Teaching Math to People Who Think They Hate It
Strogatz is a professor of applied mathematics at Cornell University. He has recently begun a course at the university helping non-math majors with what he calls, “Discovering the Art of Mathematics.” Strogatz explains that so many people despise math due to the way they learned it. According to Strogatz, we must change the way math is taught and that depends on more inquiry-based learning initiatives. This is the same type of learning that is being emphasized in education today, whereby students investigate material through experiments and other forms of hands on learning. In this manner, students become the source of their knowledge and teachers are facilitators. Students are more involved in their process of learning as their understanding is based on what they discover.
Strogatz explains that drilling and memorizing mathematical concepts do not always prepare students for the real world. If students are only taught in this manner, their analytical and problem solving skills will suffer. I agree that we need to teach students HOW to solve problems independently, but more importantly, provide them the tools to begin to tackle these difficult problems as it is only then where they may actually apply what they know. I like how Strogatz explains that “if we only teach technique, no one will want to play the music”. In my opinion I feel there must be balance of both technique and application. Teachers must teach students the technique and skills necessary to perform certain mathematical problems. However they must also provide students the context to apply these skills in order to measure their understanding. Simply put you cannot have one without the other and there must be a balance of the two!
As an educator I can admit that at times inquiry based learning can be quite a chaotic process, as students take control of their learning and teachers become facilitators. It is important for students to learn this responsibility at a young age and participate in creating knowledge for themselves. Teachers must provide students the tools and opportunities to investigate and remember to consolidate student learning at various times within a lesson!
I'm very glad you brought this up Alessandra, I must say that one of the challenges I've experienced in my teaching career has been inquiry based learning. I have a hard time matching the curriculum up with inquiry and then finding how to implement inquiry strategies into the classroom.
ReplyDeletePart of the challenge is in creating inquiry lessons, you need to select a goal (curriculum expectation) than create a problem whose solution necessitates satisfying that goal. One place where I was able to make this work was in helping students understand the relationship between height and area of the base, in determining volume. In my example I purchased a 4"x4" post 8' long, and had it cut across the diagonal so I then had two triangles 8' long with sides of 4", 4", and 5.6". The triangles were than cut down into manageable pieces, 1cm each. Students were allowed to use their rulers and work in groups to figure out to determine the volume of a stack of triangles (between 6 and 8 triangles). On their own most of the groups discovered that the area of a 1u thick triangle is the same as the volume and you just had to multiply the area of the base by the number of triangles to find the volume of the stack. They were also able to apply this same principal to a single prism whose thickness was more than one unit (11cm-15cm) using their ruler to measure all the important lengths. The rest of the groups required some prompting but made most of the steps on their own. Still this one success took far longer to reach (from a planning perspective) than a “traditional” style approach, here is your formula, let’s try it out.
I find coming up with lessons of this sort much more difficult, and I’m still not sure how inquiry this is, was the learning experience organic enough to be considered inquiry based, or was this just a hands on example?
The other side is these types of lessons require many more resources, and technology modeling these shapes and interactions (iPads and IWB’s) defeats the purpose of making it a real inquiry experience (at least in the above example, an iPad would not have done the lesson justice). How do we mesh the desire for inquiry with the substantially greater requirement for resources and planning?
I’m always excited to see examples of inquiry based lessons, I find it so rewarding when a student manages to achieve the lesson without my interference. I haven’t seen many examples and would love to hear of any examples others may come across.
Hi Ian,
DeleteHaving students write their own questions or develop their own investigation always works on their inquiry skills. Having them work in groups will enhance this process also. When graphing data, I always find that students have a hard time choosing which variable is the independent and dependent variable. Sometimes I get students to collect their own data, figure out which set of numbers is dependent upon the other and then figure out how to graph it.
Using technology or even chart paper is great for this. Once students get used to the process you can use it for an assignment for inquiry. Any time students are thinking about a situation and using their analysis skills they are working on developing their inquiry skills
Here is an interesting 6 minute video that introduces how inquiry based learning has helped a school near St. Louis. It introduces concepts of graffiti walls, student student teaching, conversation, the use of an IWB and computers.
https://www.youtube.com/watch?v=O5sfuo3ojr4
They also mentioned the PD teachers that have ran the sessions for the classroom teachers, eMINTS (http://www.emints.org/\); it is an organization from the mid western united states
Does anyone know if we have PD sessions like this in Ontario?
What is inquiry-based learning? How does it look like? Was the learning experience organic enough to be considered inquiry based? All these questions are so genuine for all teachers with a strong passion to teach the best they can in order to provide a rich and “fertile” environment for students` learning. My understanding of this was usually focusing more on providing hands-on experiences for all students, asking the “simple” but “deep” questions and letting them investigate/research, so they can connect their ideas to the real world and get better understanding of the knowledge/skill/lesson. Here is an interesting site about inquiry-based learning that may help us as well.
ReplyDeletehttp://www.thirteen.org/edonline/concept2class/inquiry/demonstration.html
It has samples of videos that show you real-life examples of inquiry being used in classrooms.