Association of Teachers of Mathematics in Maine

Week 6: Discussion Question (Option 1)

16 Dec 2017 4:41 PM | Anonymous member (Administrator)

Write about the section "Productive Struggle, Be Less Helpful, and Special Education." Does this resonate with your experiences?

Comments

  • 17 Dec 2017 6:55 AM | Anonymous member
    This section sure does resonate with me! I have often found that lower achieving, or Special Education math students actually have number sense and mathematical reasoning but they spend so much mental energy trying to “plug in” formulas or tricks into their sense making that they end up confused and frustrated. Naturally, their next step is to ask for help, which really means “Will you tell me the steps to solve this problem.” Well meaning adults or students often do just that in the name of “help.” It is a tragedy that leaves the learner unmotivated, defeated and lacking in confidence.

    In the beginning of the year my students are often frustrated with them because I won’t tell them steps. Instead, I ask them questions about their thinking, what tools are available, etc….This approach frustrates some. They tell me “You are the teacher you are supposed to show me how!” As the year progresses however, they accept that I am not going to tell them how to solve a problem and begin to push their own thinking to look for reasonable solutions – which feels good to them!
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  • 18 Dec 2017 6:29 AM | Anonymous member
    Very much resonates with my experience with my sped students. They get very frustrated when I won't give them the steps to solve a problem. It is sometimes a struggle to keep them from shutting down on me completely but I keep encouraging them to use the skills they have learned, stay focused, and come up with a solution as I ask questions about their strategies.
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  • 19 Dec 2017 8:36 PM | Anonymous member
    This section does resonate with me. I often find the students I have with "special needs" don't necessarily need problems broken down more. They generally need help understanding what the problem is asking. Once they know that, I am often impressed with the strategies they come up with to find the answers. They often think in different ways then many other students so their creative way to answer questions is really interesting to follow. They need to be able to have that struggle where they are able to learn. By giving them too much they lose out on learning the skills they need to problem solve on their own.
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  • 19 Dec 2017 10:53 PM | Anonymous member
    Definitely resonates.
    Many kids often just want to know the rule or the steps to solve to only get the work done and not for understanding. This leads to frustration. When students are expected to show proficiency on the target they can't because they haven't processed the information to gain understanding of the content. This frustration leads to self doubt and lack of confidence.
    The more I do the less students can transfer the information. I have really tried to be more conscious of this and have students do more work to lead up to a discovery of the "rule". When students engage in developing a pattern to discover a rule, they have something to reflect back on and to build upon when they run into troubles down the road.
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  • 20 Dec 2017 3:39 PM | Anonymous member
    I find that with some of my special ed students, they will often wait for me to help them and will not try on their own. I am doing my best to not spoon feed them, but if I don't help them with each step, they tend to get nothing done. I am working hard to find the balance between helping them, but giving them time to have some productive struggle.
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    • 20 Dec 2017 7:52 PM | Anonymous member
      Hi Molly,

      It is definitely difficult to watch non-confident students try to work "on their own". For years that have had "extra" assistance to take them step-by-step through a process. They learn to be less independent along the way, which is obviously not our goal. We have to stop "holding their hands" all the time. The special education students often have a common sense about math, but don't get the opportunities to show what they really understand (beyond the addition and multiplication tables).

      Pam
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  • 20 Dec 2017 7:44 PM | Anonymous member
    In a special education math class that I have been teaching for 4 or 5 years, we have been continuously increasing the difficulty level of content at the high school. There have been multiple teachers working on how to do this “gracefully”, in order for students to meet graduation standards (based on the common core). One challenge was how to teach the “2nd level” students about Quadratic Equations.
    Identifying a, b, and c from a quadratic equation in standard form has very little meaning to the students and they often mix up the signs or use an ‘x’ when they should not. No matter how much “explaining” I did, the process of calculating the vertex of a parabola was cumbersome and inconsistent. When I started working with some modeling instead, the students were much happier about the concept of quadratics. The phrase “a picture is worth a thousand words” is very true in this scenario.
    The two problems below are certainly “guided”, but graphing the equations allowed students to work with estimation of heights and different times. Using graphing calculator-generated tables allowed students to explore how and why (after time) the heights would become negative. I also prompted students to consider how different initial heights and velocities would affect the graph and “air time”, which opened discussion opportunities.
    Yes, their was definitely some productive struggle. Students that were completely unfamiliar with anything quadratic interpreted word problems successfully by the end of the unit. Each of them also worked on an Equation Project, where they chose a scenario, developed the equation (with some help in determining velocities), worked on graph and table settings, and finally wrote (and answered) their own questions that related to their equation.

