Chloe, thanks for revising your unit plan after our phone conversation last week!
However, I still find many elements of your unit plan very unclear -- so much so that I need to have another revision from you before I can pass you in this course! I'm sorry that this is coming so close to the beginning of the next term, but I really think you need to clarify (a) your project ideas and (b) your lesson plans before you will be ready to take on your long practicum.
First, your project: I find the topic very unclear, and I don't see a connection to the mathematics of set theory here! What I see is something that looks like an exploration of (some of) the knowledge needed to undertake a particular job or profession. I find the choice of a "rural train station master" an odd one in the context of an urban Grade 12 class in greater Vancouver -- there are very few train lines and rural station masters in BC at all these days, and this would probably not be a prominent career choice for your students! And in general, the topic seems to be one around career planning. I don't see anything of set theory notation, calculation or applications here, really. I think this project needs to be re-conceptualized so that it engages students in doing the mathematics of set theory in contexts interesting to them. Once you have come up with a good idea, you need to be able to describe it so that students (and your SA, FA and I) can understand clearly what tasks students will need to do. You should also include a clear marking rubric as an attachment.
Then, your three lesson plans: I find that the lesson plans are still very unclear in terms of what you will be doing, what your students will be doing, what kinds of mathematical problems, tasks or questions you will be having them work on, and how they will be working. I must emphasize that it is ESSENTIAL for you to be able to imagine the actual carrying out of these lessons with your students, step by step, and to walk through in your mind who will be doing what, with what materials, at what time, and with what learning objectives at any given point in the lesson. I do not see that here yet! Without that detailed planning, I don't understand how you will be able to take on the role of the teacher in leading the lessons.
I see clear themes in the example sets you are using in the lessons. Lesson 1 is focused on sets of geometric objects; lesson 2 on union and intersection notation and concepts and Venn diagrams; and lesson 3 on applying these concepts in the context of an imagined village.
However I find your plan confusing in the tangents you are taking in each of these topics. When considering geometric objects, are you focused on reviewing (or teaching for the first time) the equations for these objects, or their categorization in sets? The terminology of 'slanted lines' is confusing as vertical and horizontal lines can also be considered 'slanted'. I like the idea of considering circles as special cases of ellipses (a nice set theory concept), but talking about polygons whose sides don't intersect seems unnecessarily confusing to me. Are you going to develop definitions of these geometric object with the group? I don't understand what you're planning to do here.
In lesson 2, the talk about plants, fish, water, etc. is confusing, especially as you categorize them as 'resources' and 'elements that consume resources'. This is certainly NOT an Indigenous way of thinking about the living world (see the work of Dr. Robin Wall Kimmerer -- for example, her book Braiding Sweetgrass, to understand this idea), and it is not a clear example. It's great to include Susan Point's stained glass windows, but how are you connecting these to both Indigenous ways of knowing and mathematical set theory?
In lesson 3, the categories for your imagined village seem far from complete. For example, how would you categorize people who are exactly 17 or 65 years old? (You need some ≤ signs here). The services you have listed are not comprehensive, and perhaps could not be. This makes the example confusing.
Additionally, in each lesson you plan to spend 20 minutes telling the history of set theory -- but you haven't given any detail about how or what you will talk about, and how students are to engage with this. I think you will confuse your SA and FA (and me) with your mention of 'erasing the vertical walls of the classroom', of student and teacher birds, and instructions to these Grade 12 students to "Work with family members, parents, aunts, uncles, neighbors, grand parents or anyone you know. Enjoy family times, oral lessons, and once-upon-a-time story from a friend of grandma." I don't think your students will understand what you are asking of them!
Thanks for including the pages from the workbook you are using in the class. I find the exercises given there are clearly engaging the students in working with mathematical set theory notation and concepts -- which is great. What I don't see is the connection between your proposed lesson plans and much of what they are expected to learn to do these exercises and generally understand basic set theory.
