Importance of Context in Lessons

Context is extremely important in everyday life as it provides us with the underlying reason for the idea.  Without context, we would often be confused during a conversation as there would be plenty of missing information and questions raised. For example, if I were having a conversation about the weather with a person and left out the location (or the context), they would be very confused as to what city I was referring to.  We learned this week that providing context in mathematics is extremely important to "hook" the students and answer the age old question of "why do we need to learn this?"
To begin, we looked at several open-ended problems in class and we attempted to tackle them in groups of four.  One of these examples we looked at was determining the number of possible toppings on a Harvey's burger if there was a total of 2048 combinations.  If this was a data management class, this would be a great introduction into combinations and permutations as it really catches the student's attention and gets them thinking.  Our group attempted to figure out the total combinations if there were one, two and three toppings and then tried to find a recursive formula using a table of values.  This was a good idea, but it was pretty time consuming as we had to make sure were weren't leaving out any possible combinations.  After this activity, we discussed the results as a group and found out that everybody tackled the problem differently but still achieved a similar answer of 11 toppings.  The context of this problem makes it a lot more applicable to everyday life compared to a boring old "black and white" textbook question.  I feel that providing context is important to keep the class engaged as well as provide an answer to "why do we need to learn this?"  In the Harvey's example, we actually touched upon Combinations and Pascal's Triangle which are both important topics in data management and statistics.  Essentially, even though we were trying to figure out the answer using a variety of creative ideas and methods we still brushed upon important mathematical concepts that are essential for the statistics unit. 

In relation to our class as future educators it can be seen that context can increase overall engagement in the subject and enhance critical thinking skills especially with open-ended problems.  The video attached to this blog shows a teacher describing her experience with cultural context being applied to fractions.  She states that her class is very much involved with sports and she feels that adding a context to fractions will help them understand greater.  She sets up her fractions with a basketball context and relates the shots made over the total shots taken.  For example, if a player made 7 shots out of a possible 10 in one game then they would have a field goal percentage of 7/10 or 70%.  She then moves into the process of solving proportions and cross multiplications all while still using the same context.  I believe that this is a really creative idea to use as students can use real NBA or WNBA player statistics while still understanding fractions clearly.  The students can then answer the question as to "why" themselves as now when watching basketball they can apply their fraction knowledge to real life NBA or WNBA statistics.