Reflect:
After reading Chapter 3, please reflect on the questions below and post your response by Monday. Feel free to respond to any of the questions provided or share something else that you intentionally did differently in regards to implementing high-level tasks.
Please note: the prompts below are to help you reflect. There is not an expectation for you to respond to all {or even any} of the provided questions!
Respond:
Option 1:
Use the Task Analysis Guide to Examine Learning Opportunities
Use the Task Analysis Guide {see fig 3.1} to analyze the mathematics tasks you used with your student over the past few weeks.
After reading Chapter 3, please reflect on the questions below and post your response by Monday. Feel free to respond to any of the questions provided or share something else that you intentionally did differently in regards to implementing high-level tasks.
Please note: the prompts below are to help you reflect. There is not an expectation for you to respond to all {or even any} of the provided questions!
Respond:
Option 1:
Use the Task Analysis Guide to Examine Learning Opportunities
Use the Task Analysis Guide {see fig 3.1} to analyze the mathematics tasks you used with your student over the past few weeks.
- Approximately what percent of the tasks were at each of the four levels of cognitive demand?
- What are some implications for your mathematics program on providing your students with the opportunity to engage in high-level tasks that promote reasoning and problem solving?
Use the Factors of Maintenance and Decline to Explain Learning Outcomes
Teach a math lesson based on a high-level task. Then consider the factors {see fig 3.2 on pgs. 49-50} that influenced task implementation and student learning outcomes.
Teach a math lesson based on a high-level task. Then consider the factors {see fig 3.2 on pgs. 49-50} that influenced task implementation and student learning outcomes.
- In what ways was the implementation of your lesson more similar to that of Mr. Harris or Mr. Stevenson?
- Which factors influenced your decisions that might have led to a decline of cognitive demand during task implementation and limited student learning?
- Which factors influenced your decisions that supported a high-level of cognitive demand during task implementation and deepened student learning?
Interact:
On Tuesday, read your colleagues' reflections and respond to at least one other post by sharing a comment, insight, or interesting possibility by Friday.
On Tuesday, read your colleagues' reflections and respond to at least one other post by sharing a comment, insight, or interesting possibility by Friday.
Logging you in...
Stephanie Clement · 279 weeks ago
When reading Mr. Stevenson’s way it really hit me that it is pretty easy to just “tell the students what they are thinking”. This is not only unfair, but not very rich. When the students are explaining their thinking I think it is so important to hear them out and only correct them if their thinking is incorrect. I don’t want my students doing problems “the way Mrs. Clement does it”. I want them to feel comfortable with a variety of strategies and to also be able to explain their thinking when they are done.
shawnseeleydotcom 44p · 279 weeks ago
That task gets hard by the time students get to number three! I am using that same task with my team during our district-directed early release time this Friday. I had assigned that task as homework during Unit 2 and had a few students tell me that their parents couldn't solve it, which was both humorous and a little concerning. It is so much fun to watch students reason together and show that they are much more capable than they or others might have initially thought!
R. Bainton · 278 weeks ago
Meribeth Rowe · 279 weeks ago
We hadn't really done any problems with the "twice as many" language so I pre-taught that concept using manipulatives. When I felt comfortable that most of my students were ready we read the Snowball out loud and then again with the students. The groups had been selected randomly. I asked the students which of the three teams they thought would make the most snowballs based on the question situation. I inquired which team they predicted would make the fewest snowballs as well. Off the kids went to work on the situation. some groups worked together and a few other groups worked more side-by-side. After a few minutes observing I wandered around to ask questions like Mr. Harris.
Show me how you started? What information was most useful in the question? Can you explain your picture to me? Even with all the wipe books in a relatively small space facing into the circle I noticed students were not watching what other groups were doing. I paused the group and offered manipulatives as two of the seven groups were completely stuck. One group explained their first step for the whole class. Work resumed until a few groups had successfully completed the problem. Each group had an opportunity to share their strategy and have members ask questions.