As you might have noticed, I'm quite concerned about your present skills in taking your own strong knowledge and capability in mathematics (which I have seen demonstrated many times in both our EDCP 342 and 442 classes!) and bringing it into effective pedagogy with your high school students. I need to see a clear connection between what you would like your students to learn and the activities of the classroom you will be leading that will get them involved with learning and understanding these things. That is the work we undertake as teachers!
Please feel free to get in touch with questions, suggestions and ideas over the next few days, and let's work on getting you to the place where you are ready to start teaching in February.
hanks for doing these big revisions to your unit plan, Chloe! This is much closer to what would be expected, and we can now consider that you have completed this assignment in a satisfactory way for this course. You don't need to do any further revisions for me, although I expect that your FA and SA might want further work on this for your practicum teaching.
Some suggestions: • The new project is interesting and challenging enough, although choosing people's skills with a random number generator is not exactly the way things go in real life! Noneless, it's an interesting project idea, and can also raise interesting questions about how you can generate truly random numbers!
• Your new lesson plans use problems that look like they're straight from a textbook. You are allowed to use textbook word problems too, so that's OK -- but you may want to vary things with some less textbook-style questions along the way.
• You'll need to work on timings and group work. Groups of 5 are really too large -- 2, 3 or maybe 4 are optimal sizes for group work I think. Your lesson 1 timings seem off to me -- that doesn't look like enough material or activities for the length of the class. The activities seem a bit too simple and general to me too, and if it were me, I would get into the gist of the mathematical ideas a bit sooner. Be sure to talk with your SA about all this.
• Think about how you can make the historical talks more involving for your students -- otherwise, they might just 'turn off' for those ten minutes, especially if they are not accountable for understanding or remembering what you are talking about here. Could you incorporate a puzzle or open-ended question as part of these, for example? Is there some way to make it really memorable and engaging?
Thanks again for all the great work and all your contributions to class. Happy New Year!
Chloe, thanks for revising your unit plan after our phone conversation last week!
ReplyDeleteHowever, I still find many elements of your unit plan very unclear -- so much so that I need to have another revision from you before I can pass you in this course! I'm sorry that this is coming so close to the beginning of the next term, but I really think you need to clarify (a) your project ideas and (b) your lesson plans before you will be ready to take on your long practicum.
First, your project: I find the topic very unclear, and I don't see a connection to the mathematics of set theory here! What I see is something that looks like an exploration of (some of) the knowledge needed to undertake a particular job or profession. I find the choice of a "rural train station master" an odd one in the context of an urban Grade 12 class in greater Vancouver -- there are very few train lines and rural station masters in BC at all these days, and this would probably not be a prominent career choice for your students! And in general, the topic seems to be one around career planning. I don't see anything of set theory notation, calculation or applications here, really. I think this project needs to be re-conceptualized so that it engages students in doing the mathematics of set theory in contexts interesting to them. Once you have come up with a good idea, you need to be able to describe it so that students (and your SA, FA and I) can understand clearly what tasks students will need to do. You should also include a clear marking rubric as an attachment.
ReplyDeleteThen, your three lesson plans: I find that the lesson plans are still very unclear in terms of what you will be doing, what your students will be doing, what kinds of mathematical problems, tasks or questions you will be having them work on, and how they will be working. I must emphasize that it is ESSENTIAL for you to be able to imagine the actual carrying out of these lessons with your students, step by step, and to walk through in your mind who will be doing what, with what materials, at what time, and with what learning objectives at any given point in the lesson. I do not see that here yet! Without that detailed planning, I don't understand how you will be able to take on the role of the teacher in leading the lessons.
ReplyDeleteI see clear themes in the example sets you are using in the lessons. Lesson 1 is focused on sets of geometric objects; lesson 2 on union and intersection notation and concepts and Venn diagrams; and lesson 3 on applying these concepts in the context of an imagined village.
