Shift 8 Tie the math to such questions as How big? How much? How far? to increase the natural use of measurement throughout the curriculum.
Students do not know measurement. That’s the bottom line and the only way to change that fact is to make measurement part of everyday instruction and part of everyday life. Just having students memorize formulas and do a lot of meaningless busy work isn’t going to help them or us as teachers to achieve this goal. In order for our instruction to be effective, we need to make it real in a way that will resonate with students and give them a deep understanding of the concept behind the formula. I felt that Leinwand’s example of how to take an objective like finding the surface area of right circular cylinders and making it fun and exciting was ingenious. You can put a story behind it by making the cylinder a can of soup or a barrel of hazardous waste or some other intriguing thing like skin around the human body. You can add units of measurement and also ask for an estimate. You can talk about the formula itself, how it came about and why it works. And then you can break the formula down and pay attention to the elements of the formula. All this adds flavor to the task at hand and sets the stage for meaningful teaching. Leinwand chooses to talk about an adult male who was completely burned and needed new skin. The questions he asks his class engage the students thoroughly and the thoughts provoked are amazing. They come up with a variety of ways to find the answer and then to defend it and convince their teacher that their outcome is correct. The way in which Leinwand approaches what he wants to teach causes the students to care about what they are learning because it is “relevant, because we’ve peaked their curiosity, and because they can personalize the situation.” Interesting and thought provoking contexts should always be used as a basis for delivering effective math lessons. After reading the chapter on Shift 8, I tried hard to remember even one math lesson that was so much fun and interesting and relevant and sadly I could not. I hope that today's students will have a lot more to remember because today's teachers know how to effectively impart math knowledge to them.
Helen: I agree that Leinwand's ideas and examples in this shift were exceptional. The story approach to presenting a math problem is great. It provides that context-rich environment that is needed to make math relevant and meaningful. As a teacher this is one area I need to improve upon. As you said, I cannot think of many lessons where the math concept was presented in an engaging way like this. What a shame! Perhaps that is why it is difficult for me to do it - I don't have good examples. I think it is also hard because it can be time consuming. I'm sure though that after several thought out ideas for a context it will become easier for me. As you mentioned too, taking the time to do this is essential because it allows children to think creatively and problem solve. In the end they are learning by solving the problem AND by listening to each others ideas. YES!
Helen, I can't really remember exciting math problems growing up. Most of my math happened at home. My mom taught me to sew and from the time I was 6 I could thread a needle and sew clothes right onto Barbie. I can't tell you now, but I used to know Barbies measurements. I used scraps of fabric and I remember wishing I had more of this fabric or that. I measured and cut trim and sewed on buttons. Then would start all over the next day. This never happened in my elementary school. They didn't trust me with scissors either.
Juliet, your experience of sewing with your mom reminded me of sewing with my mom. She worked as a seamstresses making wedding dresses first at a factory and then at a store where they made wedding dresses from scratch. And I helped her at the margin when she brought work home with her. It is interesting that I now remember the measurements she used to cut out her own patterns... I had totally forgotten. This is another example of how math is used in our every day lives and becomes second nature. And when we involve our children in our daily enterprises, we can teach them meaningful math concepts.
I recalled my math class in high school, it was a transitional mathematic instruction and wasn’t related to practical life at all. Teacher let us memorize lots of formulas for the test even though students didn’t understand the meaning of formulas. I agreed with you that teacher plans math lessons real in a way to give students understand easily.
I think the instructional shift of “minimizing what is no longer important and teach what is important when it is appropriate to do so” gets to the heart of math instruction. The Common Core seems to have started this instructional shift. The Massachusetts Frameworks were always asking teachers to teach concepts which have not been mastered nor do they require mastery until the following year. If teachers could have an isolated number of concepts and goals to reach by the end of the school year, the mastery of the skills would be much more efficient. I am currently frustrated with the math program my school has adopted. My students have come to me and some are struggling with addition and subtraction. This is common ground for a third grader, but rather than starting with 2-digit numbers, which is just about where they left off in second grade with minimal exposure to borrowing, the third grade program is asking the students to master 3-digit subtraction and addition. The concept of regrouping requires additional practice, but due to extremely tight restrictions sent through the ranks, we are not allowed to take additional days to review the concepts. Instead we move on to the next lesson and we are forced to squeeze in extra practice with limited time. As I look ahead to the next topic, we are jumping head first into multiplication. I simply feel the students are being asked to move rather quickly through the program and it has become a whirlwind of information for the students. As I talk with my colleagues about this program we are all in agreement that as soon as we have some control over math again we will start isolating which lessons are essential and we can spend more time on the concepts the students need to master.
