bjshaw3
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Another format for lesson planning that I’ve used has been the “I Do, We Do, You Do” structure in which I provide direct instruction, facilitate students through a guided practice portion, and then have students work independently to apply their learning. As a student teacher this year, I began with implementing this lesson plan format because it seemed to easily fit with the structure of lessons according to the math curriculum that my school uses, HMH Into Math. As I’ve grown more comfortable both with whole group instruction and the curriculum itself, I think there are numerous ways to adjust our math curriculum to better fit the inquirybased lesson plan, which would most definitely be more engaging as well as allow more time/space for differentiation to occur in real time throughout the lesson. While the “I Do, We Do, You Do” structure has been somewhat successful, I think I’m in a place as a teacher candidate and my students are in a place in their relationship with me, where we’re both ready to make our math learning more engaging, and this inquirybased lesson plan is a great method for doing this.
bjshaw3ParticipantMy top 5 checks for understanding include 1) exit tickets given after a lesson, 2) white boards to assess students realtime problem solving strategies in addition to their conceptual understanding (pictorial representations), 3) 14 checkin in which students rate themselves 14 to demonstrate how they feel about their knowledge after a lesson, 1 being I don’t feel confident in the content I just learned and 4 being I can teach this toa peer, 4) colored cards, which I haven’t implemented in the classroom, but I like the idea of students being grouped based on their conceptual understanding of a certain topic, and 5) teacher observation, which I feel I can best gather during small groups, when I can see students work through and process problems more closely.
bjshaw3Participant1/6, 2/8, 3/5, 2/3
To be successful in solving this problem, students need to conceptually understand that a fraction is a part of a whole and that the denominator does not necessarily define the size of the whole, but rather how many pieces the whole is partitioned into.
bjshaw3ParticipantThe videos that resonated with me the most, since I (student) teach in a third grade classroom, were the videos on multiplication and division, since that’s essentially all we’ve been working on since the beginning of the school year. An “ahha” that I had with regards to multiplication was that multiplication learning really starts in second grade, when students are taught to partition a rectangle into no more than 5 rows/columns. This is interesting to me as I reflect on my own students’ knowledge when it came to arrays and finding the area of rectangles, both things we’ve covered this year, and I notice that there are a good chunk of my students who gravitate toward array when it comes to solving multiplication and division problems. A second “ahha” when it comes to multiplication and division is to let the context of the problem explain the equation. Lately, I’ve noticed that my students are able to look at an equation and come up with a strategy to solve, but when it comes to interpreting and tackling a word problem, they have a hard time creating a model and therefore an equation that aligns with the context of the problem. A final “ahha” that I had with regards to division, specifically, was that students should experience the difference between efficient and inefficient thinking. That way, they can recognize the need for a faster strategy for dividing with larger numbers and hopefully come up with some ways to mitigate that through their own exploration. A “wonder” I had with regards to third grade and the progression of multiplication and division, it how to get students to see the value of each and the difference between repeated subtraction strategies in which the groups are unknown and the fair share or partitioning strategy in which to objects are unknown. In my experience, too often the students get stuck on one of these and have a hard time differentiating which one makes the most sense in the context of the word problem they might be solving.
bjshaw3ParticipantIf students are fluent in math or demonstrate math fluency, they can quickly and accurately come to the answer when presented with a math fact, and be able to employ various strategies that represent number sense in order to come to those conclusions.
Number sense includes a students’ ability to reason with numbers, and understand operations, etc. conceptually, rather than being fluent in math through rote memorization.bjshaw3ParticipantI’ve found that students can grasp the concept of multiplication, for example, but they have a hard time looking at a fact and moving toward that quick ability to come up with an answer. Often, they can find it if they have the time/space to make a model, but when it comes to knowing their times tables, for instance, they struggle. To help these students, I think it might be helpful, since now I know they mostly understand multiplication conceptually, to move toward that fact memorization, maybe using flashcards or a multiplication chart to help.
bjshaw3ParticipantSpiral review – Spiral review is built into the math curriculum at my school. Any homework assignment from their math homework journal includes various problems that ask students to draw upon their background knowledge or previous learning. Students are also regularly assessed on previous learning during tests that examine their understanding of a new concept.