A few important things I learned from this experience: Choose your problems carefully at first. Mine was too challenging for an October experience! Have one pen available to start with per group. Listen, listen, listen to what the kids are saying to each other and use that information to direct your line of questioning. I recognized a few factors that led to the decline of success in my lesson and plan to work harder on making decisions that maintain success in the future. (Figure 3.4 on pages 49-50)
Stephanie Clement · 279 weeks ago
I love how you went around and questioned them about their work. What a great way to make the task rich and get them thinking. My students did not look at other groups work the first time I did a wipebook lesson as well. Once we discussed that that was a benefit of the activity, they started doing it more. I think they thought that it wasn't okay to "copy" each other. We discussed how that is a great opportunity to look at other people's strategies.
Julie Rodriquez · 279 weeks ago
I was especially intrigued by the section on the sequence of tasks that involved "doing mathematics" and "procedures with connections". I wanted to try my hand at creating a sequence of tasks for our work in Unit 3, and since I am currently teaching division of whole numbers and unit fractions, I created five tasks with these concepts. Here is a link to my work: https://docs.google.com/document/d/1VW1cu8egXasVk.... It is definitely a first draft but I plan on using these tasks over the next couple of days and reflecting on what worked and what I need to tweak.
Note: If you are unable to get to my link, e-mail me and I will send you the document.
Caty · 278 weeks ago
I totally had the same feeling while reading about being both teachers when I am teaching. I loved how you created some tasks and inspires me to do the same as I move onto the next unit in math. I have a hard time with productive struggle because I think we can get in the mindset of our kids need to get this now or help them achieve understanding in the quickest way possible.
Caty Carino · 279 weeks ago
One of the things that I was finding myself connecting into the chapter is to let the students struggle through a problem. Often times I want to jump in and save them, when I see that they are struggling with a math problem. Or if I feel that the class as a whole is missing something or overlooking a detail in the problem.I ask questions similar to Mr. S so I can get them back on track. I need to be more in the mindset of Mr. H.
But that is not always the case, when I do the daily problems from the math expressions lessons, I find those problems are rich tasks. I love them because they aren't always related to what we are learning but it is more about activating prior knowledge and number sense. I wish I had more time to spend on these when I teach a math lesson because I could easily end up spend 10-15 minutes talking about the math problem and having students share how they achieved their answer.
My goal for myself after reading this chapter is to be more aware of the questions I am asking and letting the students be more in control of their learning so they can enrich their math experience.
shawnseeleydotcom 44p · 279 weeks ago
Recently in my classroom, I created a rich math task to introduce the concept of multi-digit division with remainders, and how to interpret those remainders. I wrote a problem for my class and gave it to them before I had done any instruction or let them know what their next unit was (Unit 3 – Multi-digit Division). Wanting to create a rich task that was “doing mathematics,” I created the problem with the goal of having students recognize when to divide, understand what the divisor, dividend, quotient, and remainder mean in context, and then to decide what they should do with the remainder. To do this, I gave the following question to my students, letting them know that I expected them to be able to explain why their solution made sense: “Cascadia Pizza’s food truck sold 724 slices of pepperoni pizza at a local event yesterday. If each pizza is made of 8 slices, how many whole pepperoni pizzas did they need to make? How do you know your answer makes sense? Justify your reasoning.”
Modeling Mr. Harris, I let students know that before they started working, I expected them to think about how they would represent this problem and had them turn and talk with a neighbor. One of the popular thoughts was drawing circles that each had eight slices, representing one pizza. Another idea that was shared was using an area model to multiply eight until it created 724 (students didn’t know about remainders yet, but it was great to see them making connections between multiplication and division). As students worked, I did my best to use probing questions: “Why are you subtracting all those 8’s from 724?” “Why are you multiplying 8*90?” "What does that 'extra four' mean?" Several of my students ended up getting to a point where they had figured that there must be 90 pizzas because they either arrived at 720 through multiplication, or ended up with four through some form of repeated subtraction/creating equal groups of eight.
None of my students knew what to do with the remaining “four” and they couldn’t tell me what that four represented. We came together as a class and shared out a few partial solution pathways, showing visually what was going on. Once we did this, I asked students to think about what each quantity represented, and then the lightbulbs started going off. Students realized that the four they didn’t know what to do with must be four leftover slices of pizza. Next, the question was what we should do with those leftover pieces of pizza. Did Cascadia Pizza make pizza by the slice, or did they make a whole pizza at a time? We decided (based on Mr. Seeley’s background of working at Papa John’s in high school) that they made a whole pizza at a time, meaning that they must have created a 91st pizza, and then had four slices leftover.