Mandy, Why is it that when we see something isn't working, that we stick it out anyways. This exactly what Leinwand was talking about. Teachers must push through the curriculum, even if it doesn't make sense. Our 2nd grade teachers start the year off with double digit addition & subtraction because it takes all year to master it...but Leinwand states that maybe students just aren't ready for these concepts. My response as a 1st grade teacher is to make sure my students have memorized as many math facts as they can to minimize their stress in 2nd grade. Is this the long term outcome of "teaching to the test"? So what is the right answer?
Mandy, that is so tough. It seems truly unfair that the teacher has no control over what he/she teaches and at what pace. You know your students better than the books do, and they need to trust your judgement. It's also impossible to keep kids on the same math track when each grade has such an incredible range of ability. It's sad because the kids who can't keep up and aren't ready to move on must feel utterly lost and probably dislike math because of it. I keep hearing kids say they aren't good at math and it really frustrates me that they're made to feel this way. Why?
I understand how frustrating it could be for you to know what your students need but have little control over what you need to do to help them progress. I mean how can they master new content if they have not yet mastered previous content. Isn’t our job as teachers to ensure that all our students develop and master important content to become successful? How can we do this, when our school districts do not support us? Imagine, being in the place of our students who are struggling to keep up. They begin to perceive themselves as “dumb,” and in some cases give up on school. It makes me sad that even when we know something is not right, we are pushed to do it anyway. I hope you and your colleagues gain control over math again soon. Best of luck.
I found this instructional shift very relevant to my mathematics teaching.
First, I agree that measurement is a very neglected standard in our mathematics curriculum. In third grade, I still have students who struggle with telling time and using a ruler or other measuring device. Sadly, it isn't reviewed frequently either in our school curriculum. Sure, it appears in Spiral Review worksheets, but not in lessons. And isn't the goal NOT to use worksheets unnecessarily?
The second point that I found very true for me is the lack of relevancy in the lessons. This is something I personally struggle with as a first year teacher - especially when it isn't already worked into the lesson for me. Since math wasn't taught to me in context, I think I forgot that I need to do this for my students. I also struggle to realize what is the real-world connection. If I have one goal for my future math lessons, it is to discover and share the life connections with my students.
Currently I am struggling to engage a few of my girl students in math, and I think it might be because they don't see the purpose. Sure, they understand the skill or concept, but they have no "why?". As Leinwand stated, "Unfortunately, in mathematics, stating the learning objective is often the best way to lose half of your class in the first few minutes" (47). I think a lot of my students shut down when they here the formula or the steps. If they don't shut down, they are giving the answers but not thinking about the "why" or the "how" behind the process. I do believe Think Math! is doing a better job of pulling explanations out of the children and encouraging them to think, but it is still missing the very important real-world connection piece.
When I read this shift, I was a little skeptical as well because the examples given of how to achieve these two ideals (relevancy and measurement) seemed too abstract and open-ended for my third grade students. Perhaps at the end of the year they could solve an adapted open problem like this, but certainly not now. It is still a struggle to get them to be independent and read the directions. I am hoping that our problem solving heavy curriculum will eventually get them to a point where they could tackle something like the skin graph problem. What is very attainable for my students now though is to think of measurement in referential terms and ask questions like, "How big?" or "How far?".
Shannon, I think I may have a relevant math question for your girls who are not yet convinced that math rocks. Ask them how many outfits they can make with clothes from thier closet. Have them select and take pictures of these outfits. Make sure they have only two pants, two shirts, two sweaters, two pair shoes, etc...you make the rules. They might just get a kick out of it!
I like the idea of engaging the female students in Shannon's class with how many outfits can you make from your closet. We just read a book called "A Three Hat Day" by Laura Geringer. We asked our first graders to work it out in their math journals, how many days could the character wear these three hats, if a different hat combination was worn each day? Both boys and girls loved trying to solve this. Something about clothes, regardless of age or gender, that is engaging. It was fun to watch the learning process unfold.
