T. N. Carraher, D. W. Carraher, & A. D. Schliemann (1985) bring forth an interesting insight in “Mathematics in the streets and in schools”. Through their study, these researchers found children involved in the street markets making complex mental math calculations daily and successfully; however, when these same children were brought into a setting with similar pencil and paper mathematical tasks, many of them underperformed. Their results showed that “context-embedded problems were much more easily solved than ones without a context” (p. 24). In their context (the market) when solving successfully, “actual items in question were physically present” (p. 25). Too often in our math classrooms we are asking students to deal with operations and mathematical problems that are “in a very real sense divorced from reality” (p. 28).
As I have mentioned in previous posts, when considering this research and others we have encountered earlier in this course during our exploration of the Jasper series, I set out to revamp some of the problem solving I was using in my grade 3 math class. After exploring many problems that I tried to base in my students’ lives and make more real to them, our next project was to have students create their own problems. I had students use Google slides, accessed by an easy bit.ly address, to compile a class set of problems. Next, we took pictures to add to the slides that showcased the problems using as many props and settings relevant to the problem as possible. This collection was then put on our class blog for students to access from home over spring break to work on. If you would like to see how the project turned out visit: http://mrskostiuksclass.edublogs.org/2017/03/17/solve-me/
Using programs such as GLOBE and virtual field trips are ways to utilize the accessible affordances offered by technology in this day and age. GLOBE not only connects classes with real life scientists and experts in their fields, but it also provides a platform for students to contribute meaningful data to ongoing studies. Showing students future careers in different fields and ways they can contribute in the present day is impactful. Additionally, GLOBE “encourages students to understand the context of their own environment” (p. 12) by immersing them in conducting research around them. As evidenced in the Carraher, T. N., Carraher, D. W., & Schliemann, A. D. (1985) study, showing students how to solve problems in context is more likely to later be recalled in context when needed.
Similarly, Adedokun, O. A., Hetzel, K., Parker, L. C., Loizzo, J., Burgess, W. D., & Paul Robinson, J. (2012) find that virtual field trips can be “viable alternatives for providing students with learning opportunities and experiences that would have otherwise been unavailable to them” (p. 608) while exposing students to scientists and their real, authentic work.
In summary, I believe that providing students with as many experiences as possible that are situated in context and engaging in problem solving not only for problems they may encounter in the work force but also for problems they currently encounter in their everyday lives as children and students, we can better prepare them with skills necessary to succeed in the math and sciences.
Adedokun, O. A., Hetzel, K., Parker, L. C., Loizzo, J., Burgess, W. D., & Paul Robinson, J. (2012). Using Virtual Field Trips to Connect Students with University Scientists: Core Elements and Evaluation of zipTrips™. Journal of Science Education and Technology, 21(5), 1-12.
Butler, D.M., & MacGregor, I.D. (2003). GLOBE: Science and education. Journal of Geoscience Education, 51(1), 9-20.
Carraher, T. N., Carraher, D. W., & Schliemann, A. D. (1985). Mathematics in the streets and in schools. British journal of developmental psychology, 3(1), 21-29.
Great post! I really enjoyed looking through the word problems your students created. There was something there for everyone, from unicorns to hockey, as well as a good variety of leveled problems, which was neat to see. While many were more basic, I noticed that there were a few students who did include more in-depth problems which would appeal to students who wanted more of a challenge (i.e., Jasmine’s conversion from days to hours and minutes, and Azalea’s problem with birds flying in and away). I also had to smile at the KIJHL problem – your kids must be very excited about Kimberly’s big game tonight! You have inspired me to try something like this with my class – I can imagine my students will actually want to do word problems given an opportunity like this. I also loved reading the comments from the students to you at the end, showing their involvement in the class blog.
One classroom-based activity I do with my students is set up a mock restaurant. Some students are servers while others are patrons. We have plastic/paper money (that looks “real”) for students to use. Patrons receive $20.00 each and are given a menu to order from. Servers take their order, then add up the total. When presented with the $20.00, a server must then determine how much change to give back to the patron. When patrons received their change, they must double-check the amount to make sure they have received the correct amount back. The students love this and it does put the learning of “money math” into context for them.
I thought the points made in your post about the article by T. N. Carraher, D. W. Carraher, & A. D. Schliemann (1985) titled “Mathematics in the streets and in schools” were really interesting. I have not read this article, but it sounds like an article worth reading. It is interesting to me that many student workers in my own area do struggle to complete mental calculations for change because they never have to do it. Today, most people over the age of sixteen (at most I would guess) have a calculator in their pocket in the form of a cell phone, so the need for mental calculations is no longer there. Having said that, I have also travelled to a country where very young children are part of the street market economy and it is amazing to see how quickly they can calculate, because they do need to. What I found interesting in your response, was the fact that children who researchers observed “in the street markets making complex mental math calculations daily and successfully” then struggled to complete similar math problems within a more formal (let’s say ‘classroom’) setting. This, of course makes sense when I think about it in terms of embodied and contextual learning, but I have never really considered it before unfortunately.
