skills for problem solving? Or do we need to sacrifice problem solving for basic skills?

The layers of complexity are extensive and overall, as we focus our attention on Mathematics in Ontario schools, I believe we need a multipronged approach to valuing and increasing student understanding of mathematics. I shared some suggestions with the Globe and Mail – go to: http://www.theglobeandmail.com/news/national/education/students-need-high-expectations-in-math/article15216621/

Here are some key things I think we ought to consider together:

i. Invest in math learning for our youngest students. Research shows that young children are far more capable of “deep mathematics” thinking and work than we expect. In our Math For Young Children research, Kindergarten students are finding all the combinations of two numbers that equal ten; Grade 1 students are understanding that two figures can have the same area, but look different; Grade 2s are composing and decomposing 3-D figures based on diagrams and images; Grade 3s are representing and graphing linear growth. The math education research clearly demonstrates that explicit and engaging math learning at a young age is not only appropriate – it is essential to future success. In fact, early math is one of the very best predictors of later overall school success.

ii. Provide teachers with high quality mathematics professional learning opportunities. Our educators need to really enjoy math and pass that on to their students. Elementary and secondary educators and the pre-service AND in-service levels need support, mentorship, strategies and tools to implement high-yield mathematics programs that promote deep understanding. This means we need a systematic, long-term strategy and investment in mathematics teaching as a province.

iv. Countries with high performance on PISA have students and families that value education and see it as accessible/applicable to them. We need to work together to help parents and the wider community see students as capable math learners. Everyone can learn math, and we all use math daily in our lives. It’s really not OK to say, “Oh I wasn’t good at math either, so don’t worry,” or “You just don’t have the math gene.” We need to prioritize math as not only important but interesting, and something that everyone can get better at. Practising through games like cards at home is fun and builds number fluency. Estimating the distance and time it will take on trips builds estimation and computation skills. Parent involvement that focuses on student learning in mathematics has a tremendously positive effect.

]]>This was a great opportunity to talk about the role of technology in future classrooms (and today). Of course I tried to prepare for the show by summarizing what I think are some key themes, concerns, challenges and strengths of infusing technology in the classroom. Because the show has limited time for each person to discuss their ideas, I thought I would provide a more ample summary of my thinking on this blog.

If you would like to see the show, here is the link:

http://ww3.tvo.org/video/188858/teaching-towards-future

Here are some more key points related to the show that hopefully further our thinking about technology in the classroom of 2030.

**1. Change is a constant in education
**

- Education and teaching are always in flux.
- This theme in focus on The Agenda – The Classroom of 2030 – is so important.
- Although it is hard to predict what the classroom of 2030 will be like, there is no doubt that technology will be part of the 2030 learning environment (in traditional and non-traditional settings)
- There is no doubt that the technology we are familiar with today will change, however, the key is to figure out how to use technology to ENHANCE learning as effectively as possible.
- Working toward technology use for production, for creating/generating solutions and for knowledge building is important.
- It is insufficient to treat technology as entertainment or as a student management tool (because the students are motivated to use the technology). That is actually not enough. We need to learn how to make best uses of the technologies available to optimize learning opportunities and deepen understanding

**2. Response to video clip of Bill Gates
**

In my research program through TMERC, we work with teams of teachers who are engaging in collaborative research to learn deeply about how children learn mathematics and in improving their practice.

*ii. Characteristics of excellent teachers
*Beliefs:

1.

Practices:

(i) *A person who is a change agent* – a person who helps students make use of the technology tools available, who understands the learner well enough to help move his/her thinking/understanding along

(ii) *A person who has a specialized knowledge* of content and how to teach students to access content, synthesize and find solutions!

(iii) *A person who models problem solving* and fosters a community of learners in the classroom

What Bill Gates didn’t mention, ironically, is that technology has a central role to play in the shifting role of the teacher and of students.

