Parent Presentation on PBL 2018
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This is a talk I gave last week in Toronto that was geared towards discussing PBL Math with parents and answering some of their questions about the pedagogy.
![“Whenever I have a question about a problem I ask the question, why?”
“I think that presenting my solution is
most useful because I am forced to
participate and learn from other people.”
“I was presenting a problem that I wasn’t quite sure I had answered right, and
with a little push from the class, the concept suddenly clicked in my mind. I was
able to finish the rest of the problem quickly and felt good about my success.”
“You can see that everyone here wants to figure out how they got a certain problem.
There’s more of an interest than just getting something right, instead of just getting an A.
It’s something you know that they want to understand how. “
“My best description is that of a light bulb. I could see where the rest of
the problem might lead and the concept that it covered.”
“There was one time during class that I put a problem up at the board and got the
entire thing correct. I was actually, in a way, disappointed because I feel like I learn
better from my mistakes.”
“I like how it is focused on yourself figuring out the problem – though that
was hard for me to adjust to – however it’s made me much more
independent math-wise.”
“This method of teaching gave me new insight into the idea of not only solving a problem, but
really taking the time to think about it and understand it.”
“[It allows] you [to] kind of add in your perspective and it kind
of gives this sense like ‘Ooh, I helped with this problem’ and
then another person comes in and they helped with that
problem and by the end no one knows who solved the
problem. It was everyone that solved the problem. Like,
everyone contributed their ideas to this problem and you can
look at this problem on the board and you can maybe only
see one person’s handwriting, but behind their handwriting is
everyone’s ideas. So yeah, it’s a sense of ‘our problem’: it’s
not just Karen’s problem, it’s not just whoever’s problem, it’s
‘our problem.’”
Carmel Schettino, 2018](https://image.slidesharecdn.com/rscgparents2018-180308030543/85/Parent-Presentation-on-PBL-2018-1-320.jpg)
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Parent Presentation on PBL 2018
- 1. “Whenever I have a question about a problem I ask the question, why?” “I think that presenting my solution is most useful because I am forced to participate and learn from other people.” “I was presenting a problem that I wasn’t quite sure I had answered right, and with a little push from the class, the concept suddenly clicked in my mind. I was able to finish the rest of the problem quickly and felt good about my success.” “You can see that everyone here wants to figure out how they got a certain problem. There’s more of an interest than just getting something right, instead of just getting an A. It’s something you know that they want to understand how. “ “My best description is that of a light bulb. I could see where the rest of the problem might lead and the concept that it covered.” “There was one time during class that I put a problem up at the board and got the entire thing correct. I was actually, in a way, disappointed because I feel like I learn better from my mistakes.” “I like how it is focused on yourself figuring out the problem – though that was hard for me to adjust to – however it’s made me much more independent math-wise.” “This method of teaching gave me new insight into the idea of not only solving a problem, but really taking the time to think about it and understand it.” “[It allows] you [to] kind of add in your perspective and it kind of gives this sense like ‘Ooh, I helped with this problem’ and then another person comes in and they helped with that problem and by the end no one knows who solved the problem. It was everyone that solved the problem. Like, everyone contributed their ideas to this problem and you can look at this problem on the board and you can maybe only see one person’s handwriting, but behind their handwriting is everyone’s ideas. So yeah, it’s a sense of ‘our problem’: it’s not just Karen’s problem, it’s not just whoever’s problem, it’s ‘our problem.’” Carmel Schettino, 2018
- 2. PBL Mathematics: creating habits for a strong future Carmel Schettino, Ph.D. RSGC, March 1, 2018
- 3. ‘Doing the math’ in 1978 ‘Doing the math’ in 1989
- 4. “what has become the acceptable american definition in society of ’doing the math’ is procedural arithmetic and algebra – Being right or wrong – but to employers & college professors ’doing the math’ is so much more. They ask students to ‘Do the math’ by reasoning through a problem, evaluating a method or picking the right tool from your toolbox.” Solomon Garfunkel, Director of COMAP
- 5. What is the world like now for our graduates?
