Math Maker: Fun With Recipes!

Hello teacher friends!!

Last week was "my math week". Alas, it was my turn to present a math learning activity to our class. Our attention was directed toward ratios, proportions, unit rates, and percentages, which can all be interrelated, however, my activity primarily focused on ratio and proportion. I decided it would be best, just as every lesson in math, to form a connection to real-world contexts so the class would be more intrigued when it finally came time to complete the activity. In doing so, I chose to connect proportionate reasoning to recipes. This excited me!! I do think the demonstration of a recipe, and sorting through the ingredients together as a class would have been a lot more fun, but due to time constraints, I was not able to execute this idea. So I stuck to my other plan. 

Coconut Cake! Photo taken by me.

Each teacher candidate was announced the role of a chef; given a "recipe card" and were instructed to modify the recipe that I provided to serve more people. This would challenge them to ensure all of their ingredients were proportionate. As we know, the proportional relationship between ingredients must be correct in order for the final product to have the right texture, consistency, and of course - to masterfully present a deliciously satisfying taste! For some, this may have been a new concept because I realize not every one in our class are world-class chefs. When I did ask, there were many people who do cook or bake. It would be more interesting to see what strategies the "non-bakers and non-cookers" came up with. Some people decided to increase the ingredients by sticking to the addition of fractions. For the more skilled people in the kitchen, mental math was good enough.

 I did struggle with the idea that this activity may have not been challenging enough, especially for our age group. I feel as though decreasing the amount of ingredients, to an odd number, would have been a little more difficult. Upon receiving feedback from Rebecca, she told me that ratios were not necessarily needed to figure out the answers. A more thoughtful extension, she suggested, would have been to provide a ratio of ingredients (3 parts liquid: 5 parts flour) and tell them that they would use a certain amount of flour. Then, the students would need to decipher the amount of the rest of the required ingredients. 

Perhaps my slight confusion in forming this activity was a direct reflection of my misunderstanding of the curriculum (specific) expectations. It seems to be something most teacher candidates are struggling with, and that is why the second half of our class time was spent matching specific math curriculum expectations to the grade level. Working in partners, we played this unique "matching game".

Photo taken by me.

 My partner and I seemed to get most correct, although we noticed the very close similarities between some expectations. We really appreciated Rebecca encouraging us all to analyze the curriculum more closely in an interactive activity, as I am sure this will benefit us in future lesson planning.

I think the other girls who presented their activities on unit rates and percents did an awesome job, and these activities are surely something I look forward to every week. Especially when I know these are games I could implement into my own math classes one day. Thanks for your wonderful tips, every one!

Until next time,

Have a beau-tea-ful day! :)

Miss Capano

Math Madness

Hello friends and future educators!

You guessed it...back for more! Two math blog posts in two days. Who am I?! This is truly math madness. But I did mention I would try to become more consistent with this! (alright, really I'm just playing catch up...woops!)

Now to get to the nitty gritty. Last week's math class before the start of reading week was rather insightful, but I would expect nothing less from Rebecca's class. She consistently offers teacher candidates the most helpful advice in order to guide us on our journey in the pre-service teacher education program and ease our minds about the difficulties. A main topic of discussion during this class was the use of manipulatives - often a necessary (and of course beneficial) addition to lessons in mathematics. Manipulatives can consist of anything from blocks, wheels, coins, lego, geoboards, counters, bead strings, cards, and measuring tapes. They typically aid a student's comprehension and are thus not a main source of learning, nor should they be. They simply add variety and depth in helping children connect mathematical theories to real-life examples. That is, forming a relationship between abstract and concrete notions.

What strategies can a teacher use to ensure students do not become dependent on manipulatives? 

Well, for starters, I think a basic way to avoid dependence is to have manipulatives made available for only certain activities, and not the entire lesson. Have your students address a math problem first without the manipulative, and then introduce the manipulative if they are struggling to grasp the concept or to present a new challenge in solving the same question. Have them understand why the use of the adjunct is helpful, and not aimlessly use the items as "toys". Just as we wouldn't want our students to become dependent on using a calculator, we also wouldn't want them to become dependent on any manipulative of choice. They are used to support a child's learning experience, not as an isolated teaching technique, and therefore should not be treated as such. What if we rewarded our students to use manipulatives after demonstrating good behaviour? Perhaps we could associate it with a points-rewards system. This could get them excited and soon enhance their enjoyment around the subject. Or maybe we could even reserve our use of these tools for the end of the week, on a Friday. Whatever we decide, it is still important to realize the validity in having three-dimensional models that are visually stimulating for some learners. Manipulatives are definitely significant in having symbolic representations and promoting interaction within the classroom.

Now it's time for me to begin preparing my math activity presentation for next week! 

See you all then, but until then,

Have a beaut-tea-ful evening and enjoy the rest of your reading week!

Miss Capano

Let's Talk Math!

Hello friends and future educators!

So, it is no surprise I have put my Math blogging on the back burner. Turns out I haven't completely stopped that bullying behaviour toward the subject, have I? Haha. But I promise to be more consistent with it, especially with all of the fascinating learning techniques we are introduced to with each passing week!

Two weeks ago, our class was challenged with a very interesting math problem called a tarsia puzzle. It is a type of jigsaw puzzle that requires you to solve various problems on triangle pieces in order to create a hexagon as a final product. Working in pairs, we arranged the triangle expressions so that the equivalent expressions were matched. It is a great puzzle for practicing algebra questions, however I feel that this activity can be used with almost any topic or subject! It makes for a great "setting the stage" activity, just how Rebecca introduced the task to us. Although, it did catch us all off guard and took longer to complete than expected, so perhaps this may be an excellent core learning activity instead. The students will definitely become immersed in trying to form the hexagon itself, therefore the timing of this activity is a factor that must be considered. Regardless of how you may choose to implement it, the tarsia puzzle is beneficial for visual learners while also encouraging cooperation and teamwork for learners all across the board. There are various free downloadable tarsia puzzles found online which is incredibly convenient for us educators!

Tyler, Paul. "Tarsia Floor Puzzle". (23, Jan, 2007) Retrieved from: https://www.flickr.com/photos/glazgow/1535224849

As a class, we also discussed the differences between conceptual knowledge and procedural knowledge and their importance in relation to mathematics. Procedural knowledge is the "toolbox" of problem solving: the equations, formulas and algorithms that assist students in reaching solutions. But do the students truly understand their use of these tools? This is what conceptual knowledge touches upon. Most of us agreed that a balance of both procedural and conceptual knowledge is required in order for students to fully grasp concepts. Procedural knowledge is easily attainable by strict memorization, but conceptual knowledge is what takes learning a step further in understanding the why or how of the procedural steps. Students may then carry that conceptualization into future learning situations; not heavily dependent on memorized facts but rather on connections they have made with the content. As a future teacher of J/I mathematics, I will be mindful in creating meaningful, relevant questions pertaining to the subject. This way, students may formulate a deeper relationship with math and better communicate their understanding of subject matter in assessments, as well as in real life situations.

"..if the curriculum we use to teach our children does not connect in positive ways to the culture that young people bring to school or prepare them for the future they are building towards, it is doomed for failure." (Delpit, L. D.)

Until next time,

Have a beau-tea-ful day!

Miss Capano  

References:

Delpit, L. D. (2012). "Multiplication is for white people." Raising expectations for other people's children. New York: NEW Press.