**3. How many teachers do we have like this in Ontario?
**In-service

100% of the teachers I work in Ontario with use both high and low technologies and are learning to be excellent teachers who:

a. Facilitate knowledge creation

b. Model learning and problem solving for students

c. Gain specialized content knowledge

In January of 2013, a PBS study found that over 70% of US teachers polled use technology as an integral part of their classroom learning. Here in Ontario, the quality of our education system is even better, so I am going to say 80% are using technology and want more technology supports and training. (National survey n=500)

Pre-service

In our School of Education at Trent we have interactive whiteboards in every room.

We have 30 iPads that are used in classes.

We encourage other low and high tech use including manipulatives, handhelds such as clickers and phones, etc.

We also have practice teaching rooms where learning teachers can practice lessons with their peers with the technology in those practice teacher rooms.

**4. Learning and teaching are complex, and so is the use of technology in learning environments
**Challenges

1. *Wow factor instead of the How factor*

We need to use technology well – not just rely on novelty.

Study of 40,000 online learners in Washington State: self-directed and already successful learners excelled but struggling learners struggled even more! (Columbia College Research Centre Study)

2. *Lack of training* and keeping pace with the rapidly changing technologies (infusion of interactive whiteboards in the UK about 10 years, but was not accompanied with sufficient training on teaching strategies to maximize learning with technology). There were some very mixed results from that infusion of technology.

Important part of this training:

How can we get students to PRODUCE KNOWLEDGE AND SOLUTIONS using the technology rather than just CONSUME knowledge.

3. *COST*: Lack of access and infrastructure

**5. Key benefits of classroom technology use / the Need to Teach Differently
**I.

We are living in an increasingly VISUAL WORLD. We represent ideas visually to convey a lot of meaning in a short time (often through images, diagrams, video clips, etc).

Recent technologies, such as the interactive whiteboard or IWB, tap into that visual communication of information beautifully. Ideas are writ-large on the IWB – enables communities of learners to develop through sharing their thinking and building knowledge together more effectively.

The touch technologies including the IWB also have a gesture component. In math this is particularly important – students who gesture (children and adult) to convey meaning have higher math scores, particularly in the area of spatial reasoning and geometry. And people who gesture retain math concepts longer. It is REALLY important to build this foundation early because it supports long-term career opportunities in the STEAM areas – Science, Technology, Engineering, Arts and Mathematics.

II. *The dynamic nature of touch technologies enables real-time knowledge creation*

Has the potential to help students make meaning of complex ideas. The images are not static. The information is not static.

The textbook: a static object that contains a specific amount and type of information.

The IWB: a dynamic object that acts as a portal to a vast range of information sources both web-based and offline (using dynamic software such as Geometer’s Sketchpad)

High quality use of technology in the classroom leads to:

Change in teacher and student roles Increased complexity of tasks

Increased student voice and agency Collaboration

Technical skills Increased use of outside sources

**6. What are the obstacles in providing more personalized curriculum options to many more students?**

This question assumes that a more personalized curriculum is desirable, and I agree that this is something we have been striving for in education, particularly in the last quarter century.

Challenges to a personalized curriculum

1. Old administrative and physical structures of schooling that have been with us for over 100 years are still in place in Ontario:

a. Physical classrooms with limited flexibility and related norms of isolation

b. Stop and start learning with bells and subjects separated out from one another into very discreet chunks

2. Lack of access to technology (still not equitable or fully distributed)

“Imagine a classroom, a school, or a school district where all students have access to high-quality, engaging mathematics instruction. There are ambitious expectations for all, with accommodation for those who need it. Knowledgeable teachers have adequate resources to support their work and are continually growing as professionals. The curriculum is mathematically rich, offering students opportunities to learn important mathematical concepts and procedures with understanding. Technology is an essential component of the environment. Students confidently engage in complex mathematical tasks chosen carefully by teachers. They draw on knowledge from a wide variety of mathematical topics, sometimes approaching the same problem from different mathematical perspectives or representing the mathematics in different ways until they find methods that enable them to make progress. Teachers help students make, refine, and explore conjectures on the basis of evidence and use a variety of reasoning and proof techniques to confirm or disprove those conjectures. Students are flexible and resourceful problem solvers. Alone or in groups and with access to technology, they work productively and reflectively, with the skilled guidance of their teachers. Orally and in writing, students communicate their ideas and results effectively. They value mathematics and engage actively in learning it.”

