Chapter 2

Establish Mathematics Goals to Focus Learning

Reflect: 

After reading Chapter 2, 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 establishing goals to focus learning. 

 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:   

Select a lesson that you recently taught and re-examine the goals for that lesson.

  • Would you classify the goals as learning goals or performance goals? 
  • In what ways did you communicate the purpose of the lesson to your students?
Now imagine you will be teaching the lesson again. 
  • What is it that you want your students to understand about the mathematics of the lesson? Rewrite the goals so they are clearly learning goals that make explicit the mathematical ideas, concepts, and relationships you want students to understand. 
  • How might these more explicit goal statements better guide your decision-making as you prepare for the lesson and teach the lesson? 
  • Using the revised and more explicit learning goals, develop two questions for assessing your student's progress toward the goals during the lesson, and design an exit task related to the goals to gain information for planning subsequent lessons.

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. 

Comments (28)

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Renae Hanson's avatar - Go to profile

Renae Hanson 59p · 285 weeks ago

Hi Guys - As you are reading through these chapters, be thinking about which of the eight teaching practice(s) you would like to focus on for our February Teacher Leadership sub-day. We will be looking more closely at rich tasks when we get together in October! :)
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shawnseeleydotcom 44p · 285 weeks ago

A lesson that I recently taught was on comparing multiple representations of multi-digit multiplication in Unit 2 of our fourth-grade curriculum. I had decided before I started this unit that I wouldn’t teach the standard algorithm until the end of the entire unit because it’s a fifth-grade standard, and I wanted to ensure that students deeply understood the mathematics behind multi-digit multiplication before I introduced any “shortcuts.” As a quick side note, I read this book toward the end of last school year and it has dramatically changed the way I teach my mathematics lessons, which is why I have a learning goal for this lesson already.

The goal I had in mind for this lesson were that students would be able to:
Identify and make connections between different representations (standard form, expanded form, algebraic notation, and area model/place value sections method) of multi-digit multiplication and explain the connections between the different representations both verbally and in writing (similarities and differences), highlighting the use of the properties of operations involved in each (distributive, associative, and commutative).

I would identify my goal as a learning goal because it requires students to actually understand the mathematics behind the different representations so they can explain them to a partner and the class verbally and in writing. This goal also allows me to change students’ view of mathematics; it is not a checklist or set of right answers, but reasoning and finding meaning.

In communicating these goals to students, I let them know that math is not a race to a right answer, but rather the process of slow, deep thinking, making connections between ideas and representations, producing conjectures, communicating reasoning, and providing justification. My students know that I care about correctness and that we value precision in our classroom, but they also know that we are not raising them up to be calculators.
1 reply · active 285 weeks ago
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shawnseeleydotcom 44p · 285 weeks ago

Part 2 (connection kept timing out)

To warm them up to the idea of making connections, the previous day, I removed all the digits in a two-digit by one-digit multiplication problem, replacing them with different colored dots, each color representing a different digit, including the product. I let students know I had complete confidence in their abilities to solve this task using everything they knew about multi-digit multiplication. I asked students to work together in random groupings on their Wipebooks to solve my “multiplication puzzle,” and then we discussed how they knew they were right, and what steps they took to get there.

On the day of the lesson involving the goal I mentioned (making connections), I displayed multiple representations on the screen at the same time, using the same colored dots from the day before. Students immediately recognized the problem they solved the previous day and jumped in, making connections between the multiple representations. I then had students work as a class to explain what digits went where in which representation and why. We had a great time doing it and students were highly engaged (I’ll be honest, I was a bit worried about it!).

After we finished comparing the representations and reasoning through them, I turned off my projector, removing the colored dots, leaving just the digits, symbols, and boxes for different methods. I then asked students to represent and solve different multiplication problems in multiple ways, which they had little difficulty in doing since they made such great connections on their own earlier. It was a hit!

Two questions I would use to assess student progress on this learning goal would be:
1) What language are students using to make connections between representations?
2) Are there any misconceptions that are hindering students from making connections between multiple representations?