    Pam

    *** Since I can't upload an image:
    a. The trajectory of a rock thrown up off a cliff and it's path to the ground.

    b. The trajectory of a ball thrown up in the air from the balcony at the top of a lighthouse that drops eventually into the water/ocean below.

    The questions asked for each are about initial height, maximum height, height after time and how long it takes the objects to hit the ground / surface of the water.
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  • 21 Dec 2017 11:45 AM | Anonymous member
    Being too helpful definitely creates problems for students in the long term, but in the short term it is a quick fix where everyone feels successful because the student has completed the work (sort of!), the teacher or educational technician has done their job of “helping”, and things are tidied up before moving to the next class. It is pretty clear why this scenario happens over and over for these kids and they develop a sense of learned helplessness. Over time they learn that if they just wait it out, someone will come to their rescue. Breaking that cycle is somewhat heartbreaking because if it continues for too long the student starts to believe they can’t do it and they have had no reason to develop strategies for getting “unstuck”.

    True to the book, most of the modifications for math at our school specify breaking problems down into procedural steps to clearly define the algorithm for students with special learning needs. AHHHH!!! Sometimes this does produce student who can “get the right answer” but have no clear understanding of what they are doing. We would never consider a student to be a reader if they could only decode words and not comprehend the text, but we do it all the time in math.

    I loved that Behrend boiled things down to one rule: understand the problem.
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    • 14 Jan 2018 2:08 PM | Anonymous member
      Fighting time was always my big issue and would cause me to give answers and hopefully something would click for the student, so we could all move on to the next class. :( I get the quick fix.
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  • 23 Dec 2017 10:18 AM | Anonymous member
    As a math educator, I see the importance of productive struggle for all students. I think educators sometimes have difficulty finding the fine line between scaffolding and rescuing students who struggle; we want all students to be successful. I agree with Behrend’s, “only one rule: understand the problem.” Students also need to know why the rules of mathematics work. Reading comprehension can also get in the way of understanding, and reading mathematics content is a skill to be developed. I find that once students understand what is being asked of them, they are willing to put in the effort to solve the problem
    I’m interested in Storegard’s book , My Kids Can: Making Math Accessible to All Learners. It would make a excellent book study, especially with education technicians who are often left out of professional development.
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    • 01 Jan 2018 2:01 PM | Deleted user
      I agree with you Pearl with educators finding the fine line between scaffolding and rescuing students who struggle. All students understanding (comprehending) the problem is what it comes down to. Students with comprehension problems need the time to make sure they understand what their math problems are asking of them. Part of my response to this prompt was "My support staff sometimes gives more support when it is not needed." I agree with you with professional development being provided for the educational technicians as they are supposed to support and are not provided with these opportunities to further their learning.
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  • 25 Dec 2017 4:20 PM | Anonymous member
    I found this section to be very interesting. I used to think that knowing the formula or trick was the way to go. I think I had that idea because math was "not my thing" and I was happy to simply do the trick or formula just to be done with it. Math was frustrating to me and I often felt embarrassed that I did not know the right answer or how to even get there. I did not have teachers that made sure all kids felt successful and "good at math." Over the years, I have trie to provide a different math experience for my students and have struggled in the past to know exactly how much help is too much. I want to provide experiences that give the students productive struggle, but do not want that to turn into frustration and sense of failure. I have also found it hard to get the kids to move away from thinking there is one way to do something and that that is the teacher's way. Getting the kids to venture out and explore with confidence is tricky. It is something I will continue to foster in my classroom. I will pay more attention to what are often called "accommodations" to be sure they are not more than that and that they foster understanding and are not simply breaking things into smaller parts to be memorized. I would like to get the book My Kids Can: Making Math Accessible to All Learners, K-5 by Judy Storeygard, to learn more about how to improve my skills in this area.
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  • 26 Dec 2017 11:24 AM | Anonymous member
    I couldn't agree more when it states there are problems with both - breaking down the problem and teaching tricks/procedures to do the problem. I have seen this more than I would like to say. I think differentiation comes in the form of more time, better conditions, or different ways to participate. I think of one of my students - Rosey (obviously not the real name!) - and Rosey could definitely benefit and does from more time. Better conditions for her include coming in to see me for one on one with the lesson - this helps with her focus and distractions. Rosey is able to be successful with math - and we also put one problem or two on each page - which helps with anxiety. As others have said - Rosey has math sense - it's just other things get in the way. For me - I ask her what we are going to do next - and why is she doing this. The unfortunate piece to this is that Rosey can't stay after every day.
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  • 27 Dec 2017 6:00 PM | Anonymous member
    This section resonates with my experiences as a student and teacher. When I was in school math was very hard and I needed time to understand what the problem was asking me. I encountered many educators that just wanted me to get the right answer and not take so long to think about how to get the answer. The thinking about how you got the answer is so important in making connections to the real world and building foundation knowledge. As an educator, I have worked with students that have struggled in math but what I have noticed that many of them are a lot like me. You need time to really understand what the problem is asking and then time to think about how to apply this to previous learning.

