Posted by dlander2012
Sunrise at Haleakala, Maui- the dawning of a new day…
The MathConnect Conference in Calgary on February 2 hosted a colorful spectrum of speakers http://mathconnect.org/wp/presenters/
The following write-up summarizes messages about teaching math that I took away from some of the presentations.
Dr. Carol S. Dweck
As noted near the end of my Mindset blog, many students have given up on math because they believe they are not good at math, and will never “get” math.
Teachers and parents are supporting a fixed mindset when they tell students, “Don’t worry, not everyone is good at math.” This kind of feedback writes kids off, gives kids lower confidence that they could ever do it, releases them from the responsibility of ever doing well in math.
On the other hand, teacher who are developing a growth mindset would say, “Let’s break this down even further and try some strategies together to see how you can get better.” When teachers and students believe skills can be developed, it opens students up to learning.
The highlight of my day definitely was meeting Dr. Carol Dweck in person. I got to tell her about our Learning Services’ team’s Mindset book study, how we involved ourselves in examining our mindsets, as individuals and as a team, and how we continually reflect on our growth.
Dr. Rafael Núñez
Dr. Núñez’ presentation worked to uncover the topic, “Where does math come from; making sense of human ideas.”
“Mathematics is a paradoxical conceptual system.”
- Math concepts are not directly perceivable through the human senses. For example, we cannot see infinity…
- Mathematical entities are imagined by humans, not visible in our environment, so how can we make sense of them?
Can we relate mathematics to other kinds of perception? If we can, maybe we can use those relationships to help us teach math. Conceptual metaphors help fictive motions make human imagination possible.
Metaphors– For example we can perceive the domain from a cold heart to a warm heart, so maybe numbers are also perceived as a domain, as if they have a location in space.
Fictive motion– “We often talk effortlessly about static objects as if they were moving.” For example, “The fence stops after the tree.” The conception we construe in that the fence is moving may provide the inferential structure required to conceive mathematical functions as having motion and directionality.
Gestures– we use hand and body gestures to enhance communication; to help the speaker express him/herself, which in turn, help the listener make meaning. Perhaps the intentional use of relevant gestures in teaching mathematics could support students in construing meaning as well.
Are there any mathematics that are hard-wired- the basic number line perhaps? Is this an embedded part of the brain, or something we need to learn? Núñez’ Yupno Study concluded that mapping a number to a point in space doesn’t come naturally-it seems that something as simple as a number line is not inherent, it is learned, and so, we need to intentionally teach it. If this basic simple model in math is not understood, concepts that depend its understanding will not be understood.
Núñez’ summarized his message by saying that “the portrait of mathematics has a human face”; articulating meaning is necessary because mathematics is such a complex conceptual system.
Also, like development along a continuum, the understanding of mathematical concepts relies on the understanding of previous concepts. If we do not understand what comes before, we will not understand what comes after.
Diana is the Program Coordinator of the Robertson Program for Inquiry-based Teaching. During her presentation, Diana shared the “Math for Young Children: A Lesson Study Research Project” that she is working on. The driver behind this project is current research showing that success in early math skills are a better predictor of success in later years, than success in early literacy skills.
The lesson study involved a step-by-step approach.
- With the support of facilitators, teachers did a lot of reading and professional learning about some key concepts in mathematics. They then chose a topic they wanted to focus their work on.
- Students’ strengths and needs were assessed in this chosen topic. Teachers interviewed students and got them to work on some activities to see where their development was at in that concept area.
- Based on the findings from the work with students, the team of teachers and facilitator co-designed exploratory lessons to help students develop their skills and overcome some misconceptions. During the exploratory lessons, the teachers observed each other’s students.
- After debriefing to determine explicitly what needed to be taught to move the students forward in their development, the teachers built “public lessons” that they would all teach.
- Teachers taught the public lesson.
- Teachers debriefed the lesson and determined next steps.
The “public lessons” the teachers co-developed, as well as a summary of the Lesson Study can be found on Math for Young Children space on the Trent Math Education Research Collaboration website.
Why do we Resist the Evidence?
At the end of the day, the presenters assembled as a panel to address questions from the audience. A question one person asked was, “Why do we resist the evidence- why do we ignore the research and continue to use teaching methods that are not always the most effective?” Should we not embrace new evidence just as we embrace the dawning of a new day?
