Five Ideas for 21st Century Math Classrooms

Gasser, Kenneth W. "Five Ideas For 21st Century Math Classrooms." American Secondary Education 39.3 (2011): 108-16. Print.

I am reading this article because:

It is about problem-based mathematics in the classroom,

it is about mathematics instructions in a secondary school

it is a recent article,

it addresses 21 century skills

it is teacher written

Much of this article is motivated by ideas the author found in three places.

1.  "A Mathematician's Lament" - Paul Lockhart

2.  Various articles from and about the "Partnership for 21st century skills"

3.  "A Whole New Mind" - Daniel Pink

All three of these sources are worth looking at for my action research because they deal with progressive thinking about mathematics education, 21 century skills and or problem based mathematics.

Another article referenced in the References section is:

Coticˇ, M. & Zuljan, M. (2009). Problem-based instruction in mathematics and its

impact on the cognitive results of the students and on an affective-motivational

aspects. Educational Studies, 35(3), 297-310.

This looks like a relevant article for me, but I could not find it available in full text on WIlson Web so it will have to wait.

Gasser is a teacher of mathematics with six years experience.  In preparing the article he draws on his experiences as an educator, comparative studies of students across cultures and his knowledge of the literature surrounding the world our students will be facing.  With that in mind he addresses 5 changes to mathematics classrooms that he believes will help our students compete globally in the modern world.  These changes are:

1.  Incorporating problem based instruction

2.  Fostering student led solutions

3.  Encouraging risk taking

4.  Having fun

5.  Providing ample collaborations time

Incorporating problem based instruction

His ideas about what problem based learning matches my experience with the problem sets used by Exeter and at the conference I attended on problem based learning.  His description of PBL is not as expansive as the descriptions I've read in other articles specifically relating to PBL.  For instance, his second, fourth and fifth suggestion for change are already an integral part of the problem based learning approach as defined in articles like:  Hmelo-Silver, C. E. , & Barrows, H. S. (2006). Goals and Strategies of a Problem-based Learning Facilitator.  This difference is important to me right now because I am starting to feel like there are two separate paradigms that go by the same name.  Or perhaps PBL, from a mathematics education perspective, has branched off and has become less broadly defined.  I need to come to an understanding of what is meant when other refer to PBL and what is meant when I refer to it.

Fostering Student Lead Solutions

This section strikes a chord with me because it hits on some of the reasons I am looking to implement PBL more comprehensively in my own classroom.  Specifically having students analyze, organize and present information, seems to me to be one of the keys goals of a good mathematics classroom.  Getting them to look for their own paths to find solutions rather than waiting for the 'recipe' and then applying that recipe to problems that are only superficially different seems wrong headed, boring and not quite learning.  Gasser cites studies that show that the student lead solution approach has the potential to make students better thinkers.  In light of the 21st century dilemma of how to develop global citizens that can accomplish jobs that cannot be outsourced or done better by a computer it seems that  turning out better thinkers ought to be a necessity.

Risk Taking

This section, touched on the importance of fostering students who are not afraid to take risks and who see failure as a necessary step in the path to success.  It reminded me of all the things that I like about Judo Math and its emphasis on not being afraid to fail.  Decoupling failure and shame is a necessary component of risk taking.  In a PBL environment this means creating a culture where questions are as important as answers and that evidence of thought when presenting problems and solutions is as important (and probably more important than) as correct solutions.  It is not about what the right answer is it is about what was learned in the process of finding it.

Having Fun

This suggestion is not an explicit component of PBL as I have seen it defined previously but it makes perfect sense.  Fun in the sense that  problems and experiences are compelling and worth solving to those charged with solving them.  Gasser cites evidence that effective learning does not take place in environments that are not motivating.  His ideas for instilling fun onto his lessons are a bit different than mine because they seem untied to the problems.  But I do plenty of the things he touches on in and ad hoc fashion.

Collaboration Time

Gasser talks about the importance of collaboration time both for students and for teachers.  He notes the ability to collaborate effectively as a 21st century skill.  He also notes that there is a benefit to allowing students to share their strengths, solutions and questions with others.

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I didn't get much in the way of tactics or techniques from this article but I do think the author does a great job of encapsulating what I want to mean when I say Problem Based Learning.  There are additional ideas that he doesn't include but these are good broad stroked to start from.  I wonder if there is enough detail to sufficiently distinguish this from Project Based Learning.