"All you can change is you." True of so much of life.
I guess I didn't quite understand the definition of an "authentic" task. I would have guessed an "authentic" task is one where the educator doesn't know the answer and so learns with the student? What would you call that?
Cathy Fosnot calls them "Truly Problematic Situations" and that a good task does not need to be real, it needs to be realizable. All of that is only true if the teacher is honestly interested in the students as developing reasoners. Nicely said Dan!
Edward de Bono wrote many books on problem solving and thinking. All of them I love. He wrote one book called Children Solve Problems that is full of "authentic problems" which I look at as problems with no immediate answer and many pathways to solutions and interestingly many solutions. They are problems like How do you get an elephant onto the second floor of a building? or How do you keep a cat and dog in the same house from fighting?" These problems open up children's minds to the possibilities and delight them in the many ways they can think about them. Then there are problems I like to call Magic. Take 2 pieces of heavy paper that is 9" by 12". Coil one into a cylinder that is 9' tall and carefully tape it together with no overlapping and take the second and coil it into a cylinder that is 12" tall and tape it the same way. Then place the cylinder that is 12" tall inside the cylinder that is 9" tall and ask "If I fill the 12" cylinder with rice and then lift it up emptying it into the the cylinder that is 9" tall how, high will the rice fill the cylinder? and why do you think that? What happens is Magic. These are authentic problems in my mind. Problems like what do you notice about the three tennis balls packed for sale in the plastic cylinder and so on are authentic. I want young children to FEEL like mathematicians when they are working not just follow a teacher's taught plan. That I think makes the problem authentic.
"Liz is actively seeking divergence, rather than convergence." Although this wonderful post isn't about AI, I'm obligated to note that *by design* chatbots based on large-language models do the very opposite of this. And of course they can't move around either to physically illustrate the change of position on a number line. What a great example of human teaching using technology in ways that benefit human students.
Authenticity is hard to define for others as it’s a subjective and highly contextualized concept. (This is not limited to math, of course). You are right that the teacher is the mediating (and therefore defining) force in whether a task is perceived as authentic by his or her students. But I do think that the move toward “authentic tasks” in C&I and educational publishing is still a good thing. If it’s a choice between an end-of-chapter or IXL worksheet or a set of “authentic tasks” that place math concepts within a context of some sort, then we’re making (a little) progress, no?
I loved watching her encourage the kids experimenting with the "greater than" numbers instead of jumping to an example of "less than" numbers.
It makes me think of the weather "future scan" on the news. There are so many variables involved and so many different yet similar models.
This teacher allowed students to develop multiple models to accomplish the same goal. I anticipate kids trying to get a number "as close as possible" to achieve the same thing.
Since we are on the homestretch of the school year with the stress of end of year testing, this video was just what I needed.
As for real world tasks—yeah, show me how simplifying rational expressions in the Algebra 2 classroom translates into a real world task. I appreciate Dan Meyer's expression "Math is the aspirin we use when we have a mathematical headache" (paraphrased) Using that approach, meaning, how to be efficient, how to extend integer fraction techniques, how to determine values that fail in the original problem and not in the reduced form, helps my students immensely.
I develop real-world tasks for math and personal finances. In Algebra, I use sports and activities like hitting tennis balls to collect data for Statistical data analysis. Some real world and some fun needs to be implemented in the math classroom.
"All you can change is you." True of so much of life.
I guess I didn't quite understand the definition of an "authentic" task. I would have guessed an "authentic" task is one where the educator doesn't know the answer and so learns with the student? What would you call that?
Cathy Fosnot calls them "Truly Problematic Situations" and that a good task does not need to be real, it needs to be realizable. All of that is only true if the teacher is honestly interested in the students as developing reasoners. Nicely said Dan!
Edward de Bono wrote many books on problem solving and thinking. All of them I love. He wrote one book called Children Solve Problems that is full of "authentic problems" which I look at as problems with no immediate answer and many pathways to solutions and interestingly many solutions. They are problems like How do you get an elephant onto the second floor of a building? or How do you keep a cat and dog in the same house from fighting?" These problems open up children's minds to the possibilities and delight them in the many ways they can think about them. Then there are problems I like to call Magic. Take 2 pieces of heavy paper that is 9" by 12". Coil one into a cylinder that is 9' tall and carefully tape it together with no overlapping and take the second and coil it into a cylinder that is 12" tall and tape it the same way. Then place the cylinder that is 12" tall inside the cylinder that is 9" tall and ask "If I fill the 12" cylinder with rice and then lift it up emptying it into the the cylinder that is 9" tall how, high will the rice fill the cylinder? and why do you think that? What happens is Magic. These are authentic problems in my mind. Problems like what do you notice about the three tennis balls packed for sale in the plastic cylinder and so on are authentic. I want young children to FEEL like mathematicians when they are working not just follow a teacher's taught plan. That I think makes the problem authentic.
"Liz is actively seeking divergence, rather than convergence." Although this wonderful post isn't about AI, I'm obligated to note that *by design* chatbots based on large-language models do the very opposite of this. And of course they can't move around either to physically illustrate the change of position on a number line. What a great example of human teaching using technology in ways that benefit human students.
it seems like a simple concept. any time i’m surprised, i’m inspired to learn.
Authenticity is hard to define for others as it’s a subjective and highly contextualized concept. (This is not limited to math, of course). You are right that the teacher is the mediating (and therefore defining) force in whether a task is perceived as authentic by his or her students. But I do think that the move toward “authentic tasks” in C&I and educational publishing is still a good thing. If it’s a choice between an end-of-chapter or IXL worksheet or a set of “authentic tasks” that place math concepts within a context of some sort, then we’re making (a little) progress, no?
I loved watching her encourage the kids experimenting with the "greater than" numbers instead of jumping to an example of "less than" numbers.
It makes me think of the weather "future scan" on the news. There are so many variables involved and so many different yet similar models.
This teacher allowed students to develop multiple models to accomplish the same goal. I anticipate kids trying to get a number "as close as possible" to achieve the same thing.
Since we are on the homestretch of the school year with the stress of end of year testing, this video was just what I needed.
As for real world tasks—yeah, show me how simplifying rational expressions in the Algebra 2 classroom translates into a real world task. I appreciate Dan Meyer's expression "Math is the aspirin we use when we have a mathematical headache" (paraphrased) Using that approach, meaning, how to be efficient, how to extend integer fraction techniques, how to determine values that fail in the original problem and not in the reduced form, helps my students immensely.
Thanks again!
I develop real-world tasks for math and personal finances. In Algebra, I use sports and activities like hitting tennis balls to collect data for Statistical data analysis. Some real world and some fun needs to be implemented in the math classroom.
pardon my naivete. Can I come to know you do not understand x?
Excuse my naivete, Can I know you do not understand x.?
The formatting for my response didn't show up right, so I'm responding with a blog post -- I promise doing so was not deliberate self-promotion!
https://writinginthestream.com/2024/04/24/response-to-authentic-tasks-have-failed-us/