    I have been in classrooms where decisions have been made to move forward with the curriculum and to "help" students by breaking down information but it is not the students doing the work. In my observations it has been the educator because they think they are helping the students stay on track with the other students in the classroom. I agree with a previous poster that all students can learn math and I would love to read Judy Storeygard's book "Making Math Accessible to All Learners, K-5 (2009).
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  • 28 Dec 2017 8:03 PM | Anonymous member (Administrator)
    How to "let" students experience productive struggle definitely resonates with me. I have seen way too many times the teacher step in and provide "help" that then removed the productive struggle from the problem. Tracy mentions we didn't become teachers to make sure kids could pass "that" test and we also didn't become teachers to remove the learning for the students. Awareness of the difference between productive struggle and destructive struggle is critical and takes some experience. Knowing how to help a student who is struggling can be difficult. The suggestions offered in the book are helpful. I often find myself asking a struggling student to, "Tell me what you know about the problem" as a way to get the student to engage in the problem. They sometimes are not sure what I'm asking them but I encourage them to read the problem again and then tell me what they know. Knowing what questions to ask that encourage the student to think about the problem from a slightly different angle takes experience. Teaching students "tricks" or to memorize rules is definitely not the way and I was glad to read about helping students by encouraging them to model the problem, use manipulatives and especially to reread the problem.
    Margin symbols are not something I've seen before but like the idea. I have seen a teacher use symbols like "OYW" for "on your way" which helps the students know that some of their work is correct but not all of it. I might see how I can use margin symbols with my students.
    With my current students I am also aware of their "lack of confidence" in their ideas about their lack of ability to do math. The students have had years of not understanding math. My first challenge is to get them "doing math" that feels like "real" math and build their confidence. I let them know that they can do the math but that it might take more work and longer than they think it should. There are lots of class discussions and sharing of ideas and small group work where the group solves the problem and have to look to each other for help and not to me. If a student asks me a question during group work time, I have to make sure I redirect them to their group members for help first and then I will ask a probing question that is meant to perhaps think about the problem from a slightly different angle. I walk away and give the group more work time before I circle back around and check in with them.
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  • 29 Dec 2017 8:36 AM | Anonymous member
    Wow, this really is a struggle. I like the idea of more time. All students need "think" time. As teachers, I don't think we give enough time for all students. In second grade manipulatives are a great way to show place value and then lead to addition and subtraction with meaning. I too am interested in sharing Judy Storegard's book and DVD to our special education teacher and her staff. We cannot teach math they way we were taught. There has to be the understanding with appropriate support from the ed tech.
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  • 30 Dec 2017 5:25 PM | Anonymous member
    This section is targeted towards students with special needs, however it can be helpful for all learners. Behrend found she only needed one rule to teach her students with learning disabilities and that was “understand the problem.” Many students do not take the time to analyze what is actually happening or being asked of them, their top concern is to finish it and move on. Like in the example of adding columns of numbers, many students who correctly follow a formula do so blindly. Opening the door to mathematical understanding is vital for everyone to learn and grow. Having extra time to understand is necessary if our goal is mathematical proficiency. Yet as I write this I note the hypocrisy in what I am saying and doing. I have a couple students struggling with dividing fractions and I have tried multiple representations of what is happening when dividing a fraction by a fraction. As the class progresses and these two students continue to struggle, I feel rushed to have them learn and have unfortunately done exactly what should not be done and that is breaking into “small chunks to be memorized.” I know they are not understanding yet and I need to find different ways to help them. I am anxious to check out Judy Storeygard’s book for ideas.
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    • 03 Jan 2018 7:39 PM | Anonymous member
