Upon reading Authentic Tasks in a Standards-Based World by Edwards, Harper, and Cox, my inner battle begins to rage once more. My desire to take students to a deeper level in their learning is coupled with my desire to cover all of the standards. But how can I do both? The limiting factor is always this: time. Whether we like to admit it or not, the decisions we make as teachers are all too often dictated by time.
In the Authentic Tasks article, the authors use “The Meeting for Lunch Problem” as an exemplar. Students were given a very open ended question that asked where three people in different cities could meet for lunch such that each person had to travel the same distance to get there. Students were given the freedom to investigate and most of them successfully discovered that finding the circumcenter was indeed the method that would lead to a solution. If I am being honest with myself, this is where I would have likely ended the activity. After all, this lesson provided students with an application to a required standard. Check it off and move on, right? Not for Edwards, Harper, and Cox! They encouraged their students to ask probing questions and allowed them to take the activity in a new direction. When students discovered that in some triangles, the circumcenter was obviously out of the way for the three travelers and a foolish way to decide on a meeting place, they developed a revised goal in the “Meeting for Lunch” goal. Together with their teachers, they decided to find the meeting point that would result in the least total distance traveled for all three people involved. Even though this was uncharted territories (even for the teachers), they pressed on. After a lot of studying and a bit of research, they found that the “Fermat Point” would achieve their goal of finding the least total distance. Now, mind you, the Fermat Point is not mentioned anywhere in the Common Core State Standards (CCSS). Does that make studying it a waste of time? Absolutely not. These students applied their knowledge of the various circle centers in this problem as a lead-in to the critical thinking and problem solving that enabled them to extend their learning. They performed at a higher Depth of Knowledge level than they would have had they stopped after simply finding the preconceived circumcenter solution. The students took ownership of their learning.
Unfortunately, in the back of mind is still this issue of time. I wish I could push my students to a deep level of understanding with each and every topic, but I would simply run out minutes in the day and days in the school year. Even though I can’t turn every lesson into a three day mini-project in the computer lab, I must strive for balance. When I see a great learning opportunity to push my students, I must take it. Other times I must use my professional judgement to decide when that extra push isn’t quite as necessary. The most important thing is that my students are learning how to think at a deeper level on a regular basis.
Another highlight of the article for me was its quote from the Common Core State Standards for Mathematics (CCSSI 2010):
These Standards do not dictate curriculum or teaching methods... [A] teacher might prefer to teach a topic of his or her own choosing that leads, as a byproduct, to students reaching the standards for topics A and B. (p. 5)
How refreshing! For some reason, this quote makes me feel better about going deeper with some standards than with others. The very institution that developed said standards is giving me permission to do it my way! I can hardly wait.
Professor Golden: I would appreciate feedback regarding the detail of my writing. Did I give enough detail to make my viewpoint known? Did I provide the right amount of information about the article to facilitate my reader’s understanding? Thanks!
In the Authentic Tasks article, the authors use “The Meeting for Lunch Problem” as an exemplar. Students were given a very open ended question that asked where three people in different cities could meet for lunch such that each person had to travel the same distance to get there. Students were given the freedom to investigate and most of them successfully discovered that finding the circumcenter was indeed the method that would lead to a solution. If I am being honest with myself, this is where I would have likely ended the activity. After all, this lesson provided students with an application to a required standard. Check it off and move on, right? Not for Edwards, Harper, and Cox! They encouraged their students to ask probing questions and allowed them to take the activity in a new direction. When students discovered that in some triangles, the circumcenter was obviously out of the way for the three travelers and a foolish way to decide on a meeting place, they developed a revised goal in the “Meeting for Lunch” goal. Together with their teachers, they decided to find the meeting point that would result in the least total distance traveled for all three people involved. Even though this was uncharted territories (even for the teachers), they pressed on. After a lot of studying and a bit of research, they found that the “Fermat Point” would achieve their goal of finding the least total distance. Now, mind you, the Fermat Point is not mentioned anywhere in the Common Core State Standards (CCSS). Does that make studying it a waste of time? Absolutely not. These students applied their knowledge of the various circle centers in this problem as a lead-in to the critical thinking and problem solving that enabled them to extend their learning. They performed at a higher Depth of Knowledge level than they would have had they stopped after simply finding the preconceived circumcenter solution. The students took ownership of their learning.
Unfortunately, in the back of mind is still this issue of time. I wish I could push my students to a deep level of understanding with each and every topic, but I would simply run out minutes in the day and days in the school year. Even though I can’t turn every lesson into a three day mini-project in the computer lab, I must strive for balance. When I see a great learning opportunity to push my students, I must take it. Other times I must use my professional judgement to decide when that extra push isn’t quite as necessary. The most important thing is that my students are learning how to think at a deeper level on a regular basis.
Another highlight of the article for me was its quote from the Common Core State Standards for Mathematics (CCSSI 2010):
These Standards do not dictate curriculum or teaching methods... [A] teacher might prefer to teach a topic of his or her own choosing that leads, as a byproduct, to students reaching the standards for topics A and B. (p. 5)
How refreshing! For some reason, this quote makes me feel better about going deeper with some standards than with others. The very institution that developed said standards is giving me permission to do it my way! I can hardly wait.
Professor Golden: I would appreciate feedback regarding the detail of my writing. Did I give enough detail to make my viewpoint known? Did I provide the right amount of information about the article to facilitate my reader’s understanding? Thanks!
RSS Feed