Week 3 Response – Instructional Strategies

So, we’ve looked at the importance of introducing “rich” problems and allowing our students time to “wrestle” with these and come up with their own solutions and strategies.  If only Math teaching was that easy!  In Week 1, I had you read the section from the Van de Walle text on using a 3-part lesson, but for those of you who haven’t really seen this in action, you may still be feeling a bit “fuzzy” about the whole thing.  There are two online readings below that may simplify the 3-part lesson for you:

http://www.edu.gov.on.ca/eng/literacynumeracy/inspire/research/LearningBlocks.pdf  (Focus on Page 6-7)


During Tuesday’s class, we will have a look at the teacher’s role during each part of the 3-part lesson.  Perhaps in your response you could discuss what challenges teachers/students might face during each part, and how the teacher can effectively deal with these challenges.

Another area of focus this week will be creating a balanced Math program.  Yes, just like a balanced Literacy program, Math should include time for shared, guided, and independent Math.  Please read through the Ministry document, Early Math Strategy, Pages 33-37, which gives an overview of the parts of a truly Balanced Math program.  In your reponse, I’d like you to discuss which of these parts you think Math teachers tend to focus on or use most effectively, and which parts could use more attention.  What are the benefits of each part for the student?  What challenges to teachers face in trying to encorporate all 3 parts into their program?  Feel free to discuss (or debate) any other ideas related to this issue!

Enjoy your Family Day, and see you on Tuesday and Thursday this week!


13 thoughts on “Week 3 Response – Instructional Strategies

  1. three part lesson plan
    I think that some of the challenges for teachers of the three part lesson plan are as follows:
    In the beginning stages it can be difficult for the teacher to create questions that engage the students and make them interested in the problem. The teacher has to be very experienced and very aware of the students in the classroom to be able to guide a proper three part lesson plan. I think that in order to conduct one of these lessons, the students must have practiced working together and sharing ideas in groups on a regular basis. Also, it can be difficult for teachers to find out what the students already know as many are going to be at different levels and therefore the teacher must conduct lessons that each of the students can connect with and discover the students’ abilities early on.
    During the three part lesson, the teacher could have some difficulty trying to get the students to discuss the problem and help each other. The students who are struggling will have the most trouble communicating and here the teacher can sit with the students and ask them questions to help guide their learning. Additionally, students can explain their theories to one another to demonstrate that they understand the problem.
    After the lesson some teachers may have difficulty getting students to discuss their discoveries or having the students move forward with the program. The teacher can encourage students while they are working and give them input so the students will feel confident when they present in front of the class. It is important to have the students understand that there can be more than one answer sometimes and that learning and sharing is most important; we can learn through our mistakes.

    • As with most things in life, experience definitely helps when it comes to teaching through problem solving with three part lessons. But don’t expect to do it “perfectly” – as I showed very clearly at Tuesday’s class, even an “experienced professional” such as myself still messes up on a regular basis!! However, just as we encourage and expect kids to learn through their mistakes, we can also learn from our own as teachers.

    • I think that what Jaime is saying about engaging the students during the beginning part of a three part lesson is very true. We want to draw all learners in, but each of them bring different things to the table in regards to personal experiences so it can be challenging to create a problem that all students could relate to. As Jaime said we have to be “very aware” of our students.

  2. A challenge for teachers during the “Getting Started” phase might be to not give away too much information by showing students how to solve the problem. This may be especially difficult for teachers who are used to teaching math the “old” way. A challenge for students during this phase might be that they may lack the prior knowledge needed to understand the strategy being focused on because they may have been taught math the “old” way where they didn’t develop a deeper understanding of math.

    A challenge for teachers during the “Working On It” phase might be to remain neutral. Students are constantly looking for teacher approval and as teachers we love to praise students but teachers must be careful to maintain an expressionless face and not let on whether their students are on the right or wrong track. This phase might be challenging for weaker students who might not understand their partner’s method of solving the problem but might be too embarrassed to say so or too shy to share their way of solving the problem. Weaker students may also rely on the stronger students to do all the work and may not reap the benefits of solving problems in groups. Another challenge might be that with so much independence students might get stuck and not know where to go from there.

    A challenge for teachers during the “Consolidation and Practice” phase might be that student’s solutions may be difficult to interpret. During this phase teachers need to think quickly and on their feet to find the connections between each group’s strategies and ask questions to guide student explanations. It may also be a challenge to keep each student’s attention while they are listening to or reading another group’s explanation. This phase may be a challenge for students at the beginning when the math community is just being established and students are just beginning to feel confident enough to take risks and understand that mistakes are a positive thing because they can learn from them. It may also be a challenge for students to learn how to ask appropriate questions and give and receive constructive feedback to their peers. And it may be intimidating for students to explain their thinking. Their strategy may make sense to them while they are working in groups but students may struggle to explain their strategy to the class.

  3. I agree with Sasha’s statement about how teachers need to practice how not give away too much imfomation, but to guide students to think about their answers. I realized I was nodding my head as students were answering the questions, although I wasn’t verbalizing what they were doing was right I was still telling them they were on the right track. Now I am practicing not to say anything until they are done their thinking and even if the question is right ask them to explain a certain spot in their work or clarify something. This way I hope I am modeling to the other students how to ask questions and get clarification if they are not understanding an explination.

    • Students are very perceptive…they definitely pick up on our verbal and non-verbal cues! Asking them to clarify or re-state is a great strategy to ensure understanding. A helpful version of that is having another student restate what was said – that keeps the listeners accountable, but if others have a hard time restating then it lets the first person know that they needs to communicate their thinking more clearly, without the teacher being the one to say so.