An exit ticket that I used for this was in providing students with a “Troubled Teacher” problem, which is my spin on the Puzzled Penguin problems in our curriculum. I showed students a multiplication problem that was incorrectly represented and asked students to identify my misconception and then fix it in their math notebooks. This allowed me to check for student understanding quickly before moving on.

If you want to see the activity I did, here is a link to my Google Slides presentation, which includes blank “puzzles” my students created for each other (and their parents) for homework, and a link to my Instagram post where I show the process involved in this lesson.

Google Slides: https://docs.google.com/presentation/d/13IihTSCFQ...

Instagram: https://www.instagram.com/p/B3qEAnCA1kT
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Julie Rodriquez's avatar

Julie Rodriquez · 283 weeks ago

While reading Chapter 2, I found myself responding AND reacting to the information shared. There were moments where I was nodding my head, "yes" in agreement with what the author shared about writing goals for our teaching, such as goals provide a "road map" for our teaching (p. 17) and the importance of creating learning goals rather than performance goals for our students. I was reminded often that when we set quality learning goals, this leads us to consider and include the other seven effective mathematics teaching practices in our lessons, such as reasoning, creating mathematical representations and productive struggle. The Common Core 8 Math Practices also become more embedded in our teaching/lessons when we take the time to write quality learning goals. The author refers to Hattie's research findings, stating that goal setting influences how a teacher designs a lesson, how students learn, and how teacher's may react and revise their lessons (p.31). This is really important to chew on.

Two statements in the reading that I want to remind myself of as I plan lessons are these:
1. Implementing tasks that promote reasoning and problem-solving increase the likelihood of students reaching their goals (p. 30). Reasoning and problem-solving should be a part of every lesson (not just for the days we teach a performance task).
2. The use of visual and physical representations (models, diagrams, objects, etc.) are CRUCIAL for students to deepen their learning (p. 34). The author says most students benefit from visual representations; however, I think even the most capable math student becomes a stronger student when he/she can articulate their understanding of number sense and reasoning when using a model, a diagram, a picture, or some other visual to make sense of the math. Students need to have a conceptual understanding of the math in order to make sense of the procedural component.

Reflection: I want to re-look at many of my learning targets and determine if they need some tweaking to be more reflective of learning goals rather than performance goals.

Question: Could a learning goal be written as a question for students to consider and answer throughout the lesson?
1 reply · active 283 weeks ago
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shawnseeleydotcom's avatar - Go to profile

shawnseeleydotcom 44p · 283 weeks ago

Julie,

I've been wondering about my own learning targets as well. I'm thinking about looking at the overall unit and working backward. What is the overall goal of the unit? How do I want students to learn to think about the math in this unit? In each "Big Idea" how should each of my lessons support that idea?

I'm wondering how much tweaking I might have to do so that my lessons support new learning goals rather than performance goals.
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Caty Carino's avatar

Caty Carino · 283 weeks ago

As I was reading chapter 2 I could really connect with establishing and using the learning goals. When I was in college and before I started teaching, my professor talked about backwards design where we design a lesson starting with the learning and assessment goals and then work backwards to create a lesson to meet the rest. When I was in college it seemed like a silly task, because one I was not in my own classroom, so I did not understand how learning goals and targets actually work in a classroom and two I wasn't super familiar with curriculum. One quote that stuck with me was on page 31 "Formulating clear, explicit learning goals set the stage for everything else" Since I have been teaching for a few years now and truly feel like I have my feet under me. I am interested to see how I can look back at my lessons and make my targets more reflective and to ensure that I am focusing more on learning goals rather than performance.

Another things that stuck out to me while reading was on page 30 when the books says, "Students who perceive an emphasis learning goals in the classroom use a more effective strategies, prefer challenging tasks, persist in the face of difficulties, and have a more positive attitude " This quote totally embodies the type of classroom environment I want during math. I have been focusing a lot on growth mindset this year and I have seen an improvement in attitudes towards math. I think I can even take this a step further with really focusing on the learning goals to help create the environment where productive struggle is okay.