      Fractions are difficult for many high school students as well. They might have "learned" the rules at one point...but are very shaky applying them. Division of fractions seems to be the biggest cause of frustration... So as part of a fraction operations review, I asked students (in small groups) to come with a way to explain why 10 divided by 1/2 is 20 that a kindergartener would understand (no flipping fractions and multiplying; no cross-multiplying allowed in the explanation). That was a challenging exercise... When a few students needed a reminder of the rule, I asked them how they explained 10 divided by 1/2 - that was sufficient to get an "oh yeah" and they were off running...
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  • 01 Jan 2018 1:37 PM | Deleted user
    This question hits home for me as an educator. I was a special educator before becoming a regular educator. I have always believed that all kids can learn in their own ways with the appropriate support systems. I feel that all students in my classroom have the ability to work through mathematical struggles, challenges and are able to learn at their own pace and understanding. We as educators have the natural instinct to "rescue" kids who are struggling. With students with IEP's, I find that often the support staff (unintentionally) tend to give support that is not needed when the students are more than capable of answering for themselves. I am lucky as my support staff and I discuss what they should be helping with and when they should step back.
    As a classroom teacher I support all students in my classroom, no matter their learning levels, with their thoughts and thinking as they work through their math problems. The math curriculum that we use allows all students to work through problem solving no matter their level of learning. It is hard when students have challenges when thinking mathematically, but givng all the students an opportunity to think for themselves and show how they solved a problem whether right or wrong is important. Giving "ALL" students independent think time and letting mistakes happen while trying to solve problems allows us all to learn from those mistakes.
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  • 01 Jan 2018 4:58 PM | Anonymous member
    This section resonates with my experiences. Within my classroom I want all kids to feel successful and it is hard when they are struggling not to just jump in and "rescue" them. This year in particular I have been trying to find ways to help all my students to be successful without just spoon feeding them the answer or the method for getting the right answer. I have been trying to get students to work from where they are at to help them to move forward on their own. I feel that using the Math problem makeover method can help students at any level have productive struggle. I want to take a look at the math problems I am using with my students. I find in particular my special ed students struggle when there are multiple steps they are suppose to show when completing the problem and I find I am sitting right with them moving them through. I had bought a group of math problems that have the number bonds, and number sentence spots already on that are suppose to serve as scaffolds for the students when completing the problems, instead they serve as a major struggle. I would like to makeover these problems so that all of my students complete them, which will hopefully move away from having to "rescue" my students. As a result of this class I have started giving the students a number of the day that they can come up with their own ways of displaying that number. The kids all feel successful even if they struggle with math because they are able to show their understanding of numbers in their own way without being told how they need to show their understanding. Each time the kids learn from each other and they are able to display higher level math knowledge then I could have even imagined.
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  • 03 Jan 2018 8:32 AM | Anonymous member
    I have really enjoyed reading all the insightful, thoughtful and thought provoking comments prompted by this discussion question. I teach an alternative 6th grade math class, and I can't help but feel the crunch of time or "lack of" pretty much every day. Productive struggle does need time, and expectations of covering certain standards and curriculum, and reduced math class time seem to be at odds with the time students really need to become confident mathematicians. Many of my students have had a lot of "guidance" with problem solving and have learned many "tricks". I find after a period of getting used to not having this "help" and of being given more freedom with strategies, they become more forthcoming and enthusiastic about what they "know about a problem" and are more willing to take risks with strategies to solve it. They really get into drawing representations of the problem and thinking about whether their thinking makes sense and is their solution reasonable. My task is to structure class time so they have the time they need for "productive struggle", and I am still working on that.
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  • 03 Jan 2018 1:51 PM | Anonymous member
    After I read this section I spent the next few days watching my interaction with my struggling students in a small group session to see if I was one of those being described in the section as having a tendency to "rescue" ... and truth be told, yes, I certainly was!