  4. I too am trying hard not to ‘lead’ my students in a certain direction. For example I would often find myself agreeing and encouraging students to take a certain approach. I am trying hard, and finding it difficult at times, to sit back and not give away what approach I think would be the best to solve a problem. I think that it is beginning to lead to richer conversations taking place in the classroom. The reason for this is that the kids are becoming more responsible for defending their answers and why they chose a certain method.

    In general I think teachers still prefer to give a lesson, followed by individual practice questions, and sometimes followed up with consolidation in the form of “does anyone have any questions about that concept?” I agree with the article that students need to be given ample time to talk about and share their answers and this is where they are effectively consolidating their thinking.

  5. I have found that some teachers spend too much time in the before stage, introducing the problem or unit almost obsessive in assuring themselves that the student understands what the lesson will be about. I have been asked to work in grade 7 and 8 classroom and some of the math I don’t have a full understanding of and I, when students are having difficulty ask other students ,who have a better understanding, to demonstrate their understanding. I find it very easy to have students work with partners, supporting each other and working together. Why struggle silently and alone when you can take someone else on the adventure and discover the answers to problems together. I constantly walk around listening so that one person in the group does not overpower the other member of the group.
    I find that many students get blocked and don’t open their minds to find other ways for finding the solution to problems. By introducing the after lesson stage students are introduced to others thinking which can lead to adding to everyone’s schema.
    The one thing about three part lessons is that I have to be prepared that the lesson may take longer than than one math period.
    I have learned to love exploring math and finding more than one way to solve the problem.

    • It’s interesting how we often plan for a Literacy or History lesson to take more than a page, but yet we can feel that each Math class needs to be a “separate entity”. Perhaps its because we often feel like kids forget their Math from one day to the next, so if we can just expect them to hold their understanding for one class then we’ll be able to figure out what they know before they forget it tomorrow?

      By allowing, or encouraging, a Math lesson to take more than one period, it also emphasizes the importance of that skill or concept and gives students more time to explore and process it. Imagine showing up at the ski hill to learn how to snowboard for the first time, and being introduced to the equipment, strapped onto a board, sent down the hill to try it alone a few times first, then being guided on what we were and weren’t doing well, then sent down the Giant at Loch to master that skill, all in a 50-minute period. (disregard the fact that the chair lift often breaks down or has to stop for someone who has dropped their ski poles….) Just like a “normal” Math lesson, that’s a lot to cram into one lesson, and while our most “successful” students might manage (just as those with a tremendous sense of balance and athleticism might master snowboarding quickly, while the rest of us fall on our butts and embarass ourselves and our children – does it sound like I’m speaking from experience???), the majority of students are left feeling insecure and a bit shell-shocked. So giving time also gives familiarity, confidence, and a deeper understanding.

  6. I agree with the challenges that everyone else has discussed so far. I also think that in the “during” part of the lesson it would be a challenge to ask those “probing” questions to help students gain a deeper understanding. I think it would be difficult, at first, knowing what to ask students and when to ask it. And not, as others have said, to give away too much information or let students know how they’re doing.

    I think a challenge for some teachers in the “during” and “after” part of the lesson, would be to not try to get all students to use the “best” (most efficient) strategy. I hope that makes sense. I think a teacher can maybe suggest a strategy if the one a student is using is effective, but really inefficient. But also that a teacher needs to be able to accept a student’s strategy if they really want to use it, even if it is not an efficient strategy, as long as it works for the student.

    • Probing questions are definitely a “practiced skill” and come with experience; however, thinking about the lesson and possible challenges or misconceptions helps you to be prepared with questions. Also, most teacher’s guides have probing questions in with the lessons so that can be useful as well.

      You make an interesting statement that teachers should accept a student’s strategy even if it’s not efficient, as long as it works. That reminds of me of kids who insist on reading Sponge Bob or Diary of a Wimpy Kid books in Grade 8 even though they are far beneath their reading level, just because it’s what they are comfortable with and they find them funny and easy. At what point should the teacher accept a student’s less-efficient strategy as opposed to encouraging them to use one that is more appropriate? Input, anyone???

  7. The first time I taught a legitimate math lesson was when I supplied for Lisa on Friday afternoon. It was interesting and scary for me because I was trying to get students who were not quite on the right track to get there but I was having difficulty thinking of probing questions or the right kinds of questions to ask. Also, I am not familiar with the subject and I was hesitant to really challenge students just because I am not yet comfortable with the math curriculum. I think this is something that is going to take some time and it is difficult as well as a supply teacher because you do not have the kind of connections with students and know the students well enough to know who will need the extra help and who will understand. Thankfully, there were a couple of students who really understood the math and they explained it to their peers and I tried to clarify as well. I think that teaching 7/8 math is something that I will have to work on!

    • Yes, Jaime, I admit I “threw you under the bus” somewhat and wouldn’t have left that activity for a supply teacher who wasn’t in my Math course…ha ha. However, I thought it would be a good learning experience for you so you could experience what works/doesn’t work/is most important when students are learning through problem-solving. You hit the nail on the head with the importance of probing questions, as knowing how to get the students thinking without telling them WHAT or HOW to think is a real challenge but is so crucial to helping them connect with what they already know and to make sense of the problem.

      It’s also certainly more challenging for a supply teacher to do, as they aren’t familiar with what the students have already been taught (or how), so it’s harder to help them make those connections. But again, Jaime, you were very intuitive to recongize that being familiar with the curriculum (ie – being aware of what the students have done at previous grade levels and what they should already know) helps you to anticipate what concepts or strategies they should be familiar with in order to help guide their thinking. This knowledge comes partly with experience, but also with solid lesson/unit planning and possibly some extra research when needed to gain a better understanding of the concepts.

      Thanks for being open to that experience and jumping in with both feet to try to make it work!

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