- 6. "The best advice I can give anyone is to think about acquiring skills and knowledge that can easily be transferred from one place to another." – CNN/Money Magazine April, 2016
- 7. What do employers want in 2018? – -Top Skills Employers Want in College Graduates in 2018 , December 1, 2017
- 8. 2015 Country Collaborative PISA Rank Math PISA Rank Singapore 1 1 Japan 2 5 Hong Kong (China) 3 2 South Korea 4 7 Canada 5 10 Estonia 6 9 Finland 7 13 Macao (China) 8 3 New Zealand 9 21 Australia 10 25 Taiwan 11 4 Germany 12 16 United States 13 39 Results of Collaborative and Mathematics PISA Tests from 2015 show that some countries do well in both categories but others do well in one or the other one.
- 9. “Strong academic skills will not automatically lead to strong social skills. As workplaces around the globe are demanding – and paying higher wages for – people with well- honed social skills, schools need to do more to help their students develop these skills.” - Andreas Schleicher, director of PISA test administration
- 10. W. Stephen Wilson “Mathematics is about solving problems, and anyone who can solve a complex multi-step problem using mathematics automatically demonstrates their skill whether they communicate well or not.” Professor of Mathematics and Education at John Hopkins University
- 11. What is our responsibility as math educators?
- 12. What do you remember from high school?
- 13. Which statement is true? 2 10 > 1 6 6.897 x 0.689 > 3.5 8 8 8 8 8
- 14. Of course we forget what we learned… 0 20 40 60 80 100 120 Biology Students Physics Students Problem Solving Knowledge Retained at MIT in their Field First Year Learned Three Years Later 55%
- 15. • Individuals who take college-level mathematics courses at or above the level of calculus have minimal losses of high school algebra for half a century. • Individuals who performed equally well while in high school but took no college math courses did slightly better than guessing. • In contrast, the best predictors of test performance (e.g., Scholastic Aptitude Test scores, grades) have little to no effect on the rate of performance decline. Bahrick, H. P., & Hall, L. K. (1991). Lifetime maintenance of high school mathematics content. Journal of Experimental Psychology: General, 120(1), 20-33.
- 16. Constructivist vs. cognitive behaviorist theories
- 17. It Pays to take your time “Repetition of information improves learning and memory. No surprise there. However, how information is repeated determines the amount of improvement. If information is repeated back to back (massed or blocked presentation), it is often learned quickly but not very securely (i.e., the knowledge fades fast). If information is repeated in a distributed fashion or spaced over time, it is learned more slowly but is retained for much longer”
- 18. Does the way you learn effect your retention? Roediger & Pye, 2012, p.245
- 19. What Affects student learning in most positive ways?
- 20. “Obviously, the elaborative interrogation and self explanation are related because both strategies encourage or even require students to be active learners, explaining the information to themselves (perhaps rephrasing in language they understand better) or asking themselves why the information is true.” – Roediger & Pye, 2012
- 22. What does learning math via pbl mean?
- 24. Considerations for students when invited to participate in learning:
- 25. PBL Framework Connected Curriculum Justification not prescription Shared Authority Ownership of Knowledge • Scaffolded Problems • Decompartmentalized Topics • The Connected Nature of Mathematics • Dissolution of Authoritarian Hierarchy • Discourse moves to improve equity • Send message of valuing risk- taking and all ideas • The point is the “why” • Foster inquiry with multiple perspectives • Value curiosity & Assess creativity • Encouragement of individual and group ownership • Metacognitive Journals • Student Presentation • Revoicing and Teacher Discourse Moves Schettino,2013
- 26. 1) which mathematical ideas are key, and why they are important 2) which ideas are useful in a particular context for problem solving 3) why and how key ideas aid in problem solving, by reminding us of the systematic nature of mathematics (and the need to work on a higher logical plane in problem solving situations) 4) how an idea or procedure is mathematically defensible – why we and they are justified in using it 5) how to flexibly adapt previous experience to new transfer problems. Conceptual understanding in mathematicsGrantWiggins,April2014
- 27. Evaluate Problem-BasedLearning Cycle Self-Regulated Learning Independent Problem Solving Skills Content Knowledge Generalizing Adapted from Hmelo-Silver(2004) Homework time