    In the session, I set my students up to work through an activity using manipulatives to represent real coins, charts on the table top with the image, value, and name of the coin, as well as whiteboards and plenty of space to spread out and dig in. As I watched my 3 students work I noticed that 2 were struggling to make groups of $1.00 using various coins. Before 2 minutes had passed, I was involved in trying to rescue one of those students as he counted out 21 pennies as part of his $1.00. Instead of letting him explore and see for himself that he could add 4 more pennies or take 1 penny away to even out the amount, I jumped in and started telling him to get rid of the extra penny so he'd have an even amount, and then I stopped right in my tracks and pulled back. The section I had just read came flying into my mind and made me realize that what I was doing wasn't helping at all. I wasn't creating confidence or a strategy, I was giving him a rule I thought was best for how I thought the problem should be solved and wasn't giving him ANY opportunity to engage in productive struggle.

    Luckily, as I stopped myself mid-stream, he ignored my "suggestion" (probably because he didn't understand what I was saying) and moved on in his way to use his resources to successfully solve the problem for himself, which he did, and then went on to find several more way to combine coins to make $1.00.


    My new mantra.... as is stated in Chapter 6, pg 131, "We need to focus on the development of the young mathematicians in front of us and let them focus on the assignments in front of them."
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    • 10 Jan 2018 7:06 PM | Anonymous member
      Nicole,

      I am so glad that I am not the only one who has those "aha" moments mid-sentence! :) It is wonderful that your student didn't take your suggestion... :) I think I need to adopt that mantra, as well... our job is not to do the math ourselves, but to provide our students with the opportunities to work out the math for themselves!