The panel offered several indirect responses to the question, and I also have some theories of my own, but I’d love to hear your response to the question, “…so why DO we resist the evidence?”
Posted by dlander2012
On Saturday, I had the opportunity to attend the MathConnect Conference in Calgary. The first keynote speaker of the day was Carol S. Dweck Ph.D., author of Mindset.
Dr. Dweck’s “research focuses on why students succeed and how to foster their success. More specifically, her work has demonstrated the role of mindsets in success and has shown how praise for intelligence can undermine students’ motivation and learning.” (http://mathconnect.org/wp/presenters/)
Although I learned a lot about her work through the Mindset book study our Learning Services team participated in last year, it was great to hear her story in person. I am using this blog post to share some elements of the presentation that stood out most for me.
Dr. Dweck told us that Alfred Benet originally developed the IQ test to see which students weren’t succeeding with the current curriculum, and used the results to change that curriculum. Like other theories and concepts that have been applied out of context (e.g. Bloom’s Taxonomy, Gardner’s theory of multiple intelligences), educators have misconstrued the intent of the IQ test, and the result has led to the idea of intelligence being a fixed trait.
Current research shows “the brain can be developed like a muscle”; every time you stretch out of comfort zone, neurons grow new connections. So intelligence CAN be developed.
2 Opposing Beliefs
Fixed mindset– intelligence is a fixed trait
Growth mindset– intelligence is a malleable quality; a potential that can be developed
As a result of her research, Dweck has developed several “mindset rules” which help us differentiate between fixed and growth mindsets:
Fixed mindset– look smart at all costs; tell me when I’m right
Growth mindset– learn at all costs; tell me when I’m wrong
Students with a growth mindset care more about learning than about grades. Good grades are the bi-product of effort and a successful learning path, not of an innate intelligence.
Fixed mindset– learning should come naturally; if you have ability you shouldn’t need effort
Growth mindset– work hard, effort is key; ability is increased over time
Geniuses are a result of the work and effort they put in over time- building on successes and addressing their shortcomings, over and over again; continually trying until they succeed.
Fixed mindset– hide mistakes: In the face of setbacks, these students said they would spend less time on the subject from now on, why spend time on something I’m not good at?
Growth mindset– capitalize on mistakes, formulate new strategies to address the problem. In the face of setbacks, these students said they’d spend more time studying and work harder in class.
Fixed mindset– Praising intelligence develops a fixed mindset- in Carol’s research, these kids wanted a task that they could easily be successful on.
Growth mindset– Praising process and effort develops a growth mindset- these kids wanted a harder task that they could learn from.
Human beings are born as natural learners, so how do we make sure our students remain learners? Kids are tuned in to what the environment values; if we value effort, hard work, and progression of skill development, they will, too. Growth mindset has kids embrace learning and growth, and understand the role of effort in creating talent; it can be taught everyday in our classrooms.
How can we help students develop a growth mindset?
- Praise effort, struggles and persistence despite setbacks.
- Praise the strategies they try and choices they make.
- Praise choosing difficult tasks, praise learning and improving; do not praise marks
- Use the word YET- “not yet” puts you on a learning trajectory- “I’m not there yet, but I will get there.”
How does this relate to teaching math?
Many students have given up on math because they believe they are not good at math, and will never “get” math.
Fixed mindset– Teachers comfort students who are doing poorly, telling them, “Don’t worry, not everyone is good at math.” This kind of feedback writes kids off, gives kids lower confidence that they could ever do it, releases them from the responsibility of ever doing well in math.
Growth mindset – Teacher says, “Let’s work to understand what you are not getting, and try some strategies to see how you can get better.” When teacher and students believe skills can be developed, it opens students up to learning.
Mindset Website http://www.mindsetworks.com/default.aspx
Students are very interested in how their brains work and how they can get smarter. I’m really excited about the Brainology application Dweck’s team has developed. “Brainology raises students’ achievement by helping them develop a growth mindset.” Guided by Brain Orb, students learn how the brain works, how we learn, and some brain-based learning strategies.
The website also has a teacher toolkit to support teachers in developing a growth mindset in their classroom.
Our students are so fortunate that our school division is embracing Dr. Dweck’s work. Won’t it be great when all of our students demonstrate a growth mindset!!