Math Class With Less Direct Instruction?

I have a request and if you would be so kind to indulge me, I’d appreciate it. If you can answer the following, I would appreciate it. Tag me on Twitter (@lmhenry9) and/or post your answer in the comments (or blog about it and post the link in the comments). Thanks.

How does a math class look/operate/function that is NOT based on direct instruction? What does a typical day look like? How is direct instruction infused in when needed?

Background on my question:

Andrew Stadel in January had posed a question on Twitter about finding and implementing tasks. Since then, I have been pondering on and off how I would change how I currently teach. I do quite a bit of direct instruction. I know that I should be looking at other options and not relying on DI so much. However, I find that when I ponder how my class would change, I feel completely clueless. And when I start to really think seriously about it, someone (usually an adult) says something to me like “You do such a great job of explaining to your students.” Usually this is prefaced or followed with an explanation of what the person has seen in another class and what was lacking that I seem to provide. And then every fiber of my being says, “See – you shouldn’t take that out of your class.” But yet, I keep coming back to making changes in my class structure.

I know there are things I could be doing differently, but I don’t know how to. I teach based on how I was taught. Granted, that was a long time ago and it worked well for me. I’m sure it still works well for motivated students who are usually at the top of their class. I want to make sure that whatever changes I make benefit as many students as possible and in particular help those students who generally would fall in the middle and bottom.

I know I should be integrating rich tasks into my class – how does that work? When you have students who are not used to doing rich tasks and are used to being taught to, how do you help them make the adjustment (especially students who have tended to struggle with math)? I have so many questions going through my head it is hard to articulate it all. The more information and detail you can provide would be helpful.

I’m not looking to flip my classroom, meaning that I am not looking to move the “direct instruction” portion out of my class time. There are many reasons for that but the main one is the lack of available internet for many of my students. I am looking to minimize the amount of direct instruction and to provide it in a meaningful, natural manner. So how does that look?

I appreciate you taking the time to read my questions and I even more appreciate those of you who will take the time to respond. Every bit helps. Thanks.

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11 thoughts on “Math Class With Less Direct Instruction?”

  1. suevanhattum says:

    I guess I’m an ‘old math dog’ too. I know I lecture well, and I’m good at pulling students in, so there’s lots of participation. I’ve added lots of activities, but those are still well under half my (college) classtime. I too would like to move to a model that’s less direct instruction. But I know my students are so used to math being this way, they would feel lost if I took out the direct instruction, and blame me. I try to wean them from teach’ers answers gradually. So my ‘direct instruction’ is full of “Let’s think about what we should do next.”

    I’m eager to see what replies you get.

  2. Lisa,

    I responded at my blog. As I suspected, I had a lot to say. I hope this helps. 😀 Keep reflecting and questioning, your answers will come.

    Teri Ryan

  3. I am in the first year of using a workshop delivery model in my math classroom (7th grade). I use Carnegie Learning which is a blended curriculum. We have three days a week of collaborative classroom workshop and two days of MATHia personalized learning software,

    On workshop days we follow a format of Opening (think warm-up, correcting homework, and discuss learning goals for the day)-this takes 5-7 min. Mini-Lesson this is the 10 min max (hopefully) direct teaching where I model my thinking while solving a problem. I also model marking the text a literacy strategy, Work Time is the bulk of the class period where students work in collaborative groups to solve rich problems. This is lasts 30-40 min. Sharing and Reflection is the final 5-10 min where we wrap up learning for the day. I never know how workshop could possibly work in a middle school classroom, but I am telling you it does and I cannot say enough how much I love it. One the two MATHia days I pull small groups usually based on exit slip data from the previous day. Students work independently on the computer and I focus on working with the small groups/conferring with individual students.

  4. Awesome question. After reading your post, I ended up with a few things I was curious to know.

    Basically, what’s your picture of how kids learn math? To make that big question a bit more concrete, of the topics that you teach, which is the hardest for kids to learn? What makes it hard? How do the kids that successfully nail down that topic end up learning it?

    Or, another question: what’s wrong with DI, anyway?

    1. Lisa says:

      I believe that students need practice using the concepts that are needed to solve a problem. The more practice they do, the more equipped they are to solve problem situations. I think students who do not practice mathematics do poorly. Students tend to struggle with concepts that are not as concrete – where they have to really think through how to solve the problem rather than being able to follow a process. But I think the bottom line is that the students who take the time to really practice and internalize the mathematics are the ones who do the best.

      As far as what’s wrong with DI – if you look at how we are evaluated, everything points to student-centered learning. Students should be doing, not me doing. Students should be explaining, not me, etc. But when they don’t have the knowledge – they have to get it from somewhere. DI seems to be the best way to impart that knowledge (well, at least it’s the quickest way). I think with some branches of mathematics, discovery can be done. But I have a harder time coming up with good discovery lessons for Algebra.

