Week 6: Call to Action (Option 2)

16 Dec 2017 4:42 PM | Anonymous member (Administrator)

Review Papert's image of low-threshold, high-ceiling problems. Choose a problem from an upcoming lesson and talk about how to lower its threshold and raise its ceiling. What changes did you make? Once you're done, think about the same problem in terms of open or closed beginnings, middles, and ends, as Dan Meyer described. Any further changes?


  • 17 Dec 2017 8:46 AM | Deleted user
    I decided to rework a Math Forum Problem, Holiday Ornaments from the Fundamental Problem Library (#16989) for a small pullout group of accelerated second graders. It has a lot of words in it, and although I know these students can solve the problem, it will take some scaffolding for them to decipher the problem's wording.

    To lower the threshold, I decided to present the problem in pieces (like the mitten problem), beginning simpler. I'm using student names so they will have greater interest. To keep the ceiling high, students explore possibilities prior to looking for one answer so that they understand there are multiple ways to match boys and moms. This also keeps the middle wide open. I kept the Math Forum question until the very end, so the exploring would go on for a longer period of time. (These boys like to solve a problem, and then call it quits!)

    Here is my remake.
    Problem 1: 2 boys, one makes 2 ornaments and the other makes 3. 2 moms, one makes same as son and the other makes twice as many. Question: How many different numbers of ornaments can they make?

    Problem 2: 4 boys, each making a different number of ornaments. 4 moms, each making a different number, related to her sons. Questions: The lowest number they could make, the highest they could make, and if they made 46, which mom matches to which boy.

    Google Doc: https://docs.google.com/a/mdirss.org/document/d/1t4UDJ7h53MBh2z-YZmjvWg8BWNyeVRSYiRfVIdBX-9I/edit?usp=sharing
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    • 27 Jan 2021 7:34 AM | Early Childhood Education
      Found your post interesting to read. I can’t wait to see your post soon. Good Luck with the upcoming
      Update. This article is really very interesting and effective
      <a href="https://thesoftroots.com/early-childhood-education/">; Early Childhood Education</a>
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  • 20 Dec 2017 7:50 AM | Deleted user
    I thought this chapter had lots of TRUTH. The meaningful accommodations were great! And those Margin symbols were interesting.
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  • 29 Dec 2017 8:45 AM | Anonymous member
    So I took this idea and thought about some of the investigations that I do in Geometry. I frequently use the investigations from Discovering Geometry. The problem with the investigations is that they are wordy. The kids see all those words and they quit. They don't understand what to do. For example, there is an investigation that has the kids drawing a triangle, cutting out the triangle, tearing the angles off, adding them together to discover that the angles add to 180 degrees. My kids struggle the directions. I thought of changing it to "What do you notice about the angles of a triangle?" But then I will get statements like, they are all acute, or there is a right angle and two acute, or there is one obtuse and two acute. It makes it accessible to all, but not really getting to the sum being 180 degrees, which would maybe be the ceiling. I thought of changing it to "What do you notice about the sum of the angles of a triangle?" to direct it a little more.

    I looked at some of the examples on openmiddle.com I love the examples and will be using them regularly.

    I feel it is not only a fine line between struggle and helping, but is also a fine line between the amount of words used. While I get that reading is a struggle and wordiness is a turn off, it is also important being able to decode when a lot of words are used. Frequently an instruction manual is very wordy. Some are thick books, sometimes in 3 languages or they are on dvd's. Recipes are wordy. Are they not going to make a good appetizer that was tried at the office party because the recipe is too long? What are they going to do with the extra support piece left over after putting a basketball hoop together because they didn't bother reading that thick book of assembly instructions?
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  • 04 Jan 2018 12:22 PM | Anonymous member
    Before reading this chapter, I had decided to take Friday as a day for children to work alone or in pairs to solve a two step problem. I took problems from the workbook and eliminated the extra words and demands for using a precise strategy. Manipulatives and paper and pencil were provided to take away limits on thinking strategies. The children loved working this way and felt less threatened and open to experimentation.

    I have checked out the site referred to in the book which shows problems with numbers not included in the problems. I want to try that this week. This opens up the problems even more which will excite the children. I look forward to modifying even more the problems from our workbooks.

    I will introduce the the words"Productive Struggle " to the class. I think having a discussion of what that means will be important for the children to understand that struggle can be good and to be expected. Then they can be excited about having a problem to solve rather than intimidated and frozen with dread.
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  • 15 Jan 2018 8:55 AM | Anonymous member
    I struggled with this chapter to make it relevant to my Pre-K classroom. I had to think very hard about what math related problems we discuss or experience in our curriculum but there was one that came to mind. In the chapter 4 discussion I mentioned our attendance activity and how asking students to think about how they can figure this out without our traditional counting of heads. For some children, this is still a difficult task. I might try asking this group if all the kids are in class today, most will observe a missing placemat for snack or an empty cubbie or two. For those needing more of a challenge I will be curious to see how they choose to solve the attendance question.
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