ReplyDeleteHowever I find your plan confusing in the tangents you are taking in each of these topics. When considering geometric objects, are you focused on reviewing (or teaching for the first time) the equations for these objects, or their categorization in sets? The terminology of 'slanted lines' is confusing as vertical and horizontal lines can also be considered 'slanted'. I like the idea of considering circles as special cases of ellipses (a nice set theory concept), but talking about polygons whose sides don't intersect seems unnecessarily confusing to me. Are you going to develop definitions of these geometric object with the group? I don't understand what you're planning to do here.
In lesson 2, the talk about plants, fish, water, etc. is confusing, especially as you categorize them as 'resources' and 'elements that consume resources'. This is certainly NOT an Indigenous way of thinking about the living world (see the work of Dr. Robin Wall Kimmerer -- for example, her book Braiding Sweetgrass, to understand this idea), and it is not a clear example. It's great to include Susan Point's stained glass windows, but how are you connecting these to both Indigenous ways of knowing and mathematical set theory?
ReplyDeleteIn lesson 3, the categories for your imagined village seem far from complete. For example, how would you categorize people who are exactly 17 or 65 years old? (You need some ≤ signs here). The services you have listed are not comprehensive, and perhaps could not be. This makes the example confusing.
Additionally, in each lesson you plan to spend 20 minutes telling the history of set theory -- but you haven't given any detail about how or what you will talk about, and how students are to engage with this. I think you will confuse your SA and FA (and me) with your mention of 'erasing the vertical walls of the classroom', of student and teacher birds, and instructions to these Grade 12 students to "Work with family members, parents, aunts, uncles, neighbors, grand parents or anyone you know. Enjoy family times, oral lessons, and once-upon-a-time story from a friend of grandma." I don't think your students will understand what you are asking of them!
ReplyDeleteThanks for including the pages from the workbook you are using in the class. I find the exercises given there are clearly engaging the students in working with mathematical set theory notation and concepts -- which is great. What I don't see is the connection between your proposed lesson plans and much of what they are expected to learn to do these exercises and generally understand basic set theory.
ReplyDeleteAs you might have noticed, I'm quite concerned about your present skills in taking your own strong knowledge and capability in mathematics (which I have seen demonstrated many times in both our EDCP 342 and 442 classes!) and bringing it into effective pedagogy with your high school students. I need to see a clear connection between what you would like your students to learn and the activities of the classroom you will be leading that will get them involved with learning and understanding these things. That is the work we undertake as teachers!
ReplyDeletePlease feel free to get in touch with questions, suggestions and ideas over the next few days, and let's work on getting you to the place where you are ready to start teaching in February.
Warm wishes
Susan
I've uploaded your new revised unit plan here: https://drive.google.com/file/d/1u9Xrfylc2zs9D6e85kDQ6crY431t8ZPt/view?usp=sharing
ReplyDeletehanks for doing these big revisions to your unit plan, Chloe! This is much closer to what would be expected, and we can now consider that you have completed this assignment in a satisfactory way for this course. You don't need to do any further revisions for me, although I expect that your FA and SA might want further work on this for your practicum teaching.
ReplyDeleteSome suggestions:
• The new project is interesting and challenging enough, although choosing people's skills with a random number generator is not exactly the way things go in real life! Noneless, it's an interesting project idea, and can also raise interesting questions about how you can generate truly random numbers!
• Your new lesson plans use problems that look like they're straight from a textbook. You are allowed to use textbook word problems too, so that's OK -- but you may want to vary things with some less textbook-style questions along the way.
• You'll need to work on timings and group work. Groups of 5 are really too large -- 2, 3 or maybe 4 are optimal sizes for group work I think. Your lesson 1 timings seem off to me -- that doesn't look like enough material or activities for the length of the class. The activities seem a bit too simple and general to me too, and if it were me, I would get into the gist of the mathematical ideas a bit sooner. Be sure to talk with your SA about all this.
• Think about how you can make the historical talks more involving for your students -- otherwise, they might just 'turn off' for those ten minutes, especially if they are not accountable for understanding or remembering what you are talking about here. Could you incorporate a puzzle or open-ended question as part of these, for example? Is there some way to make it really memorable and engaging?
Thanks again for all the great work and all your contributions to class. Happy New Year!