According to Leinwand, there are several areas of instruction that can be minimized simply because students don’t need really need to know or do the practice. His example of multiple digit multiplication or long division is a good one. I think students should know how to do the computation, but not tons of practice. I think this multi-step process is better with calculators. Students need to be efficient with the calculator. I’m also on the fence with Algebra I for 8th grade. I recall learning that 8th grade brains aren’t ready for the advanced thinking needed for algebra. But, if they don’t get it in 8th grade, it messes them up for 9th grade physics and the 10th grade physics MCAS. And then forget college! This makes me believe that the trend to teach to the standardized test has pushed everything back a year. Parents absolutely do not want to see that their child is only satisfactory, so we push through the curriculum. I have 3 boys in first grade who are old enough to be in 2nd grade. The parents kept them back just to give them that extra year.
Juliet: You have three students who stayed back? That is amazing, but so unheard of. I wish more parents would follow that example and realize that sometimes children are not just ready to advance. Everyone develops skills at different rates.
I also agree with your thoughts on long computation and calculators. It is important to have practice to understand how the procedure works but there is no reason to "drill and kill." Once students understand the process that the calculator is going to do, then let them use a calculator. We are already such a technology driven society that we might as well take advantage of it. This will also free up students to think more deeply about math and focus more on the underlying "whys" and "hows" of math; we won't be boring them with what they see as pointless exercises.
Shift 8 asks teachers to teach only what is important to teach and only when students are ready to learn it. Instinctively, this shift makes complete sense, but practically, actually making it happen may not be possible.
I cannot count the number of times I’ve heard a student ask, “Why do we have to learn this?” or “When am I ever going to use this?” Even though I majored in math as an undergrad, I asked these questions of some of my own classes. Occasionally when a student asks these questions, I can’t help but think, “I really don’t know why you need this right now.”
Last year my district started using a new math program, which meant that the teachers and the students were struggling to get used to it. At times the teachers desperately wanted to skip, change, or postpone units in our new program. However, when meeting with curriculum coordinators we were told to trust the program. It is difficult to trust the program when I see kids struggling, but what if I’m wrong and it really does all come together? So for me, the tricky part is balancing your teacher instinct to stop moving forward, and “trusting the program” and the district’s choice to use the program.
Anjali, I can completely understand how that would be a difficult situation... wanting to trust your instinct but then needing to listen to the district as well. I suppose the best you can do at this point is provide all the feedback possible, and if they say to trust them because it'll work... give it more time?
You know exactly how I am feeling about this new math program I have to follow. I have been on the phone with parents for the past few weeks because their child did not get an "A" on their math test. I am constantly trying to explain that due to the new program then there is going to be a small gap between what the program expects them to know and what they actually know as a result of having a different program last year. This is frustrating. I am hoping that next year there will not be this gap and the beginning of the year will go smoother. I hope this year has been easier than last year for you.
Adjusting to a new math program that is also of a different math philosophy is really hard. I do worry about the math gap that is created, especially for higher grades. My own daughters had this experience just from changing from elementary to middle school.
Also, at my school, we are 'mapping' our curriculum as a school project. And the selling point is that a parent can see exactly what their 8th grader learned in 1st grade. The curriculum map is NOT a personal education map -- it's just a long list of what a school taught that year and then it will be updated. Follow? We were told that parents will be able to see the continuum of their child's education, but it doesn't account for all the changes in curriculum that easily happen over 8 years. So how can we really see the holes in one student's education? Follow?
So with a new math program, who is keeping track of what students are missing and need extra instruction on? I'm just not sure how this works.
I agree with that higher standards should not mean teaching more math and harder than to more students at earlier and earlier grades. First of all, we need to think about what is important to teach appropriately. As Leinwand mentioned, teacher needs to minimize some areas of instruction simply. Also it is very important to teach instructions when students are ready and they need to know. I noticed that so many students are struggling with multiplication and division. Especially when they move to 3digit number problems, some students don’t master 2 digit number problems yet. So teacher needs to let them have a deep understanding of problem concepts.
Rebecca, Even with first graders, when is more time on a concept a good idea and when is it just more drill & kill? 6 year olds need breaks from a tricky concept and then a revisit. We just spent october on addition, and this month it will be subtraction. I teach simple lessons everyday and tend to keep a steady pace. I like to fill in with extra help during math games or carve out time somewhere else in the schedule. Older grades have a lot tighter schedules so I imagine flexibility is not easy. When to move on? This is a good question.
Instructional shift 8 states that we should “minimize what is no longer important, and teach what is important when it appropriate to do so”. I completely agree with this shift. Throughout high school and college I often found myself sitting in class (not necessarily a math class), asking myself why I needed to know what my teacher or professor was rambling on about. I think that there are certain skills and concepts that students don’t necessarily need to know or master, at least not until a certain grade or age. Bombarding students with unnecessary concepts will most likely just confuse them, and have them asking us “Why do we need to know this?”