My goal is to try and guide my future lessons by applying clear learning goals and design my lesson that is engages with the learning goals in mind.
4 replies · active 277 weeks ago
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Renae Hanson's avatar - Go to profile

Renae Hanson 59p · 283 weeks ago

Caty - I've been nodding the entire time that I've been reading your post. I like how you noted "Formulating clear, explicit learning goals sets the stage for everything else." - I believe that if we have really thought through our goal for the lesson (perhaps the goal might stretch for a week? or few days?), there is no question that our teaching will be better. We will have an easier time incorporating the other 7 teaching practices and the 8 mathematical practices will be evident. When I think back to the days when I was just compliant in writing my goal up on my white board, I feel like I've come a long way in understanding the value that a clear learning goal has for both students and teachers.
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Stephanie Clement's avatar

Stephanie Clement · 283 weeks ago

Caty,

I really want to start planning backwards as well. What a good way to have the end goal in mind for both us and the students. Reading your post reminds me that I need to spend more time teaching about growth mindset. It is so easy for them to feel like math is hard and give up quickly. Effort can be so challenge to teach and motivating them can be hard at times. Maybe more of a focus on growth mindset can help my students out with having a better learning attitude.

Thanks!
Stephanie
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Eric Richards's avatar

Eric Richards · 283 weeks ago

I agree with Stephanie about Growth Mindset. It is so critical that I keep that in the forefront of my math work. So many of my students have a negative self-image when it comes to math and they are getting so much better in believing they are all mathematicians. I am so excited to see the "turn", but it is amazing when we switch content, you need to "start over" with some and re-build their confidence and perseverance for struggle.

I am also going to integrate setting goals into the beginning of each content unit. I want the kids to begin with setting a specific goal what they want to learn and a "habit" they want to improve on with regards to mindset.
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Susan H's avatar

Susan H · 277 weeks ago

I love the quote you pointed out from page 30. This is what we all want in our classrooms, and if we can create learning goals instead of performance goals, it will be a step in the right direction! Your description of working backwards to create lessons focused on the end goals makes a lot of sense!
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R. Bainton's avatar

R. Bainton · 283 weeks ago

Something that really connected and had me reflecting is what the author said on page 32, that learning goals help students “persist in the face of difficulties.” I often see kids give up to easily when the encounter a task that provides a struggle for them.

This made me stop and think about my learning targets and wonder if they are learning targets or more performance targets. We talk often about how the math is ‘easy’ but explaining it is the hard part.
1 reply · active 283 weeks ago
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Caty Carino's avatar

Caty Carino · 283 weeks ago

I like how you have those conversations in math. I see the struggle in math when kids just give up if the problem is hard or is text heavy especially. One thing that has helped is focusing on justification where students need to prove why their work answers the question. I have seen such an improvement because they know they will have to explain. Also, another thing that helped with the struggle is doing number talks, it helped create a space where it is okay to think outside the box. The number talks really helped with thinking about what they are doing, and being able to tell me what was going on in their brains.
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Traci Cline's avatar

Traci Cline · 283 weeks ago

I am not as cerebral as many of you! My limited brain space can only do so much. My thoughts are this: I get the difference between learning targets and performance targets but where do I find the time and energy to really think and develop that detailed of a learning target? How do I put that on my board (as we have been asked to do) in such a way that my students understand?
3 replies · active 283 weeks ago
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Renae Hanson 59p · 283 weeks ago

I was wondering about how daunting (and time consuming) it might be to write a learning goals instead of performance goals, too. I think having a deep understanding of the content standards would make writing learning goals much easier. I still find myself needing to pull out the standards document, read the standard, then read it a second or third time to try to understand what that really looks like. I wish I had them memorized!
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Liz Cuddie's avatar