While I feel that I have many more resources available for science now, I continue to struggle a bit with integrating digital-technology into my math curriculum. Thank you for inspiring me with you suggestions and for reminding me just how incredibly important context is when trying to engage and motivate students in the math classroom.
Thanks for sharing your restaurant project, Mary! I like the way you have structured it and I bet your students enjoy playing along and taking turns in different roles. I really like how it can become cross-curricular too with the writing, art, and drama.
Thanks for the great post and the link to your class problems. I have tried to get my students to create problems as well but it was quite lack luster. I think the use of technology and allowing the students to create problems they connect with is likely one of the keys to success. The visuals also add something as the students have to think about what would help solve the problem they have created. What would they need or want to see? I have become a very big fan of putting things in context for my students.
One of the math exercises I have changed up was that of surface area. Now instead of abstract problems that talk about wrapping a gift or painting a room or box, I actually have the students do it. For example, students are provided with a box (all differing shapes and sizes) they must use their box to calculate how much wrapping paper they would need. They have a partner double check. They then must bring their measurements to the clerk (that’s me) who cuts the amount of paper they desired and they have to see if works to wrap the gift (too much excess? not enough paper? could they wrap it differently and use less?) I have found this to be much more successful than just a word problem that talks about wrapping a gift.
I really like your wrapping paper problem, Catherine! I think that is a great, practical way to put learning into perspective and why you would need to know how to calculate these things. Thanks for sharing 🙂
Coming from the high school science point of view, I am definitely guilty of “asking students to deal with operations and mathematical problems that are “in a very real sense divorced from reality” as you stated in your post. This is especially true for grade 12 chemistry where the focus is on solving a variety of problems that gives the course a very dry and uninteresting experience for students. Your project on grade 3 students making their own set of problems turned out absolutely amazing!
I’d like to ask you a follow up question on the amount of time that it took for your class to generate these problems and the amount of scaffolding you had to do to get there. Secondly, how worthwhile in your opinion was investing in this time instead of simply moving on to the next topic in the curriculum?
Thanks for sharing,
Thanks for the response. I would say that we worked on the problems I revamped (putting more into context of my students’ everyday lives) for about 3 weeks as part of our math class. I found that this not only provided a good review of the concepts we have covered so far this year (addition, subtraction, money, measurement, skip counting) but it also encouraged my students to work together to solve the problems. By taking pictures of my students to incorporate them into each problem was very motivating for them too. I had them choose one of the problems to record in their digital portfolio (a video of them showing their work and explaining how to solve the problem). Next, we spent a few whole math periods (the previous problems only took up a portion of our period) coming up with problems, solving them, typing them up, and getting a related picture. I am excited to see who worked on them over the break and think it was definitely worth the extra class time to do a project like this!
“Showing students future careers in different fields and ways they can contribute in the present day is impactful. ”
I completely agree. In order to engage students, they need to see a purpose in their learning. They need to feel that their activities and learning matter. For some kids, this purpose needs to be very immediate, such as feeling like they can make a difference today, right now, in this moment. For some students, having a long-term goal to work towards or to situate their learning can motivate them to persevere through challenges and strive for more learning. Connecting students with experts is so valuable for its content and skill learning, but it can also be so valuable for intrinsically motivating and engaging students.
P.S. I love the approach you used to your students making their own problems!
Thank you Allison for sharing the anchored instruction problems you created in your class and the link to the slides in your blog! Your student-generated anchored problems were a great way for children to be invited into the mathematics. The mathematization of their worlds (snow, pets) was also accompagnied with a video of them showing their work and explaining how to solve the problem. In what ways do you think “making their mathematics thinking visible” was assisted by the affordances of the digital technologies you chose? Is there a connection you see between this aspect of Jasper problems and Globe/virtual field trips?
Thank you for the extensions to your math class practices,
I think whenever there is an opportunity to immerse learners in their learning, whether it be in a hands-on learning environment or through virtual reality, learning will be enhanced. With my particular math project I think that the use of Google slides enhanced and assisted the lesson because it was easily accessible through a bit.ly link (no sign in and easy to type in the address bar). Everyone could work on it at the same time (each student had their own slide that I had created and they just needed to find their own name), and I had the Google slide presentation projected on the board at the front of the room so students thought it was amusing to be able to watch their typing (and others’) live on the big screen. Not only was it motivating for students to see their own work up on the board, but it also added to their creativity by seeing other students’ ideas up on the screen as well.