      I hope that helps answer your questions. Thanks, as always, for making me think. 🙂

      1. Wow, you put that really clearly and succinctly. Such a good writer!

        Anyway, I think that I basically share your picture of how kids learn math. Kids need to practice the skills we want them to develop, and discovery is often the least efficient way to teach something. (Unless you want to teach kids how to discover stuff, in which case discovery is the only way to teach it…)

        “DI seems to be the best way to impart knowledge.” Totally agreed, but the kids need to be ready for the explanation. (By the way, I prefer “explanation” to “DI,” since DI has so many different meanings.) So, how do we get kids ready for an excellent explanation?

        I’d be really curious to know what you do to help make sure that a kid is ready for an explanation. Like, suppose that you know that on Tuesday you want to explain how to use substitution to solve a system of linear equations. What do you do on Monday to make sure kids are ready for that?

        Part of the reason why I’m curious is because, in that situation, I’ll often do a non-explanation lesson on Monday, in preparation for the explanation on Tuesday. But I’m also just curious because I’ve never seen your classroom! What’s it like?

        1. Lisa says:

          I’m not sure if I really “do” anything to prepare my students for an explanation. I do usually introduce new terms that are used in the concept and I do let students know what the Learning Target is (which we have to do), but beyond that, not much. Part of that for me this year is the fact that I am doing all new curriculum and many times, I haven’t had time to set things up as well as I would like. I suppose if I had more time to really think things through, I would set up DI with a problem situation first, but I honestly haven’t gotten there yet.

          What’s my classroom like? Well… I would probably classify it as mainly a “traditional” math class with some newer things blended in. Usually I start with some sort of opener. I sometimes tie in the “do now” into what is coming up in the lesson (review of a previous skill) and many times, I am incorporating practice problems for the state test. Usually, we go over homework problems and questions the students have from the previous night’s assignment. As this year has gone on, I have not been as happy with my starting into class. That’s probably another discussion for another blog post… Once we’re past that, I’m either into the lesson or the practice activity for the day. Yesterday, I did the lesson over graphing linear inequalities. I try to incorporate questions throughout the DI part of the lesson. Sometimes it goes better than others. I usually go through 2-3 examples for each type of problem. I have used “I do, we do, you do” many times although lately I have gotten away from that and need to head back in that direction as we work through examples. Wrap up will oftentimes have an exit slip (although, again, I have gotten away from that and that is NOT good) and if there is time, time for students to begin their homework.

          Today I had students choose a homework problem from yesterday’s assignment and graph them on whiteboards. Many had not done the assignment and had indicated they not attempted much because they didn’t understand it. With one of my classes, we spent a few minutes talking about where they could look for help. Although I was kind of pleased with how things went yesterday, something went wrong and now I’m trying to figure out where. I had already planned a jigsaw activity today for them where they a) solved the inequality for y to graph (if needed), b) graphed the inequality, and c) chose a point in the shaded region and checked it in the original inequality to see if it checked. The activity went fairly well and I was able to get around and help several students.

          So, that gives you a small snapshot of my class the last couple of days. There is definitely room for improvement. Now to figure out how.

  5. I think DI teaching can be done in a rich way by asking the right types of questions. The reason others feel you are good at explaining means that you are leading them to a place that solidifies their understanding.
    My goto sites for more ‘traditional’ rich tasks are Don Steward’s blog
    And Nrich

  6. misscalcul8 says:

    So my answer has been somewhat long and drawn out Lisa. I think my advice is to offer students more opportunities to analyze, sort, compare, justify, and define. Give them examples and ask them for the rule. Make them work problems and define a relationship. Don’t explain first. Make them work, notice, label, discuss. Explain to students who are struggling. Be less talkative. Things that seem obvious to us are not obvious to them. Give them graphs, expressions, equations and make them sort by different categories. Make them write observations. The best way to get students used to that is to START. Start doing it and don’t give them a choice. Make it a routine. Make it the normal experience of your class.

  7. Max Ray (@maxmathforum) says:

    I’m posting mostly so I can subscribe to the comments for now. I’m hopefully going to finish this week with some lesson-plan templates for a local middle school that had the same questions: what are other formats of lessons besides “I Do – We Do – You Do” and how are they used. Once they’re done I’ll add them here if they’re helpful. But mostly I’m curious to hear how others respond to Lisa, answer Michael’s questions, and think about DI. Thanks for asking the question, Lisa!

  8. Beth says:

    Lisa – your post intrigued me. I am a veteran teacher and have some traditional views. At the same time I want to engage my students in discovery learning, rich worthwhile tasks, problem solving.

    I wrote a blog post about a recent lesson … let me know if it is what you had in mind.

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