Adrianna- I think about the reading specialist at our school. Her philosophy is "easy reading, makes reading easier." And so I think "easy math, makes math easier." Not that we aren't going to have challenging math in school, but that we teach "what is important when appropriate."
Andrianna, I think teacher's should be able to answer "why do we need to know this?" and if they can't, rethink the lesson or unit. I Tana's idea that easy math make math easier! Well, why not? Teach an important concept with a real world connection. If the concept is mastered, the extra time consuming practice isn't necessary nor helpful if students are confused. Practice makes perfect isn't always the right route to go.
I agree with Leinwand’s instructional shift 8. We should teach what is important at the appropriate time and minimize what is no longer important. I remember in my math classes in high school my teachers spent so much time getting us to memorize and regurgitate formulas that I never really understood why. Every time we started a new topic I remember remarking, “Ohh great, another formula to memorize.” To this day, I can only recall few formulas from the top of my head, others I would need to look up. I believe when math loses touch with real-word expectations then it loses meaning for most students.
It frustrates me that teachers have to teach everything prescribed to them by their district even when they know some students are not ready to move forward and cannot possibly succeed without revisiting and mastering previous content. Curriculum mandates and standardized tests puts a great amount of pressure on teachers to rush through the material and students to develop at a rate faster than they may be ready to do so, thus setting up both parties for failure. This creates a classroom of students who are sinking and others who are swimming. I think this influences some students’ decisions to drop out of school because they see that school is not for them and that teachers are mainly concerned about those students who they believe will go far in places. This is why, I like the idea of 1-year postponement mentioned in this chapter. This can allow sinking students to catch up to their classmates, and develop at a rate that they are most comfortable with. But how can we influence the decisions of policy makers, especially when everyone is so concerned about our students lagging behind in math when compared to other countries.
I specifically liked Leinwand's list of mathematical content that he views as "bath water." Fractions were always a challenge for me at a young age. I had to really study. Who cares about sevenths and ninths?.....I had never seen any type of measuring cup in our kitchen with sevenths or ninths listed on it.
I was fascinated to read his thoughts on the cycle curriculum mandates and testing standards. It makes sense of how we get ourselves trapped into teaching skills for standardized tests.
Finally, it was grounding to read Leinwand's thoughts on expectations for "nearly all students." There is flexibility in his language (nearly all students) and yet high standards to master what is truly important for students to attain when it comes to math. Currently in our classroom, we have discovered there are some students who need mastery on some basics. We will be working with them during our "math center" time to achieve this.
I support the instructional shift to minimize what is no longer important and teach what is at the appropriate time. It seems easier said than done though. Students should not just be memorizing formulas and symbols, because there’s a slim chance they’ll retain that information from year to year and remember it when they actually need to solve a math problem in the real world. I love that Leinwand wrote about the nervous laughter coming from teachers when he asked for the formula for the volume of a sphere. Who knows that off the top of their heads?! Many adults know that if they need to figure this out, there is a way to find it. Students are taught and expected to know complex and rarely used formulas, at earlier ages. Why? Leinwand mentions that the standardized tests put pressure on school administrators, but why aren’t we doing what’s best for the kids? It’s unfair to expect the mastery of certain concepts before students are ready for it. All it does is lower their self-esteem and increase their distaste for math. I appreciate his advice to skip the last two chapters in the book in order to give students more time with the important content. All educators should feel that they have the power to do what is in the best interest of their students.
I completely agree with what you are saying. I once heard an educational speaker talking about the importance of allowing students to advance into the twenty-first century and part of this is allowing them to use technology. As the students get older and become adults, there is nothing they cannot discover on their own because they have an endless supply of technology at their fingertips. The students should not be required to memorize anything because as an adult, I cannot remember the last time I was forced to memorize information. Instead I research the information I need and then answer the questions. This is the skill we need to be teaching explicitly, not wasting our time on memorizing facts. The need to teach to the test is becoming devastating to the development of our students. I am oping Leinwand's shift starts being considered as the states adapt to the new Common Core.
Shift 8
ReplyDeleteTie the math to such questions as How big? How much? How far? to increase the natural use of measurement throughout the curriculum.
Students do not know measurement. That’s the bottom line and the only way to change that fact is to make measurement part of everyday instruction and part of everyday life.