This quote still seems quite relevant in 2012… It is what I strive for every day in my teaching and what the teachers I collaborate with in elementary and secondary schools are also striving for. In my Bachelor of Education Mathematics classes, I am trying to support the aspiring teachers that I work with, to understand what this means and how they can be a part of shaping high quality mathematics programs here in Ontario and further afield. But will this quote hold up for the classroom of 2030?

I have been thinking about the classroom of 2030 lately because there is a TVO themed series on The Agenda attempting to tackle this topic. And now, as it turns out, I am on a panel for this same series – taped at Trent on March 3^{rd} and aired on March 4^{th}. I am asking myself, what does the teacher of 2030 need to do and be? Not a simple answer, because learning is complex and dynamic. Simple answers to this question seem to lead to short-sighted solutions that lack longevity and substance.

I have also been asking teenagers in High School and young adults in University for their opinions (I hope to spread the net further over the next several weeks). In every case, two themes have been identified by these students: The first is the unquestionable infusion of technology for learning. It is absolutely expected, demanded, and described in some detail by these students. Immediate and wide-ranging information is literally at their fingertips as students use handheld devices, tablets and laptops to search and find everything from how hydrogen sulfide is produced to historical events in war-time Cambodia to video documentation and presentations of every shape and size. On YouTube there are currently over 800 million unique visitors every month. Over 4 billion hours of video are watched every month in 53 countries in 61 languages (see YouTube statistics). Wikipedia, a print information databank has over 29,477,075 pages and over 4 million articles. There’s a lot to weed through… Students today are telling me that the teacher of tomorrow must facilitate access to information that is clustered thematically based on the topics in focus, and that they can facilitate quality control in terms of the recommendations of sources for information, but most importantly, the teacher must be able to help students see the relevance and applications of this information to SOLVE PROBLEMS. The students I am talking to want to be knowledge creators and solution finders for the vast problems our earth and its populations face. Now THAT is humbling. And it tells me that we have our work cut out for us.

The second thing that students are telling me is that the classroom – a place to actually meet and work together and solution find together, is important. Although they are very keen to engage with online learning environments both in asynchronous and synchronous learning situations, they tell me that this is not enough. Students today are telling me that the physical classroom or gathering space is a necessary part of deep learning. How interesting!

If this is true, then teachers of 2030 must be able to facilitate students in becoming knowledge creators, problem finders and solvers, collaborators and communicators both in technology assisted learning environments AND in face-to-face learning environments. And this leads me to yet another question: What should we be doing in Education programs to help pre-service teachers prepare for their future teaching experiences? How do we equip these aspiring teachers to begin their careers? And what about those people who are not looking to work in a typical classroom?

I’m thinking about this… and maybe in watching The Agenda: Classroom of 2030, it will spark some more thinking for you as well!

Check out these two TVO segments that have already aired on the topic of

The Classroom of 2030:

Will kids like schools better in the future? How different will they have to become? Watch the Video

Digital Promise: Personalized education. Schools of tomorrow will leave no one behind. Watch the Video

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I have been working with two teams of teachers who are investigating the use of number lines to help young children (ages 4-7) think about proportional reasoning, magnitude, and number relationships. One group of teachers is at a school in Toronto and one team spans two schools in Peterborough. Although the communities are quite different, some astounding similarities have emerged.