      Thank you for sharing!
      Danielle
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  • 04 Jan 2018 9:25 AM | Anonymous member
    This section validated my experience exactly! I am always torn between helping too much and letting students work through problems themselves. As teachers, we want to help students complete the work, but often we aren't helping them to think for themselves and solve problems independently. I love the suggestions and ideas that were given in this chapter. I thought I was helping by breaking down problems into smaller chunks and steps, but I can see how I'm taking the thinking away from my students. I see why students aren't able to think for themselves, and persevere in solving new problems. I am excited to start applying some of these techniques for all students, not just students with IEPs.
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  • 04 Jan 2018 11:15 AM | Anonymous member
    Productive struggle is hard to achieve in the classroom. But, it is an important place to get each student to so that they can build confidence in themselves as a math learner. As a teacher, I feel that the keys to getting students to productively struggle with information lie in questioning, chunking information into smaller pieces and intently listening to my students. Telling is NOT how students learn. They need to explore and "struggle" a bit as they build and construct their own understandings.
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  • 04 Jan 2018 2:34 PM | Anonymous member
    I have 7 SE/Title 1 students in a mainstreamed classroom and I see all students have difficulty with struggling through problems. Teachers, myself included have good intentions, I start out giving students time to explore and struggle, but as time passes us by and curriculum demands increase, we jump in to help our students. I also think many students do not like to struggle, they want to do the work, get the answer, and move on. Several years ago, I started to give students answers to problems to eliminate the focus on 'getting the answer' and expected them to work together. I explained to students they needed to show/explain two ways to get the answer. I saw the anxiety of students decrease and a more willingness to do the problem.
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    • 15 Jan 2018 12:29 PM | Anonymous member
      I use a similar technique for daily warm-ups. I divide the board into four sections ( 2 on top and 2 on the bottom) with a problem with the answer in the middle. The students are asked to find at least 2 ways to get the answer and then we share the possible approaches on the board. Many times, at least one of the strategies will be drawing a picture or a model. As 8th-graders, many think they should have moved on from pictures, but often it is the students that can use that approach who have a true understanding of the problem. Also, they often come up with more than 4 strategies as a class.
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  • 04 Jan 2018 2:47 PM | Anonymous member
    I have often been frustrated with the modifications and accommodations for our special needs students. Some support staff do the thinking for the students so the student doesn’t understand the concept. In my class I try to encourage support staff to support but allow the student to explore and work through the learning. Often time these students excel when they understand the problem and the activity is presented in a low threshold, high ceiling method. They are able to explore and solve the problem in a less prescribed method.
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  • 04 Jan 2018 6:13 PM | Anonymous member
    This section does resonate with me, for sure. I had an experience with our math coach. Thank goodness she was there. We were working on the standard that deals with 10 times more. A spec. ed. student raised their hand to explain where the ten times more was in a picture projected. The math coach was leading this lesson and I have to admit I started to panic when the student approached the board. I was worried about loosing momentum and worried about the students confidence. Boy was I glad she was there. The student took their time explaining their thinking. There were uncomfortably long pauses.My first reaction was to say "what I think he/she is saying is...." Very lovingly and wisely the math coach encouraged me to be quiet. This turned out to be the most amazing experience for my whole class and myself. The student was able to make bigger connections for other students, and explain his thinking in a way that others understood. It was an important lesson for me to learn.... the difference between rescue and productive struggle.
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  • 06 Jan 2018 9:30 AM | Anonymous member
    This section does resonate with my experiences. I was reminded about a story that John Holt related in one of his early books that I read years ago, where he ended up doing the math problem for the student (prompts, etc did not move her in the direction of solving any part of it on her own!). I often see students opt out of trying in SAT Prep classes...because the questions are different.
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  • 06 Jan 2018 9:52 PM | Anonymous member
    I did a 3-act task with my special education students the other day. They watched the introduction and were curious. They had to come up with how many boards to buy in order to make a giant jenga. For act 2, I gave them only the information that they asked for. Each group simply used some multiplication and division with the numbers given and thought they had the answer. They are so used to being given all of the information needed. They were a frustrated with having to ask for relevant information. One of them asked me why I was making it so difficult for them. By the time they get to high school they have been trained to be more passive in math class. It is hard to get them to change.
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  • 09 Jan 2018 9:49 AM | Anonymous member
    I am challenged by truly identifying when a student needs hints, probing questions, or reteaching. It has been my experience that once students are asked to work independently they look for "help". I find that as a teacher I struggle with giving them the time to work through their thinking. I have been working on asking questions to push their thinking and using what I know they can do dto move the almost can do once here I often give more support with the areas of Not Yet.
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    • 10 Jan 2018 7:11 PM | Anonymous member
      Carrie,

      It was interesting for me to realize that I have learned how to gauge when a student needs to not appeal for help in reading, but when it comes to math I feel like I definitely need to rescue them! Perhaps it is because I struggled myself in math when I was in school...? I also struggle with figuring out how long to let students process through the problem before I try to give them some pointers.

