# “Yes, but did it work?” & “How are you going to test us on this?”

Yesterday I did this activity in which, using sticky notes, as a class we built a histogram of random data that created a normal distribution. Overall I think that activity went well. It took a bit longer than I anticipated, mainly because it simply takes time for students to find the average of each of  ten sets of ten numbers. Next time I might assign this piece for homework, so that they come to class prepared to creat the histogram.

So we created the histogram and talked about normal data and everything went well. At least, I think…

While reflecting two things occurred to me. First, I began to wonder, did this activity “work”? Did it accomplish what it was set out to do? At first blush it seems that it did. Everything went smooth, students appeared to be engaged, and I’ve put an anchor in their mind that I can draw back to for the rest of the unit. I then realized that there are some lessons/tasks/activities that have results that are not immediately seen or are quite subtle. It may the quiz next week where I see this pay off. It might be tomorrow in class discussions. It might be in four weeks when a kid is reading Time magazine and sees a graph similar to this and thinks “hey, this looks like normal data…” My sincere hope is that it helps them in the rest of the unit and in life, but if it doesn’t help some students then at least I gave them a visual they can relate back to. At least I didn’t begin the unit by saying “Today we are going to learn about z-scores…”. The benefit of some math tasks may not be immediately seen, but that doesn’t mean they shouldn’t be utilized.

The second thought I had was while I was reflecting on a comment a student made during this activity. She asked, “Mr. Cresswell, how would you test us on this?” My response was simply that I wouldn’t test her on this directly, but that the concept we were about to discuss would be valuable. This student seemed to believe that anything that happens in math class should be directly assessed on the test. If it wasn’t going to be or couldn’t be, then why is it happening in class? I suppose I realized many students believed this during my first year of teaching, but occasionally it comes roaring to the front of my brain. Many students believe school is about passing tests and getting good grades. Assessment is viewed as an end, not a means to an end in which they learn and become better thinkers. We need to continue to try to shift this paradigm because, I believe, students will buy into these types of tasks if they’re viewed as a piece of the learning process and not something that is irrelevant because it isn’t going to be tested. (Sorry the wording of that sentence wasn’t great…)

What do you do to to help shift that paradigm?

# I need help with an explantion

I need help explaining this problem to a student. The picture of the problem and his solution is shown below in the image.

“Calculate the probability of tossing a coin 8 times and getting 4 heads.”

His reasoning was that since there’s a .5 chance of getting a heads on each toss, then there should be a .5 chance of getting 4 of the 8 tosses to land on heads. (Note he used the same reasoning to get .25 for #11.)

I tried to explain to him that it was a binomial experiment but that didn’t convince him of a flaw in his reasoning.

I then tried to show him an example of only 4 tosses, in which the question was what’s the probability of getting 2 heads. I showed him the entire sample space, shown in the image below. I then found the probability by looking at all the possible ways to get two heads, and dividing it buy the number of outcomes in the sample space. I then showed him that the binomial experiment formula got the same answer as my reasoning.

He countered that I was double (or triple) counting some combinations. His claim was, for example, that HHTT was the same as HTTH since order didn’t matter, and therefore the sample space was much smaller then I was making it. This implies, in his mind, that there are only four options.

I need your help explaining the flaw in his reasoning, because I  not doing a good job of finding it or convincing him. Is there a better way for me to explain/teach this?  (By the way, I love when students do this. I wish I had more discussions like this one, where students didn’t just accept my first response but really probed my reasoning.)

# Making Review Less boring

We are closing out our probability unit and instead of giving my students 30 problems of review to complete in class I designed a “station” activity. The station format idea actually came from a couple colleagues of mine, and it really helps to get kids up and moving. Also, as the title implies, makes review a little less boring.

I wanted to put a creative twist on this so I came up with the following station activity. There entire activity is self contained, meaning that you don’t need our textbook to use it as I designed the problems. You should be able to run it as is, or modify/improve it as you like.

Also, Ted-Ed deserves it’s own paragraph for it’s awesomeness. Now that I’ve actually gone through and used it to flip a lesson (or part of an activity really), I’m really excited about using it next year in my flipped classroom (or even my non-flipped classes)!

In addition, my good friend and colleague Eric Beckman, recorded the activity for me. Here is my reflection, and the activity resources:

Station Reflection

Stations 1 & 2: In these stations students were asked to watch two Ted-Ed lessons the night before (Station 1, station 2). I then used some of the provided questions, and created my own, for them to answer after watching the lessons. I loved that I get great data on their responses and that students can participate in discussions. I can review all student responses, both open ended and multiple choice, as you can see in the screen shot below. I can also give feedback to the open ended questions, and students will be notified when I give that feedback. You can also download all the responses as a CSV file. The discussions centered around the problems seemed really thoughtful, so I was happy with that. The videos also provide a different perspective on the concepts for the students, which I think was helpful for some.

This did however take them more time than I anticipated. I had one student from each group create an account, which took time, and some of the questions were tougher for them then I anticipated. Next time I will have them set up with Ted-Ed accounts when they come to class, and will also likely reduce the number of problems they have to answer. Because some groups took a while, some groups didn’t complete all the stations.

Stations 3-5: These were the basic probability problems. Students did well on these to varying degrees. I could’ve given these problems all as one station, but breaking it into multiple stations broke it up for that students. Sometimes simple things like that make math more approachable for students. It’s also important to have the key available for students so they can get instant feedback if I’m not available.

Station 6: This station asked students to solve two problems and then create two short video lessons using my iPad to explain their solution. Every time I do this I get mixed results, but the good results outweigh the bad. The downside is that students really don’t like doing it so some push back a bit. However, it forces students to take their understanding to the next level. They will learn it better if they are forced to teach it. It makes them take an extra step in understanding, as they don’t want to explain it incorrectly on record, or mess up and have to re record it. I need to do more of this, as the students that really try get a lot out of creating short lessons explaining concepts.

Stations 7 & 8: More practice problems, similar to stations 3-5.

Activity Resources

Station Packet (PDF)                    Station Packet (Pages)                Station Packet (Word) – I make no promises about formatting….

Station Packet Answer Key

Ted-Ed Lesson for Station 1        Ted-Ed Lesson for Station 2        (These are editable, so feel free tow tweak to fit your needs)