Fact fluency practice – Station rotation activities often included an independent station with a choice board that includes digital math games that allow students to practice math facts, such as multiplication facts. Sometimes I also use these as warm ups.bjshaw3ParticipantHow to interpret word problems that include multiplication and division (identifying which aspect of the word problem represent the “groups” and which aspect of the word problem represents the “objects”)
Being able to independently determine what model might be helpful in solving the problem
Writing the answer to a word problem in a complete sentences and/or labeling the answer in the context of the word problem
Bar models in multiplication and divisionbjshaw3ParticipantNovember 14, 2022 at 9:01 pm in reply to: 1.2 – SHARE: Math Misconceptions: What would you do? #2410With a student who completes the following problem like this, 320+50=820, I might first recognize to myself (internally) that this student is needing support with recognizing place value in the problem. I would then prompt the student to walk me through the strategies and thinking they used to solve the problem. If they can recognize their own mistake, I might engage them in a conversation regarding how they might fix it. If they are unable to recognize their mistake or if they aren’t sure how to fix their mistake, I might have the student solve the problem using a place value or HTO chart and base10 blocks.
bjshaw3ParticipantNovember 14, 2022 at 8:48 pm in reply to: 1.2 – SHARE: Math Misconceptions: What would you do? #2409Mathematics is computation. – As a student, I thought this was very much the case. Math included learning various operations and how to come to a correct answer using those operations, procedures, and strategies. As a teacher, I know this is not the case. Mathematics is more problem solving than basic computation.
Math is just memorizing rules. – As a student, I remember learning a bunch of different “tricks” for memorizing the operations/procedures/formulars/steps in math. As a math teacher, I try to avoid only teaching those tricks, at least when initially introducing a topic. I want to give the students the proper strategies to solve the problem without those tricks, first.
You are either good or bad at math. – I’m totally guilty of calling myself “not a math person” when I was a student, and even in my adult life. As a math teacher, I know all students are math people!
Math is just about getting the right answer. – I absolutely agreed with this statement as a student, and even remember my friends who considered themselves “math people” saying that they enjoyed math because you could reach a correct answer and there was only one right answer. As a math teacher, I know math is about problem solving and the strategies/reasoning/understanding it takes to get there.
Math is creative. – I definitely had a hard time seeing this as a student. I don’t have very many memories using modeling and working with manipulatives when doing math, but as a teacher, this is the majority of our math instruction which gives students the opportunity to be creative when working with math concepts.
Math is exploration. – As a student, no. Math was just about numbers and computation and operations. As a teacher, absolutely! We have built in tasks in our curriculum to give students the opportunity to explore various ways to model math word problems and math equations.
There are many ways to problem solve. – As a student, I think I probably would have agreed with this statement. However, when it came to math (especially in higher grades like high school), I’m not sure I remember being given many opportunity to vary how we problem solve. As a teacher, I know there are SO many ways to problem solve! The students are explicitly taught multiple strategies to do so.
Mistakes help our learning. – I was one of those students who got really down on myself for making mistakes because I typically did pretty well in school. So, I didn’t view mistakes as necessarily helpful for my own learning because I got really down about them. As a teacher, I know that when students make mistakes, this is a great way for them to grow, learn, and better understand a given concept.
bjshaw3ParticipantI felt fairly comfortable solving the problem. While it’s been a while since I’ve seen a word problem like that one, I was able to consider it in real world context (working retail, grocery shopping, etc.) and draw upon my background knowledge of proportional reasoning to remember how to consider the various discounts.
I was initially stressed when I saw that the word problem was at a slightly higher level than the typical third grade math that I’m used to teaching everyday, but after reading and interpreting the question and drawing on my background knowledge, I felt okay.
I’m not sure that I necessarily had strategies in place to solve the problem, since it didn’t necessarily ask us to come up with what money would be left after those discounts were applied, however, I do think proportional reasoning and knowledge of percentages was helpful.
I was initially thrown off when I got the problem incorrect, but then I realized the text box where answers go was only looking for a “yes” or “no” response with no explanation. Then, I felt accomplished when I got the problem correct.

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