Christopher Danielson’s “Which One Doesn’t Belong?” Now in Print

160831_1lo

Stenhouse just released Christopher Danielson’s book, Which One Doesn’t Belong?

It’s a must-have if you’re a parent or a teacher with any interest in helping your children or students learn to speak mathematically.

There are few tasks that offer so much mathematical value yet require so few instructions as Which One Doesn’t Belong?

You see four mathematical objects. You ask kids, “Which one doesn’t belong?” You help them negotiate their overlapping and conflicting answers, developing vocabulary and the capacity for argument and abstraction along the way. That’s it.

160831_2lo

You can find loads of great WODB prompts online but you can’t find Christopher’s unique presentation, narrative, and teacher’s guide, which is its own kind of graduate-level course in pedagogy.

Highly recommended.

About 

I’m Dan and this is my blog. I’m a former high school math teacher and current head of teaching at Desmos. More here.

5 Comments

  1. Pre-ordered the book, but have Q for you, Dan. Hearing about pushback on things that don’t “belong”. In an inclusive school environment, they don’t focus on how things are different, but what is in common. So pushback is mainly on language. Should have asked Christopher at his fab Math on a Stick area at MN State fair this week. Thoughts?

  2. Any guidance on what age is best for this kind of thing? I think my kiddo is still a bit too young, but curious what you or Christopher have experienced.

  3. Thank you for sharing this. I’ve been trying to keep up with the twitter chat but there is so much going on I would have missed this. Thank you!

  4. Cassandra:

    Pre-ordered the book, but have Q for you, Dan. Hearing about pushback on things that don’t “belong”. In an inclusive school environment, they don’t focus on how things are different, but what is in common. So pushback is mainly on language. Should have asked Christopher at his fab Math on a Stick area at MN State fair this week. Thoughts?

    Great question. I’ve invited Christopher to stop by and comment.

    My own thought here is that the language of “doesn’t belong” is undercut by the fact that each object both belongs and doesn’t belong, depending on the criteria. If each set featured one item that objectively didn’t belong, I might be more concerned.

    Kevin Hall:

    Any guidance on what age is best for this kind of thing? I think my kiddo is still a bit too young, but curious what you or Christopher have experienced.

    The format here is essentially contrasting cases, which (as I’m pretty sure you already know) was studied by Schwartz as it relates to variance. So my opinion is that the pedagogy knows no maximum age, but that Christopher’s particular objects are geared towards elementary-aged children.

  5. Cassandra points to a question that I’ve thought a lot about. Hearing about pushback on things that don’t “belong” in an inclusive environment. I’ll share a couple of my thoughts on this. The first is that I would never ever ever do “Which One Doesn’t Belong?” using four children as the examples.

    I think—as with many resources—that the ways teachers talk with students about tasks is an important variable. The task is about the differences in abstract objects, not human beings. The goal is to celebrate the diverse thinking of young mathematicians. We can also talk with kids about the language of sets. Each page is a set (in the formal mathematical sense), and sets have members. We are imagining implicit rules for membership (again, a formal mathematical term) in the set. We can address the fact that mathematical objects are different from human beings. In short, I would say that being sensitive about the language when working with kids is a very good idea, and in being sensitive to it (but not avoiding it) we can use it to open conversations about inclusivity.

    I desperately wish that Kevin had left the age of his kiddo in the comment! My experience is that four year olds and up can have a good time with the target task. For sure kindergarteners through high school. While two and three years olds are less likely to engage in the identification of commonalities and differences, there’s no reason a book full of interesting and complicated shapes can’t be in regular rotation along with the other picture books. We read out loud with children long before we expect them to read themselves, and they learn through the exposure. Math is like that, too.