Liz Cuddie · 283 weeks ago

I was kind of thinking the same thing Traci. Does this mean that we need to re-write current learning targets? I like the idea of extending them more to not be so performance based. I also like the idea of fostering a growth mindset and encouraging them to really dig deep. I would love to see more examples of what this could look like with our curriculum.
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Julie Rodriquez's avatar

Julie Rodriquez · 283 weeks ago

I was wondering about using a question sometimes for a learning goal - a question that students will be able to answer at the end of a lesson. For example, with lesson 3.5, instead of "I can simplify before multiplying two fractions", how about "How is simplifying fractions before I multiply useful?" OR "What does it mean to simplify fractions when multiplying?" Still trying to wrap my mind around this idea.
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Traci Cline's avatar

Traci Cline · 283 weeks ago

Rachelle, any thoughts on how we do get students to persist through the difficult times? I am finding my students are struggling with just persisting and doing quality work through anything right now. I would love to work with someone to see if making my learning goals more focused would help with that.
1 reply · active 283 weeks ago
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R. Bainton's avatar

R. Bainton · 283 weeks ago

I agree, Traci, my struggling kiddos are hanging on, but it can be painful at times. I, too, would love to work with others to see if having learning goals would help them more. More time is always needed.
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Christine Wilson's avatar

Christine Wilson · 283 weeks ago

As I read through the chapter I at first was confused. When I saw the learning goals/targets I thought they were wordy and not kid friendly. Then I realized that the were for the teacher. I saw the later goals as more kid friendly. When I look at my learning goals I usually take it directly from the Teacher Guide. Like today they needed to understand how to "simplify before they multiply." Since I didn't sit down and look at the math practices I didn't know what the "learning" was in that regard. I think the target was more performance based but as I taught the lesson I really focused on what was happening when they simplified and how it helped them get a more clear answer. I keep thinking about what we've been doing and trying to keep in mind "conceptual understanding" and not procedural learning. Of course we always need more time :)
1 reply · active 257 weeks ago
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Sara's avatar

Sara · 257 weeks ago

I've always had an internal struggle with learning goals being for the teacher or the student. I think we need to have both. The kids need to know what they will be learning in words they can understand, but we need to have the goal of the standard we are trying to get them to learn.
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Liz Cuddie · 283 weeks ago

I love the idea of the target being the destination and the road map. I currently post all of my learning targets for each unit on one of the classroom walls and continuously refer to them throughout my teaching. This has helped me keep focused and allows opportunities to revisit prior learning and glance ahead to what is coming next in the unit. I feel like it also helps the kids to be more reflective of their learning. I would like to tweak with those target perhaps, and add some "whys" - make them more of learning rather than performance goasl. I just feel like I need more feedback and clarity on how to do this.

In this chapter I also liked the questioning strategies used. This is always an area where I could use extra modeling and support. Although I don't always have prepared questions for each lesson written out ahead of time, rather I just go with my gut and throw out questions as I teach. I could create more generic prompts ready to go to remind me to encourage deeper thinking and justification from students. I could even make an anchor chart of generic questions prompts that students could use as they do their student talk. The teachers in chapter 2 all consistently asked about justifying answers, pressing for elaboration, creating and explaining models....all really great prompts for great discourse and looking into the "window of student learning".
2 replies · active 279 weeks ago
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Julie Rodriquez's avatar

Julie Rodriquez · 283 weeks ago

Liz, Posting all of the learning targets for a unit in the classroom is a great idea. I have all of the learning targets for the unit on a document the students self-reflect on at the end of each lesson but having it visual for all to see on a wall could be more powerful.