      Thanks for sharing!
      Danielle
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  • 09 Jan 2018 7:26 PM | Deleted user
    Productive struggle definitely resonates with me and I often have to set a timer for up to 10minutes where students are not allowed to talk to each other or ask for help from an adult. The only time an adult will approach them is of the student needs the problem reread or reworded because I have a large ELL population in my class. Those first few minutes the first few times I do this are uncomfortable at first for students. They often watch peers get started or will stare at the timer for a few minutes before they start working on the problem. As this has now become part of our routine, when I start the timer, students get to work as best they can because they now know when the timer goes off, they can talk with a peer and this allows them to talk through their thinking and bounce ideas off each other. If they are unsure of a strategy or question, they will ask and I often put it back to their partner to talk about. I continue to stress the importance of remembering all we have learned so far this year along with their prior knowledge to help during that “productive struggle” time and I continue to try to be less helpful so they can feel the success of figuring it out.
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  • 10 Jan 2018 7:03 PM | Anonymous member
    In reading this section, it became clear that I definitely jump in too quickly when I perceive that students are struggling with a concept. It is the natural interventionist in me-- I have been trained to scaffold students, and I always struggle with the question, "How much scaffolding does this student need at this moment?" Whether it is because I work with multiple students at a time who need varying degrees of scaffolding, or whether I just can't stand to see them struggle... I am not sure! I think sometimes I am just frustrated that they are not understanding a concept, even though I have taught it to them several different ways. I need to remember that not all students are going to learn the same way, at the same rate... and that my job is to figure out what they need, and how to provide them with it.
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  • 14 Jan 2018 2:20 PM | Anonymous member
    Before conferences 6 years ago, students filled out a paper. One of the questions was, "What is something I can do for you?' One students answered, not to tell her the answer, but to help her figure it out on her own. I will never forget that. I needed to slow down. It didn't matter to her that the end of class was near. She wanted to learn. She wanted to understand. She wanted the productive struggle.

    Working with the library media specialist, she reminded me that struggle is how your brain grows. Students would come to her and ask a question. Her reply would be a question or go back and think. I have learned to value think time much more as an experienced educator. I wish I could go back to the beginning years and allow more think time for those students.
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  • 15 Jan 2018 12:46 PM | Anonymous member
    I definitely am a "rescuer"which needs to change, but something that I am getting much better at is helping my students understand problems. I have finally realized that many of my students who seem to be poor problem solvers are actually challenged readers. They can't solve the problem if they don't know what is being asked. I tell my students that it is like solving a mystery and each detail is a clue. I have the students read the problem through twice and then they look at the individual parts. For words/ phrases such as "sum", "difference", or "twice as many" we write the operation symbol above the word. For pronouns such as "it" or "they" we write what the word represents and so on. Once the students understand the words in the problem, the math can become much clearer.

    My next goal is to give them more time to work on their own. I feel like I am constantly looking at the clock and thinking "we need to move along", which denies the students the time they need to think on their own.
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  • 15 Jan 2018 2:52 PM | Anonymous member
    I've been trying to read the chapters before reading the prompts, so that my responses are more authentically based on my initial thoughts. I've fallen behind on the prompts, but not the reading, so I was tickled pink to flip back to this section and see I'd marked it all up with exclamation points and underlines!

    YES -- this very much resonates with me. In particular, "The problem with the break-it-down approach is, if an educator (Classified or certified) breaks down the problem and directs what to do for each step, then the educator is the person who has done the problem solving, thinking, and learning."

    I have wrestled with this at varying levels for my entire career. I've seen some cases where ed techs flat-out do the work for the student and other cases where the ed tech works tirelessly to truly have the work be the student's, and other countless cases somewhere in the middle. The problem that I see is that so many IEPs demand this as an accommodation! And if the ability to parse out problems is described as part of the disability, what then? And should our goal for some students truly be to get them to a level of competence of being able to DO versus being able to UNDERSTAND? This is a bigger question than we can answer here, but in some cases there may not be anything wrong with helping a student get to a level of being functionally able to complete a task that will serve them well in life, even if they couldn't articulate the logic of the underlying concept. (For example, dividing fractions!)

