I think that’s fairly telling of how students have been trained to be wary of context in math class.

But if they choose to answer the second question and say it takes 26*6 minutes will we assume they answered the first question? How will we know that they really don’t understand the context of the problem?

Our goal should be (and I know Dan’s is) to work toward the day when students don’t expect their teachers to ask questions that are answered with a single operation.

You and everybody else need to be commended for your commitment and willingness to share. I think this is what these forums should also include, if something is not working, what does?

How to make them care about trying to figure this out as opposed to just being checked out.

As far as the ! goes, I am the crazy, !!, energetic type so !’s appear often in my life and classroom. I would not be frustrated with the 26 miles at a 6mph pace answer as it does require deeper though, but AM often frustrated when I get (5)(0.5) = 25 and such. But, I am frustrated with myself, not my students because they know what I have taught them. It is those times that I think, how am I teaching wrong and how can I fix it? For them to not think, “Is my answer reasonable?” means that I have not deeply instilled in my students the correct way to think about math. What I would like to know is how as a teacher do I do this with 6th grade students? Because just telling them to do it (over and over and over) obviously isn’t working.

Noting that you recognize this issue, would you also be able to offer what have you done to evolve this thinking in your students.

It would be helpful to me if you can offer insight on how you go about addressing this situation in your classroom how often etc. I will assume some kids get it quicker than others, are you able to bring it back on an individual level until this child comprehends the concept fully.

Have you been able to measure the results and see if it was retained once they entered the next grade level and have their scores gone up?

Thanks

@Julie R regarding how saying to a 6th grader stop and think if it makes sense!,

IMO I think its important to help them developed the way to think about how to go about deciding if something makes sense or not.

To an adult, its easy to point to the fact that a 6 min mile was the fastest run by Benson and we can naturally assume that for him to maintain 26 in a row is not going to happen at the same speed.

It may seem silly but some kids may not realize this fact, additionally I have found that it also depends on how you communicate, the !! pts leave me to think you are expressing frustration in the classroom (hard not to sometimes), kids who don’t get it will just keep quiet because they feel dumb and don’t want to look stupid in front of others.

Possible solution: Consider having the kids in the class run around the track/school (a measured distance that has them reach anaerobic threshold or max effort) 4x without stopping for recovery and time each lap.

They will feel the effect on their body’s and see the time for each. Ask them if they ran 22 more times what they think would happen.

You can also collaborate with the gym teacher for this activity and connect the dots later or next day in the classroom.

They fail to connect the math that they do with something in the real world that is being modeled by that math and therefore never consider the unreasonableness of there solution, though computationally correct.

At my local university, I have heard that one of the early grade math workshops that they conducted a local study of the effect of the current California State Mathematics Standards for K-2 and found that the focus is teaching students to rely too much on formulas and algorithms and not enough developing the fundamental concepts that support those formulas and algorithms. As a result many more students are leaving elementary school without knowing their multiplication facts or even recognizing that 2×3 can be represented also by 2+2+2 or 3+3 or any other way. Such important connections are not being made by students, locally; perhaps elsewhere.

So, by not having the experience of connecting the math that a student dose with modeling something tangible, how can we expect a student to think outside the box? It doesn’t fit in their formulas and algorithms, which was definitely evident in the data that I provided Dan from my classes, then they will never see a different solution or recognize that their solution is unreasonable or doesn’t make sense, and therefore they conclude that math is hard or confusing. In reality, math is much more than just “number crunching!”