Since that initial lesson, my students and I have revisited this task throughout the unit, reminding ourselves that understanding what each quantity represents is vital in determining what we should do with the remainder.
Meribeth Rowe · 279 weeks ago
Had you just taught the multiples of 10 lesson prior to doing this task? So neat to see kids making that connection.
shawnseeleydotcom 44p · 278 weeks ago
I felt the same way about interpreting remainders after the last few classes of fourth grade students I've had, as well as summer tutoring. When I gave this task, we had just finished our unit on multi-digit multiplication of whole numbers, and I was hoping that students would use their now solid understanding of multiplying by multiples of ten to help them in solving.
Christine Wilson · 279 weeks ago
Susan H · 277 weeks ago
George · 278 weeks ago
In the past few years, my mentality around that has totally changed. I do far more high level tasks and I hardly ever jump in to answer the problem for them. And the most recent trend I've adopted is "not being the answer key". When kids ask me, "is this right?", I reply and tell them that I don't know the answer, but why do you think it's right? Or prove to me why it's correct.
This does require some work up front or pre-teaching from me to establish a classroom culture of: The work we will do is hard and you will struggle, but that is okay. We need to struggle in order to learn. I am going to challenge the students and I'm not simply going to give them the correct answer.
I love this new approach and feel my students are benefiting a tremendous amount. They are doing the work and the thinking. I am simply the provider of problems and the facilitator of discussions.
Jen · 263 weeks ago
Julie Rodriquez · 278 weeks ago
R. Bainton · 278 weeks ago
It was interesting to watch the groups tackle the problem. Some groups started multiplying numbers together and dividing without giving any thought to the question being asked of them. But by working with their group they had to justify their thinking. In the end most groups were successful in getting the answer.
I worked hard not to be the answer key, but rather ask questions to make them think...this was good for one of my groups that ended up having three of my higher math kids in it. The productive struggle was beneficial for them and to have to take the time to think it through. Still a work in progress for me because it is so much easier to say "yes" or "try that one again".
Susan H · 277 weeks ago
We were working on Bar Graphs. Instead of having them go straight to their journals, I put up a graph from their journals without any axis labels or a title. I asked the kids to notice and wonder. I slowly revealed each component of the graph and they were very invested to see if they were right about what they thought them might find under the "magic" black boxes. The kids LOVED trying to figure the graph out without being told how it worked. We did a few questions from the book about reading the graphs, but they wanted to create their own graphs so badly after getting to explore them. This was the next lesson in the journal, but they didn't know that! It was so exciting to see them want to progress through the subject without realizing they were right on track. They thought they got to do something different and special because it was their idea. They surveyed their friends, created titles (to make sure their friends knew what they were graphing about), and created horizontal and vertical axis labels all without prompting from me. It empowered them to create their own graphs, implement what they had discovered on their own, and was a procedure with connections.
All in all, last week was a far more engaging week in math than any we have had this year. It is amazing how much it helps to have the kids notice and wonder before being taught anything!
Jen · 263 weeks ago
I can't say enough how much our work over these last two years has changed my mindset! I want kids to have productive struggle and to persevere. I want them to make sense of problems and find their own entry points. I don't feel like it is necessary to hold their hands before they even begin a task.
Now, I think the most challenging part of introducing rich tasks is asking the right questions to help kids on their journey rather than taking the journey away. And, although I am trying a variety of rich tasks with my students, I can really see the value of having tasks that are related to one another and build upon skills. At this point, a lot of my tasks have been sort of random rather than a series where one problem builds upon the previous one. I believe if I could accomplish this, the tasks would be an even more powerful teaching tool.
Sara · 257 weeks ago
Sara · 257 weeks ago
Finding the balance between productive struggle and unproductive struggle is probably the biggest challenge for me. I don't want the kids to get to the point of shutting down, but I really want them to grapple with the concepts so that their understanding is deepened.