Just having students memorize formulas and do a lot of meaningless busy work isn’t going to help them or us as teachers to achieve this goal. In order for our instruction to be effective, we need to make it real in a way that will resonate with students and give them a deep understanding of the concept behind the formula.
I felt that Leinwand’s example of how to take an objective like finding the surface area of right circular cylinders and making it fun and exciting was ingenious. You can put a story behind it by making the cylinder a can of soup or a barrel of hazardous waste or some other intriguing thing like skin around the human body. You can add units of measurement and also ask for an estimate. You can talk about the formula itself, how it came about and why it works. And then you can break the formula down and pay attention to the elements of the formula. All this adds flavor to the task at hand and sets the stage for meaningful teaching.
Leinwand chooses to talk about an adult male who was completely burned and needed new skin. The questions he asks his class engage the students thoroughly and the thoughts provoked are amazing. They come up with a variety of ways to find the answer and then to defend it and convince their teacher that their outcome is correct. The way in which Leinwand approaches what he wants to teach causes the students to care about what they are learning because it is “relevant, because we’ve peaked their curiosity, and because they can personalize the situation.” Interesting and thought provoking contexts should always be used as a basis for delivering effective math lessons.
After reading the chapter on Shift 8, I tried hard to remember even one math lesson that was so much fun and interesting and relevant and sadly I could not. I hope that today's students will have a lot more to remember because today's teachers know how to effectively impart math knowledge to them.
Helen:
DeleteI agree that Leinwand's ideas and examples in this shift were exceptional. The story approach to presenting a math problem is great. It provides that context-rich environment that is needed to make math relevant and meaningful. As a teacher this is one area I need to improve upon. As you said, I cannot think of many lessons where the math concept was presented in an engaging way like this. What a shame! Perhaps that is why it is difficult for me to do it - I don't have good examples. I think it is also hard because it can be time consuming. I'm sure though that after several thought out ideas for a context it will become easier for me. As you mentioned too, taking the time to do this is essential because it allows children to think creatively and problem solve. In the end they are learning by solving the problem AND by listening to each others ideas. YES!
Helen, I can't really remember exciting math problems growing up. Most of my math happened at home. My mom taught me to sew and from the time I was 6 I could thread a needle and sew clothes right onto Barbie. I can't tell you now, but I used to know Barbies measurements. I used scraps of fabric and I remember wishing I had more of this fabric or that. I measured and cut trim and sewed on buttons. Then would start all over the next day. This never happened in my elementary school. They didn't trust me with scissors either.
DeleteJuliet, your experience of sewing with your mom reminded me of sewing with my mom. She worked as a seamstresses making wedding dresses first at a factory and then at a store where they made wedding dresses from scratch. And I helped her at the margin when she brought work home with her. It is interesting that I now remember the measurements she used to cut out her own patterns... I had totally forgotten.
DeleteThis is another example of how math is used in our every day lives and becomes second nature. And when we involve our children in our daily enterprises, we can teach them meaningful math concepts.
I recalled my math class in high school, it was a transitional mathematic instruction and wasn’t related to practical life at all. Teacher let us memorize lots of formulas for the test even though students didn’t understand the meaning of formulas. I agreed with you that teacher plans math lessons real in a way to give students understand easily.
DeleteI think the instructional shift of “minimizing what is no longer important and teach what is important when it is appropriate to do so” gets to the heart of math instruction. The Common Core seems to have started this instructional shift. The Massachusetts Frameworks were always asking teachers to teach concepts which have not been mastered nor do they require mastery until the following year. If teachers could have an isolated number of concepts and goals to reach by the end of the school year, the mastery of the skills would be much more efficient. I am currently frustrated with the math program my school has adopted. My students have come to me and some are struggling with addition and subtraction. This is common ground for a third grader, but rather than starting with 2-digit numbers, which is just about where they left off in second grade with minimal exposure to borrowing, the third grade program is asking the students to master 3-digit subtraction and addition. The concept of regrouping requires additional practice, but due to extremely tight restrictions sent through the ranks, we are not allowed to take additional days to review the concepts. Instead we move on to the next lesson and we are forced to squeeze in extra practice with limited time. As I look ahead to the next topic, we are jumping head first into multiplication. I simply feel the students are being asked to move rather quickly through the program and it has become a whirlwind of information for the students. As I talk with my colleagues about this program we are all in agreement that as soon as we have some control over math again we will start isolating which lessons are essential and we can spend more time on the concepts the students need to master.