- 28. Review material from past courses Trigger prior knowledge for an upcoming problem Inspire construction of new knowledge Introduce new terminology Practice new skill Challenge more able students See same new idea from different representation Concretize an abstract concept Introduce new technology skill Problem purposes
- 30. Why do some students respond negatively to Pbl? – Violates their expectations of mathematics student/teacher relationship – want learning to be easy – added stress & anxiety of questioning their intellect – Easier to assume fault lies with the
- 31. What can the teacher do? – Create relational form of trust – Acknowledge it’s not easy – Realize that what is obvious to us is not obvious to students – Realize the developmental level of the class/individual – Provide appropriate support
- 33. What can parents do? – Acknowledge it’s not easy & different – Understand the goals & skills – Trust the curriculum & teachers – Observe classes, see the mathematics being done and behaviors that are valued – Ask questions, seek to understand the benefits
- 34. ”Trying to solve a problem before being taught the solution, leads to better Learning, even when errors are made in the attempt.” “Elaboration is the process of giving new material meaning by expressing it in your own words and connecting it with what you already know.” – From “Make it Stick”
- 35. Questions? – Contact cschettinophd@gmail.com – Website and blog carmelschettino.org – @SchettinoPBL – Facebook CarmelSchettinoPhD
- 36. references – CNN/Money Magazine April, 2016 – PISA results, 2016 – Grant Wiggins Blogpost, https://grantwiggins.wordpress.com/2014/04/23/conceptual-understanding- in-mathematics/ – Inexpensive Techniques to Improve Education, Roediger & Pye, Journal of applied research in Memory & Cognition, September 2012 http://www.bryanburnham.net/wp- content/uploads/2014/01/Roediger-Pyc-2012-Inexpensive-techniques-to-improve-education-Applying- cognitive-psychology-to-enhance-educational-practice.pdf – “She didn’t teach, we had to learn it ourselves,” Dr. Maryellen Weimer, Faculty Focus, 2014https://www.facultyfocus.com/articles/teaching-professor-blog/didnt-teach-learn/ – Embedded Formative Assessment, William, D (2011), Solution Tree Press. – Hmelo-Silver, C. (2004) Problem-Based Learning: What and how do students learn? Educational Psychology Review. – Schettino, C. (2013) Dismantling the Birdcage: The experience of adolescent girls in a relational problem-based learning environment. – Brown, Roediger, McDaniel, Make it Stick, (2014) Belknap Press, Cambridge MA.
Editor's Notes
- Introduce myself –my degrees Tell my story that begins with the idea of “doing math” first click - what fourth grade "doing the math was" - enrichment, procedures, quickness on timed tests second click - what college "doing the math was" - enlightening, insightful, I am lucky that I stuck with it long enough to know the difference. Maybe you have as well, but the vast majority of students do not get to that level.
- Tell The Story of Maria being at the STEM Supervisors meeting in Florida and what Sol said. dilemma in math education today
- I have two children, my son Aiden is 20 and a freshman in college, and my daughter Aniella is 18 and a senior in high school. We did the whole college tour and the process and I can tell you I am so ready for April first of this year. That feeling once she knows where she’s going – I can’t wait. It’s so interesting that every school we went to and listened to the “info session” the admissions director or someone would mention some statistic like Young Millennials (those who graduated from 2006 to 2010) are on track to surpass four job changes by the time they hit age 32. Today, the average person changes jobs ten to fifteen times (with an average of 12 job changes) during his or her career. https://www.thebalance.com/how-often-do-people-change-jobs-2060467
- College students today are getting advice like this. technology is changing the world is changing so quickly in their career time
- 1. Communication Skills 2. Quantitative & Analytical Skills 3. Team Player 4. Technical Skills 5. Work Ethic 6. Planning & Organizational Skills 7. Interpersonal Skills
- Program for International Student Assessment even starting assessing not only math content but collaboration skills on their international assessment. New collaboration test – computer generated Seems that the US does much better at collaborating than at the actual mathematics
- It was clear to the PISA administrative board that the two skill sets do not go hand in hand, as I"m sure you can attest to from your own work and education experience.