To begin, the teams conducted task-based interviews where the teachers asked students to try a math task and sat with the student to observe, and ask follow-up questions. Our goal was to uncover students’ early understandings of number but also to see if they could intuitively use the number line as a thinking tool. Here’s an example of a task in the interview set that comes from Saxe (2010):

Here is a number line. Where would you put the number 7? How do you know?

Interesting question! Intervals are missing, numbers are missing, there’s no beginning or end intervals…. Not a simple question! Six students from each class were interviewed by the teacher with the support of our researcher team; the interviews were videotaped and analyzed as a group. Amazingly VERY young children were thinking about spacing (partitions that would help find the location of 7), they were thinking about the relative location of 7 compared to 4 and 6, and they were using their counting numbers. There’s a lot going on here and we were amazed at how four year olds and slightly older students found the tasks engaging, but also worked with the number lines very very quickly, even though they had only been exposed to fixed number lines posted on the walls in the classroom to support counting. Our observations and findings led us to want to explore the number line further. And we have!

Recently, the two teacher teams held a public research lesson, where they invited guests in to observe students engaging with number lines as thinking tools to explore intervals and conceptions of “half way” (or middle). We have learned a ton from this work, and the observations of colleagues.

Here’s a summary of some of some of what we have learned about working with number lines. This was recorded by the research team but generated by teachers in the study.

These are just SOME of the things we are learning about number lines.

What an exciting process for digging into math learning with young children.

One thing we have observed repeatedly in classrooms is that students rely on circle representations of fractions almost exclusively, even though they may not seem to be a great fit for the problem at hand. For example, one day when our teacher team was working in Kerry M’s classroom, the students were asked to draw a math model that would help them solve a distance problem. The problem went something like this: Suzie walks 2 km from her home and is two-thirds of the way to school while Bemel walks 3 km from his home and is half the way to school. What fraction model could you draw to help you represent the problem, and then solve it? There were a range of representations recorded in the class, but interestingly, many students used circle area models and partitioned the circles. Several students used linear models (number lines) to help them, which seemed quite a good fit with the problem about distance. Others used rectangular area models – often squares joined together in a long line similar to a linear model. When we asked students why they would use a circle area model to represent and solve the problem, one student explained: “It’s just easier to use circles. I was thinking about pies and how much of the pie was gone.”

As an observer, I was having a hard time imagining how the circles and pies fit with walking to school. But rather than get into those details here, what this response provoked me to think about is: why is there an over-reliance on circle representations for fractions, even when they aren’t well matched to the situation?

Is it intuitive or cultural? What are we doing to favour the circle area model over other models in our classrooms, in textbooks, in newspapers, in the manipulative materials made available to students? Is pizza the only context for fractions? It might work really well for fair shares, but that is only one component of fractions understanding that we need to understand. How does the circle fraction help a nurse or doctor figure out a critical one-quarter dosage of medication? Or to return to a food scenario, consider these area diagrams:

Three cakes are cut into two pieces. Which cake piece would you want to eat? Does it matter?

And when might we want to use discreet models (that show parts of a set)?

One of the things that we have learned through our research collaborative is that representations are a critical component of fractions understanding, and although we are gaining insights through our explorations with students, there is still a LOT to learn about how we represent fractions! For more reading, check out these articles:

Bruce, C. & Flynn, T. (2011). Which is greater: One half or two fourths? An examination of how two Grade 1 students negotiate meaning. *Canadian Journal for Studies in Science, Mathematics and Technology Education*, *11*(4), 309–327.

Bruce, C. & Ross, J. (2009). *Conditions for effective use of interactive on-line learning objects: The case of a fractions computer-based learning sequence*.** Electronic Journal of Mathematics and Technology*** *[online serial] *3*(1*).* Available http://www.radford.edu/ejmt

**And stay tuned for a new Digital Paper on Fractions!**

It’s great to have you here and we look forward to what’s to come!

Talk to you soon,

Rich

-TMERC

Rich

-TMERC