ReplyDeleteMandy, Why is it that when we see something isn't working, that we stick it out anyways. This exactly what Leinwand was talking about. Teachers must push through the curriculum, even if it doesn't make sense. Our 2nd grade teachers start the year off with double digit addition & subtraction because it takes all year to master it...but Leinwand states that maybe students just aren't ready for these concepts. My response as a 1st grade teacher is to make sure my students have memorized as many math facts as they can to minimize their stress in 2nd grade. Is this the long term outcome of "teaching to the test"? So what is the right answer?
DeleteMandy, that is so tough. It seems truly unfair that the teacher has no control over what he/she teaches and at what pace. You know your students better than the books do, and they need to trust your judgement. It's also impossible to keep kids on the same math track when each grade has such an incredible range of ability. It's sad because the kids who can't keep up and aren't ready to move on must feel utterly lost and probably dislike math because of it. I keep hearing kids say they aren't good at math and it really frustrates me that they're made to feel this way. Why?
DeleteMandy,
DeleteI understand how frustrating it could be for you to know what your students need but have little control over what you need to do to help them progress. I mean how can they master new content if they have not yet mastered previous content. Isn’t our job as teachers to ensure that all our students develop and master important content to become successful? How can we do this, when our school districts do not support us? Imagine, being in the place of our students who are struggling to keep up. They begin to perceive themselves as “dumb,” and in some cases give up on school. It makes me sad that even when we know something is not right, we are pushed to do it anyway. I hope you and your colleagues gain control over math again soon. Best of luck.
I found this instructional shift very relevant to my mathematics teaching.
ReplyDeleteFirst, I agree that measurement is a very neglected standard in our mathematics curriculum. In third grade, I still have students who struggle with telling time and using a ruler or other measuring device. Sadly, it isn't reviewed frequently either in our school curriculum. Sure, it appears in Spiral Review worksheets, but not in lessons. And isn't the goal NOT to use worksheets unnecessarily?
The second point that I found very true for me is the lack of relevancy in the lessons. This is something I personally struggle with as a first year teacher - especially when it isn't already worked into the lesson for me. Since math wasn't taught to me in context, I think I forgot that I need to do this for my students. I also struggle to realize what is the real-world connection. If I have one goal for my future math lessons, it is to discover and share the life connections with my students.
Currently I am struggling to engage a few of my girl students in math, and I think it might be because they don't see the purpose. Sure, they understand the skill or concept, but they have no "why?". As Leinwand stated, "Unfortunately, in mathematics, stating the learning objective is often the best way to lose half of your class in the first few minutes" (47). I think a lot of my students shut down when they here the formula or the steps. If they don't shut down, they are giving the answers but not thinking about the "why" or the "how" behind the process. I do believe Think Math! is doing a better job of pulling explanations out of the children and encouraging them to think, but it is still missing the very important real-world connection piece.
When I read this shift, I was a little skeptical as well because the examples given of how to achieve these two ideals (relevancy and measurement) seemed too abstract and open-ended for my third grade students. Perhaps at the end of the year they could solve an adapted open problem like this, but certainly not now. It is still a struggle to get them to be independent and read the directions. I am hoping that our problem solving heavy curriculum will eventually get them to a point where they could tackle something like the skin graph problem. What is very attainable for my students now though is to think of measurement in referential terms and ask questions like, "How big?" or "How far?".
Shannon, I think I may have a relevant math question for your girls who are not yet convinced that math rocks. Ask them how many outfits they can make with clothes from thier closet. Have them select and take pictures of these outfits. Make sure they have only two pants, two shirts, two sweaters, two pair shoes, etc...you make the rules. They might just get a kick out of it!
DeleteJuliet-
DeleteI like the idea of engaging the female students in Shannon's class with how many outfits can you make from your closet. We just read a book called "A Three Hat Day" by Laura Geringer. We asked our first graders to work it out in their math journals, how many days could the character wear these three hats, if a different hat combination was worn each day? Both boys and girls loved trying to solve this. Something about clothes, regardless of age or gender, that is engaging. It was fun to watch the learning process unfold.
