The students in my Freshman Honors class have certain expectations for how a math class works – a teacher lectures, there’s lots of drill practice, and then a test. Breaking this mold, and causing them to think of themselves as reflective learners, is one of my many missions. So this past week, when confronted with factoring, I simply refused to lecture.

My 9th graders have seen factoring before, but it was back in 7th grade, and it was only a surface treatment. So after a brief opener where we discussed what a “factor” means (both numerically and algebraically), I dropped the bomb –

- I’ve posted your learning targets online
- I’ve posted videos, resources and practice problems if you need them
- I’ve set up online practice if you need it
- You have a timed quiz on Friday (we started on Tuesday)

And….scene!

Panic….apprehension….incredulous looks….

So, you’re not going to teach us?

Nope. Now get to work.

Here are some details of what I posted:

LEARNING TARGETS

- F1: I can identify and factor expressions which involve greatest common factors.
- F2: I can efficiently factor trinomials of the form ax
^{2}+bx+c, where a = 1. - F3: I can factor trinomials of the form ax
^{2}+bx+c, where a does not equal 1 (or zero). - F4: I can identify and factor perfect square trinomials.
- F5: I can identify and factor “difference of squares” expressions.
- F6: I can factor expressions which may represent a combination of F1 to F5.
- F7: I can factor expressions “by parts” (or “by grouping”) when necessary.
- F8: I can factor expressions which are the sum (or difference) of two cubes.

RESOURCES

Each learning target featured a video – some from Khan Academy, and some from other sources I searched for – but I attempted to provide a variety of methods. Some featured grouping as a primary means, others demonstrated the box method or the diamond. This was the most important aspect of this learning experience: **I wanted students to experience a variety of approaches, evaluate them, and make a personal decision about what worked best for them.** The students did not disappoint.

I also posted other online resources, such as worked examples and flowcharts. One of my favorite resources – Finding Factors from nrich, was also included. Finally, I created an assignment on DeltaMath for each learning target, and a final jumbled assignment. The end of each day featured an exit ticket quiz and recap, to assess progress and provide “next steps” during the week.

SO WHAT HAPPENED?

Some students latched onto factoring by grouping for every quadratic, and explained their reasoning to their peers. Many of these same students later in the week found more confidence in their number sense and chose to group only for “tricky” problems. One student was particularly insistent that the box method was the best was to go for all problems. Others found the diamond method helpful – which led to deep conversations about number sense and how to make searches more efficient. And in one fascinating conversation, a student discovered a “trick” he had found online. The group debated the merits of the method, tried some practice…but as nobody in the group could figure out why the method worked, they quickly dismissed it. Good boys!!!

In the end, the quiz scores were great. But beyond the scores, I feel confident that the students have made choices about their learning, assessed and revised their thinking, and can move forward using their new tools.

WHAT DID THE STUDENTS THINK?

Today I asked students to reflect upon their learning experience, and provide me feedback.

What was your overall feeling about last week’s learning method? (1 = “Please never do that again”, 5 = “I loved it – do it more”.)

Describe something you LIKED about last week’s classes, and why you liked it.

- I liked being able to choose what i wanted to do. I could focus on my weaknesses and do less problems on what i was good at. I also appreciated the practice problems.
- I liked that if you knew a topic you could move on and didn’t have to wait for someone else or the next day of class.
- I liked that I could learn and do problems at my own speed.

Describe something you DIDN’T LIKE about last week’s classes, and why you didn’t like it.

- I did not like that you did not explain how to factor
- I didn’t have as much instruction from the master of factoring. {note – I suppose this is me?}
- the teacher wasn’t involved

This last comment intrigues me…and I’m not sure if I should be bothered by it…I don’t think I should be. In many respects, I feel I worked harder during the classes, as students were all over the place. But I also realize students don’t see all of this going on around them. I’ve become intrigued by how I can be less of a teacher and more of a facilitator in my classes, and this was a solid step forward I feel.

Now, off to plan to not lecture tomorrow….

EXCELLENT! Coincidentally, I started with this same strategy with solving systems of equations today. My students are finally comfortable with struggling, and I envision a factoring lesson much the same way! Thank you for sharing. And yes, this is a lot of work because I, too, run around like crazy, checking in on the various groups in various states of understanding. I loved it!

Thanks for the share. So many great opportunities to let students personalize their learning experiences.

This is fabulous, as always, Bob! Think about the perspective of the student (who made the comment may be bothered by).

Students have been raised by teachers who mostly, with all good intentions, spoonfed them knowledge. So often, teachers do the most work, thereby, are the best learners in the room.

Your students were given a task far outside their educational comfort zone. They had to persevere think, work, explore, and gather information. All actions teachers tend to take for their students for time and we don’t always know how else to do this.

Thank you so much for sharing this!

Thanks for sharing this Bob! It takes a tremendous amount of time and prep to “not lecture” and you are correct that students will often comment that they miss the lecture. We’ve programmed them to expect the “lecture” so they feel as though you are short changing them when in reality you are giving them wings to fly!

Agree about the prep time. Received a few twitter comments which share the sentiment that “teaching” this way requires so much more time to be ready. But worth it.

Well done! Great way to encourage students to learn how to learn, possibly the major goal of education. This will serve them well. Lots of positive response from your students, too.

Question: Did you get any feedback from your principal? The parents? How did that go?

My admins are very supportive – some have shared this post or provided positive support on twitter. No feedback from parents, but not surprising as the grades were so good this time around.

I like this approach…I’m thinking that it would be fun to apply this to one of my future units. Thanks for this post

This was great to read! I think a lot of people are unaware of the amt of work (and yet the wonderful benefits) of flipping like this. Do you teach this class by yourself or with a team? I’d like to do more of this with my Alg 2 kids but my content team isn’t quite ready to do that yet and I have to give them some time to adjust to something like this (at least I got them on Desmos!). Curious if your fellow teachers do this as well and if not how might you get them on board without completely taking them out of their comfort zone?

I teach this course alone. I have a few department members who are interested in thinking about class differently, and many friends i other departments who I share ideas with. But of course I also have a fair share of colleague who are comfortable in traditional methods; to those I can only present my experiences and hope they rub off.

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Thanks for sharing this experience Bob! I love the idea of letting the students struggle with learning in their own way. It makes the reward so much more valuable, and students are much more likely to remember what they’ve learned in my opinion. How did you know the students would take to this teaching technique so well? Was this a risk, or did you know your students well enough to hope they would respond this way? I’m curious because when I was in school, I would have thought, “Well if he doesn’t care about teaching us, why should I care about learning this?” And I really enjoyed math at the time! It’s fortunate you don’t have students as stubborn as I was!

They didn’t all enjoy it at first. Many would clearly have been more comfortable with my lectures. But as the week progressed I saw more and more buy in -students explaining what they had learned and supporting each other, rather than just waiting for me to let them off the hook. The key will be in providing more experiences like this and creating a culture where students accept their role in the learning process.

This type of self-discovery seems to work well for the topic of factoring, especially with how integral it will be in later topics in mathematics. I know in my own personal experience that when I had to teach myself something, after struggling for some time with it, that when the discovery is actually made it sticks with me more than simply being taught it and learning it for an exam. I tutor at my college and when factoring comes up, even in a differential equations class or a linear algebra class, many students do not remember, or at least struggle, with the topic. For these reasons I really like this approach, especially on this topic.