However, as a science teacher (as well as the wife of an archaeologist) I have one big beef — digging up dinosaur skeletons is not archaeology! I am uncomfortable seeing this common misconception repeated in an educational activity. Archaeology is the study of past humans. The study of ancient fossils is paleontology. When my husband talks to student groups, he is commonly asked about dinosaurs that he has dug up, and he has to spend time dispelling this myth (and explaining what it is that archaeologists do). It may seem like a trivial distinction to some, but I think getting the terminology right for a school activity is important.

Thanks for sharing your activity. I may make use of it in my own Algebra class — after updating the title!

]]>Thanks for the comment and a better articulation of my quandary.

]]>I really like your thinking about how grade level plays into this. That’s a conversation I haven’t seen (maybe because I hang out with too many upper school teachers ðŸ˜‰ ) and which seems really rich. It is my understanding that students at the early grades are still forming their understanding of number, quantity and operation, so having a concrete model is not only helpful, but actually essential, to them building their understanding of these concepts. There’s some really great examples of this in Tracy Zager’s book, which I am in the midst of reading right now.

Quoting from a quote from Kathy Richardson (pp 197-8): “Children who deal almost exclusively with symbols begin to feel that the symbols exist in and of themselves, rather than as representations for something else…The number combinations and relationships children need to understand can only be learned through counting, comparing, composing and decomposing actual groups of objects.” And further down the page: “If teachers ignore these stages and just ask the children to memorize the words ‘three plus four equals seven,’ they are, in effect, asking them to learn a ‘song’ rather than learn the important relationships these words describe.”

]]>I appreciate the three purposes of context you discuss above. I think it’s helpful to establish why one might ask a question using a fish tank rather than just giving a function. I’d agree that the difference between calling it a fish tank and just “a box” is negligible for student understanding. I can also see why given the choice, “a box” might be better in the long run. I’d also argue that providing the fish tank is significantly better than just providing the polynomial and asking students to factor it.

Consider Desmos’ Function Carnival activities, which is one of my favorite tasks in existence. What makes that not pseudo-context? My hunch is that it is pseudo-context, but the activity is just so delightful that we give it a pass, and we should! Being able to imagine a dude being shot out of a cannon is helpful for understanding the math, if not particularly useful for the understanding of cannon-shooting.

There’s no disagreement that really bad pseudo-context gets in the way of understanding and messages to kids that math was invented by math teachers to torture their students. I also think it might be helpful sometimes just to give students something with which to create mental models of what the math is actually doing.

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