In regards to your thoughts on questioning, I believe the more often you include questions about justification and elaboration in your math talk, the more natural it will become for you to ask authentic questions that deepen students' thinking and understanding. It never hurts to have some questions or sentence stems on your wall, too. :)
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Jen Mako's avatar

Jen Mako · 279 weeks ago

Your post reminds me of the speaker from the Powerful Learning Conference a few years back. She recommended posting the learning goals for entire units on a wall. She used different graphic organizers in a way to display all the students learning. I remember her stating how much buy in she had from the kids. Such a good idea! Thank you
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Stephanie Clement's avatar

Stephanie Clement · 283 weeks ago

After reading chapter 2, I know that most of the time I am writing performance goals instead of learning goals. For future lessons, I would like to focus on a learning goal for the entire unit. I can imagine that it would be time consuming to create a learning goal for every single lesson. I like the idea of having it for the entire unit and keeping that as our focus as we learn new content and practice. I also want to put a focus on keeping them “kid-friendly”. I read the learning target and refer to it throughout the lesson but I’m not confident that the students are using it like they should.
I was also interested in reading about students using more modeling and visuals. I do this often with anchor charts, but I would love to incorporate math manipulatives more so that the students are creating their own models/visuals. This would be beneficial for all students.
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Eric Richards's avatar

Eric Richards · 283 weeks ago

I am going to have students set goals for the unit after they are introduced to the new concepts. I want to then post the goals in the room for them to review, compare, and remind themselves of what they started thinking about at the beginning. We will then be able to celebrate their growth from the beginning and also celebrate their achieving a goal if accomplished. I want to make them more visual for all to see and to remind them of their own belief in what they thought they could achieve. This chapter also reminds me that my Learning Targets need to be pertinent, kid-friendly, and integrated throughout the lesson, reminding students of what we are doing, why, and did we achieve our stated goal.
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Jen Mako's avatar

Jen Mako · 279 weeks ago

I found this chapter to be a great reminder of the importance of creating learning goals, not just for students, but for teachers. I like how the author called them a “roadmap” and a guide for what educators should look and listen for during a lesson. It really seems logical to make this part of unit/lesson planning and a place where grade-level teams could focus attention. This chapter reminded me of the questions that guide PLC work: 1. What do we want all students to know and be able to do? 2. How will we know if they learned it? 3. How will we respond when some students do not learn? 4. How will we extend the learning for students who are already proficient? I think once this work is done, communicating learning goals to kids becomes so much easier and less performance based.
I also thought it was interesting when the authors discussed how emphasis on performance goals over learning goals can negatively affect student motivation and mindset. Yikes! I know I am guilty of this both in the past and present. This is just inspiration to think carefully about how learning goals are shared with students….now where to find the time!
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Susan H's avatar

Susan H · 277 weeks ago

I would most definitely classify my goals as performance goals, not learning goals. It is strange, I feel as though learning goals make so much more sense. During my classes to get my degree, we were told to focus on a specific goal, and have a "set number of problems" the student would get right in order to meet the goal. For example, I can analyze the word problem to determine the operation and can correctly solve 80 % of the given problems. This is seemed less intuitive to me than creating learning goals. I made sure to stray away from the performance goals in order to do well in the class. It is refreshing to hear that "a learning goal is critical" and "a strong mathematics learning goal should also be situated in a learning progression, and connect to bigger mathematical ideas" pg 20.
I read the performance goal out loud to the class and had them rephrase the goal using their own words. If I were to teach the lesson again, I would want them to understand the relationships between multiplication, division, addition, and subtraction. I would rewrite the learning goal as, "students will understand and justify that multiplication is the same as repeated addition, and division is the same as repeated subtraction because the same groups are used in both operations."
I love the Polygon Task (pg 25) and how the teacher put up 3 examples and 3 non-examples of poygons and had the class sort the figures and then had them explain their reasons for sorting them the way they did. The goals are for learning and reasoning, and not performance.
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Sara S's avatar

Sara S · 274 weeks ago

I feel like many of my goals are more performance goals rather than learning goals, but I also use them for the students more than i do for myself so I try to keep them kid friendly. This chapter has definitely made me rethink that. I know there is tremendous power in backward design and i have done it in the past. When i am planning my lessons, I try to always have the learning goal at the forefront of my planning. This chapter has really made me reflect on my planning and lesson design and I hope to see more student success because of it.

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