Tana, Thank you for the book suggestion!! Juliet
DeleteAccording to Leinwand, there are several areas of instruction that can be minimized simply because students don’t need really need to know or do the practice. His example of multiple digit multiplication or long division is a good one. I think students should know how to do the computation, but not tons of practice. I think this multi-step process is better with calculators. Students need to be efficient with the calculator. I’m also on the fence with Algebra I for 8th grade. I recall learning that 8th grade brains aren’t ready for the advanced thinking needed for algebra. But, if they don’t get it in 8th grade, it messes them up for 9th grade physics and the 10th grade physics MCAS. And then forget college! This makes me believe that the trend to teach to the standardized test has pushed everything back a year. Parents absolutely do not want to see that their child is only satisfactory, so we push through the curriculum. I have 3 boys in first grade who are old enough to be in 2nd grade. The parents kept them back just to give them that extra year.
ReplyDeleteJuliet:
DeleteYou have three students who stayed back? That is amazing, but so unheard of. I wish more parents would follow that example and realize that sometimes children are not just ready to advance. Everyone develops skills at different rates.
I also agree with your thoughts on long computation and calculators. It is important to have practice to understand how the procedure works but there is no reason to "drill and kill." Once students understand the process that the calculator is going to do, then let them use a calculator. We are already such a technology driven society that we might as well take advantage of it. This will also free up students to think more deeply about math and focus more on the underlying "whys" and "hows" of math; we won't be boring them with what they see as pointless exercises.
Shift 8 asks teachers to teach only what is important to teach and only when students are ready to learn it. Instinctively, this shift makes complete sense, but practically, actually making it happen may not be possible.
ReplyDeleteI cannot count the number of times I’ve heard a student ask, “Why do we have to learn this?” or “When am I ever going to use this?” Even though I majored in math as an undergrad, I asked these questions of some of my own classes. Occasionally when a student asks these questions, I can’t help but think, “I really don’t know why you need this right now.”
Last year my district started using a new math program, which meant that the teachers and the students were struggling to get used to it. At times the teachers desperately wanted to skip, change, or postpone units in our new program. However, when meeting with curriculum coordinators we were told to trust the program. It is difficult to trust the program when I see kids struggling, but what if I’m wrong and it really does all come together? So for me, the tricky part is balancing your teacher instinct to stop moving forward, and “trusting the program” and the district’s choice to use the program.
Anjali, I can completely understand how that would be a difficult situation... wanting to trust your instinct but then needing to listen to the district as well. I suppose the best you can do at this point is provide all the feedback possible, and if they say to trust them because it'll work... give it more time?
DeleteYou know exactly how I am feeling about this new math program I have to follow. I have been on the phone with parents for the past few weeks because their child did not get an "A" on their math test. I am constantly trying to explain that due to the new program then there is going to be a small gap between what the program expects them to know and what they actually know as a result of having a different program last year. This is frustrating. I am hoping that next year there will not be this gap and the beginning of the year will go smoother. I hope this year has been easier than last year for you.
DeleteAdjusting to a new math program that is also of a different math philosophy is really hard. I do worry about the math gap that is created, especially for higher grades. My own daughters had this experience just from changing from elementary to middle school.
DeleteAlso, at my school, we are 'mapping' our curriculum as a school project. And the selling point is that a parent can see exactly what their 8th grader learned in 1st grade. The curriculum map is NOT a personal education map -- it's just a long list of what a school taught that year and then it will be updated. Follow? We were told that parents will be able to see the continuum of their child's education, but it doesn't account for all the changes in curriculum that easily happen over 8 years. So how can we really see the holes in one student's education? Follow?
So with a new math program, who is keeping track of what students are missing and need extra instruction on? I'm just not sure how this works.
I agree with that higher standards should not mean teaching more math and harder than to more students at earlier and earlier grades. First of all, we need to think about what is important to teach appropriately.
ReplyDeleteAs Leinwand mentioned, teacher needs to minimize some areas of instruction simply. Also it is very important to teach instructions when students are ready and they need to know.
I noticed that so many students are struggling with multiplication and division. Especially when they move to 3digit number problems, some students don’t master 2 digit number problems yet. So teacher needs to let them have a deep understanding of problem concepts.
Rebecca, Even with first graders, when is more time on a concept a good idea and when is it just more drill & kill? 6 year olds need breaks from a tricky concept and then a revisit. We just spent october on addition, and this month it will be subtraction. I teach simple lessons everyday and tend to keep a steady pace. I like to fill in with extra help during math games or carve out time somewhere else in the schedule. Older grades have a lot tighter schedules so I imagine flexibility is not easy. When to move on? This is a good question.