- Nay-sayers of constructivist methods of teaching mathematics do not feel that you need to be able to communicate your ideas well in order to show that you have math ability. This statement shows how many mathematicians feel that working in isolation is valued and even sought after – however the number of us who are going to go onto become research mathematicians is pretty minimal. The rest of us work in the real world and need to be able to work with others, communicate effectively and still solve problems.
- Ask here what the ratio of red dots to all dots? This is something that many students have trouble retaining after middle school. The idea of ratios of different groups
- although many students who would say they are “bad at math”, visual concepts are easier? But the numeracy is harder. Especially comparison like this
- biology majors showed a loss of about 55 percent in their ability to solve problems, and a similar loss in their understanding of concepts. biology majors would have had few occasions to use their knowledge of mechanics in the seven semesters since they took the course. reviewing course content (or closely related content) in future classes offered protection from forgetting.
- there is extensive research regarding the ways in which college students lose knowledge of mathematics when it is not used, took no college math for their major, even if they were excellent math students in high school.
- first click - Cognitive Behaviorist External Truths exist that students must learn Learning a behavior that students exhibit by positive/negative reinforcement, learning is a change in behavior and needs to be repeated to be encoded second click - Constructivist All knowledge is socially constructed and dependent on the values, beliefs and people that are in the learning community Prior knowledge is always present and children have the capacity to access it when guided to its use Cognitive ability is directly challenged, students pushed to their ZPD
- When info is learned more slowly over time, distributed, retention is longer. This quote is showing that what is more important – it is very important how information get repeated - If only back/forth lecture, quizzes, etc. the information is not learned securely this is research done by cognitive scientists (in fact Roediger was one of the authors of Make it Stick)
- Three groups of students were given different ways of learning by reading a passage of information. 1 -The first group read a passage four times. 2-The second group read the passage three times and had test. 3-The third group read the passage once and was tested three times. Their performances on tests on the information in the passage was tested 5 minutes later and then one week later.
- So what does the research say affects student learning in the most positive ways? Well even cognitive behaviorists have to agree with constructivists on this one. click one - The distribution and interleaving of material and practice during learning. click 2 - Frequent assessment of learning (test-enhanced learning, continual assessment) click 3 - Explanatory questioning (elaborative interrogation and self explanation; having students ask themselves questions and provide answers or to explain to themselves why certain points are true).
- and those who originally were criticizing PBL as the "teacher doesn't teach" or "kids are just explaining things to themselves" - well the research says that in order to have learning be its most effective, this is actually a requirement. this idea of self-interrogation or self-explanation needs students to actively work to answer their own questions in this way.
- So what is the way of blending the [click] cognitive behaviorist views of best practices with the [click] constructivist best practices? click PBL yes it seems that what is asked of students in this type of classroom framework, when done well and deliberately, addresses the best practices of both learning theories and allows students to thrive as best they can.
- Here is a graph that I have given students before to try to analyze. We first look at the axes and try to rationalize what it might be telling us.. then click around and see if it helps
- First click: Their perception of the task and its context Second: Their knowledge about the task and what it will take to be successful Third: Their motivational beliefs, including their interest and whether they know enough to succeed
- describe the four main tenets and tell them that they can see the other details on my we site. Connected curriculum Justification not Prescription Shared Authority Ownership of Knowledge
- First ask the parents what they think of when they are asked what is "conceptual understanding of mathematics" take a few answers most educational theorists believe it is much more complex than just one idea so this is why it is so very difficult to teach conceptual understanding and most people just choose to teach procedures.
- How do students actually learn in PBL math classroom? start with Problem assigned very similar to the scientific method what is done in class and what is HW?
- When a student makes a decision of how to deal with a task or problem, they must choose where to direct their energy during the class or home work. click 1 - the can choose to use their energy to activate the behaviors that are effective in growing their learning (exs) click 2 - or they can choose to use their energy to activate the behaviors that will improve or protect their well-being (exs)
- The discomfort that arises with a new way of learning is foreign to students and truly brings them to the place of putting their energy in protecting their well-being the majority of the time.
- Wrapping up slide – this is the last slide before questions. Be sure to focus on the benefits from Make it Stick which is a congnitive sicentist written book.