    I have had some wonderful conversations with thoughtful, brilliant colleagues, and none of us have come upon a solution. I think this is actually worse now, with testing and mandates, and proficiency. I won't turn this into a political post, so I will leave it at that.
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  • 15 Jan 2018 8:58 PM | Anonymous member
    This was another great chapter hitting on so many of the frustrations I have and see in math classrooms. We have a packaged program that is focused on procedural knowledge. The math understanding really depends on the teacher teaching the program. A teacher may or may not go for understanding within a lesson. Time may factor as a constraint, as well as teacher involvement. A teacher who groans at math will do less work than more. A teacher with a greater number of students will do less work, not more in terms of the understanding piece. WHY? Because the program we are held to teach covers a lesson a day, and you are not supposed to get behind. If you do, you look bad and everyone is concerned that the students will miss out. Then next year's teacher must pick up the slack. When this is the culture of a school, there is a lot of work to be done to change practice.
    On a more positive note, I do see change happening. I am excited to be part of this study because I am in a position to start nudging teachers in more positive directions with their practice. I am able to encourage teachers to try new approaches and strategies to reach greater numbers of students and to improve our overall results. I plan on sharing much of what I am reading about here. Many of us are involved in learning about growth mindset, and this is giving us insight into allowing students to take ownership of their learning, to struggle through the learning process and to know when to ask for help and how to do it.
    Many of us have been taught in the "I do, We do, You do" model and it's been an ingrained part of the teaching fabric. I feel glad about being allowed to let that particular piece of fabric go. I am all for a new path.
    I remember a math program I used several years ago as a supplement to a math program we were teaching at the elementary level. Our program then covered basic math skills development, but did not allow for any creativity or exploration. I implemented a program called, "Read It, Draw It, Solve It". It became a favorite part of the school day for students and teacher alike. It was just a problem, in word form at the top of the page. It was a version of a "makeover" as described in Ch 6. Students read the problem and were at liberty to solve it in any way they thought was appropriate. It was open ended sometimes, and not other times. Students had to draw on their own resources to work out what to do. As the teacher, that was where I learned the most about my student's reasoning abilities in math. AND the math was fun, creative and engaging.
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  • 21 Jan 2018 8:47 PM | Anonymous member
    I actually went back and read parts of this chapter again. I have had a difficult year, having so many special education children. Probably the most difficult problems at first when I give a student a problem to solve is not all of them can READ the problem. I have to read the problems. Then the difficulty comes with the students not understanding, having the comprehension of what is being asked of them. I have learned to have lengthy conversations with them in particular. I have had to give them time to search out the first step, but often have to give the beginning before they can even get started. They may not master the problem from here, but most often are willing to try to work it at least.
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  • 03 Feb 2018 10:03 AM | Anonymous member
    Chapter 6
    Productive Struggle
    Often, I have ed-techs, and even the math coach come into my room and interfere with students “struggling” to solve a problem that I carefully selected for that particular class. I explain that through the struggling, thinking, discussing, and exploring they are learning.
    I monitor the struggles, by asking questions, and when the students are able prove something, they understand it.
    Allowing them to figure out why or how things work encourages dialogue, or as people now say discourse.
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  • 21 Feb 2018 4:02 PM | Anonymous member
    Sometimes when you read something and see yourself and you realize something - I am an enabler of math!! I realized that I did not give my students enough wait time - I let them say, "I don't get this!" and then give them a prompt versus asking a question of what they don't understand.

    I recently had a student move back into the "regular" classroom from special ed classes in math - they had been there for the past two years - I found that she wanted the same support that she received in there with me. I had just read this chapter and when the student said they needed to go back to the other classroom - we immediately sat down and talked about math and how they waere able to come to me because they were capable of the work - what we needed to work on was her asking questions, challenging me, but not to immediately give up. I told her that I needed to give her the time to think, process and provide me with her understanding and I would not jump in and solve things - we needed to work on math struggles and stamina.

    I have made notes on my clipboards and desk to remind me to allow students time, do not help to fast, ask questions, etc.
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  • 13 Mar 2018 8:59 PM | Anonymous member
    I am a certified Special Educator in a high school setting in math classes as a co-teacher. I see students struggle across the board, with or without IEPs. As co-teachers, we are blessed with two teachers in the classroom with 5 years of co-teaching behind us. We are Jo Boaler and Carol Dweck, Dan Meyer, and Tracy Johnson Zager believers and practitioners.
    We spend loads of time reflecting on how our lessons pan out and believe whole-heartedly in offering hands on, let's connect it to real-world situations, movers away from pure procedure, having kids work on developing grit, and the like.

    Sometimes I do too much rescuing and when I see myself doing it I feel cheesy. I want to get them through, get them caught up, you know, somehow justify how I just need to do my teaching that way! No, I don't, and I need moments like this to remind myself of what I am taking away from those students in the long run.....

    Asking students if they understand the problem is a great place to begin.....allowing them to attempt to articulate what they do know and getting them to practice the skills of assessing, analyzing, describing, attempting, staying in the game, and so on.
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