DeleteInstructional shift 8 states that we should “minimize what is no longer important, and teach what is important when it appropriate to do so”. I completely agree with this shift. Throughout high school and college I often found myself sitting in class (not necessarily a math class), asking myself why I needed to know what my teacher or professor was rambling on about. I think that there are certain skills and concepts that students don’t necessarily need to know or master, at least not until a certain grade or age. Bombarding students with unnecessary concepts will most likely just confuse them, and have them asking us “Why do we need to know this?”
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DeleteI think about the reading specialist at our school. Her philosophy is "easy reading, makes reading easier." And so I think "easy math, makes math easier." Not that we aren't going to have challenging math in school, but that we teach "what is important when appropriate."
Andrianna, I think teacher's should be able to answer "why do we need to know this?" and if they can't, rethink the lesson or unit. I Tana's idea that easy math make math easier! Well, why not? Teach an important concept with a real world connection. If the concept is mastered, the extra time consuming practice isn't necessary nor helpful if students are confused. Practice makes perfect isn't always the right route to go.
DeleteI agree with Leinwand’s instructional shift 8. We should teach what is important at the appropriate time and minimize what is no longer important. I remember in my math classes in high school my teachers spent so much time getting us to memorize and regurgitate formulas that I never really understood why. Every time we started a new topic I remember remarking, “Ohh great, another formula to memorize.” To this day, I can only recall few formulas from the top of my head, others I would need to look up. I believe when math loses touch with real-word expectations then it loses meaning for most students.
ReplyDeleteIt frustrates me that teachers have to teach everything prescribed to them by their district even when they know some students are not ready to move forward and cannot possibly succeed without revisiting and mastering previous content. Curriculum mandates and standardized tests puts a great amount of pressure on teachers to rush through the material and students to develop at a rate faster than they may be ready to do so, thus setting up both parties for failure. This creates a classroom of students who are sinking and others who are swimming. I think this influences some students’ decisions to drop out of school because they see that school is not for them and that teachers are mainly concerned about those students who they believe will go far in places. This is why, I like the idea of 1-year postponement mentioned in this chapter. This can allow sinking students to catch up to their classmates, and develop at a rate that they are most comfortable with. But how can we influence the decisions of policy makers, especially when everyone is so concerned about our students lagging behind in math when compared to other countries.
I specifically liked Leinwand's list of mathematical content that he views as "bath water." Fractions were always a challenge for me at a young age. I had to really study. Who cares about sevenths and ninths?.....I had never seen any type of measuring cup in our kitchen with sevenths or ninths listed on it.
ReplyDeleteI was fascinated to read his thoughts on the cycle curriculum mandates and testing standards. It makes sense of how we get ourselves trapped into teaching skills for standardized tests.
Finally, it was grounding to read Leinwand's thoughts on expectations for "nearly all students." There is flexibility in his language (nearly all students) and yet high standards to master what is truly important for students to attain when it comes to math. Currently in our classroom, we have discovered there are some students who need mastery on some basics. We will be working with them during our "math center" time to achieve this.
I support the instructional shift to minimize what is no longer important and teach what is at the appropriate time. It seems easier said than done though. Students should not just be memorizing formulas and symbols, because there’s a slim chance they’ll retain that information from year to year and remember it when they actually need to solve a math problem in the real world. I love that Leinwand wrote about the nervous laughter coming from teachers when he asked for the formula for the volume of a sphere. Who knows that off the top of their heads?! Many adults know that if they need to figure this out, there is a way to find it. Students are taught and expected to know complex and rarely used formulas, at earlier ages. Why? Leinwand mentions that the standardized tests put pressure on school administrators, but why aren’t we doing what’s best for the kids? It’s unfair to expect the mastery of certain concepts before students are ready for it. All it does is lower their self-esteem and increase their distaste for math. I appreciate his advice to skip the last two chapters in the book in order to give students more time with the important content. All educators should feel that they have the power to do what is in the best interest of their students.
ReplyDeleteI completely agree with what you are saying. I once heard an educational speaker talking about the importance of allowing students to advance into the twenty-first century and part of this is allowing them to use technology. As the students get older and become adults, there is nothing they cannot discover on their own because they have an endless supply of technology at their fingertips. The students should not be required to memorize anything because as an adult, I cannot remember the last time I was forced to memorize information. Instead I research the information I need and then answer the questions. This is the skill we need to be teaching explicitly, not wasting our time on memorizing facts. The need to teach to the test is becoming devastating to the development of our students. I am oping Leinwand's shift starts being considered as the states adapt to the new Common Core.
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