Start Reading on Page 5: The new math until Page 9: American Institutions Charged
Comment on the following:
1. What are your thoughts on Innumeracy in your classroom?
2. How can you relate to the answer-getting strategies used to teach math?
3. Comment on a colleagues post offering additional reflection from what was read.
I think innumeracy is a real problem in all classrooms. Unfortunately, I often feel that I am not doing an adequate job to change that. The time limitations we have are a serious detriment to the students. I feel that while I really try to help students understand the “why” and not just the “how” of math, I am forced to move on before the majority of them actually get it. By the same token, I see many students becoming bored very quickly because they “get it.” I have been making a conscious effort this year to allow those students who can apply math to real world situations to help me explain their thinking to the rest of the class. Much of the procedures we need to teach for the CCSS are completely ridiculous when applied to the real world.
ReplyDeleteAs far as answer-getting strategies are concerned, after I teach a concept, I love it when a student finds a different, often more efficient way to get to the correct answer. They usually see a more real-world solution. I think as the teacher, I generally go through the correct process to solve a problem, and then a student will often say,”Why did you do it the hard way?” I think I get hung up on the showing of work to explain how I came to my conclusion. If we could just give the students more time to discover on their own, we wouldn’t see the resistance to math and problem solving.
ReplyDeleteI liked the idea that there is a name for when students can't understand math, the equivalent of not being able to read. I do see this in my classroom, especially for any types of word or multi-step problems. Sometimes they don't even know where to start! Those that can at least start on the right track for the first step, fall apart with the rest of the steps. It's almost like they can't dissect the problem into the parts they have to solve. Applying varying operations to one problem also seems to throw them off. Even the basic understanding of what the problem ultimately want the students to solve for is confusing to them.. I spent so many hours walking students through multi-step problems, only to have them try some on their own, and not succeed. Bummer!
The way we teach math seems almost robotic. (I, We, You pattern). I've done it, but never thought it was the best procedure. I liked the idea of teaching kids to talk about math and discuss misunderstandings as they happen, not after the test! That is a good way to correct misunderstandings before the test. Again, as I mentioned earlier, it would be great to have the time for students to discover math on their own. There seems to be too much to cover to allow time for that. I would love to be taught the best way to teach elementary students math, and I think it is out there. We just aren't trained to do that!
Audrey, I think it is one of the hardest jobs for someone who teachers math to help students actually understand what the problem is asking. While you work together with students, they often understand how to do the problem because you are breaking the problem down into simple steps for them, or interpreting what the problem is asking. Then, when we send kids off to do homework independently, we find they fall apart.
DeleteYou are absolutely right on all counts. I think that often the hardest part is just getting started. I was also happy to see a name for "math illiteracy." The good news is, the kids we have coming in to 6th grade seem to have a stringer background than they had in past years. So keep doing what you are doing!
ReplyDeleteWow!! It is great to hear that you are noticing a difference in 6th grade. As students have been exposed to the modules for a few years now, we are also noticing that children seem to have a stronger math background and a better understanding of math concepts. I guess it just takes time!!!
DeleteThere is definitely a noticeable difference. We still have the kids who refuse to show work, as well as those who act like they have never seen or heard a 5th grade concept before!
DeleteThere is definitely a noticeable difference. We still have the kids who refuse to show work, as well as those who act like they have never seen or heard a 5th grade concept before!
DeleteI didn’t know exactly what innumeracy was until I read the article : the mathematical equivalency to not being able to read. I feel many children struggle with this and understanding the language of math. Word problems are especially challenging for children. They are often not able to comprehend what is being asked of them. Answer getting strategies can help students in the short term but they are easily forgotten and students never truly understand how or why they are solving problems. These “tricks” are just that. While the article seems to be bashing the I, We, You method, I do see value in this gradual release of responsibility. I have found that if you use this model, it “forces” students to participate in the lesson. Many children will allow the lesson to happen around them and not become involved unless you provide them with opportunities to practice both with you and independently. However, I don’t believe this process should be the only teaching method. Children need time to think. If we constantly jump in with the answers or provide them with the correct method, we don’t allow them the opportunity to think on their own. Someone wise once told me, “Don’t rob children of their struggle.” Sometimes forcing them to take time to think it out on their own can lead to great discovery.
ReplyDeleteKelly that is a great quote. I agree that kids really need the opportunity to pull on all their strengths to work towards a possible solution.
DeleteKelly: I must admit i say the word and thought i had never heard this before!! It is easy to relate to ELA and i love to reference it now. That is a GREAT quote and I couldnt agree more. Way to often as teachers we are the "savers" and do not give children to time to struggle.
Deletelol...I remember going to that conference with you Kelly! We had a great presenter and I clearly recall him saying "Don't rob children of their struggle."
DeleteI really like that quote and it is SO TRUE. I have had students that would try to "wait me out" hoping if they sat there long enough and didn't provide an answer, I would provide it for them. Some of them actually told me that's what they were doing! Struggling at something makes us stronger and helps us develop our problem solving skills. We learn from our mistakes, whether it is a math mistake or a life mistake. I agree that we need to force kids to participate independently because some kids do take a back seat and let the lesson happen around them, as you said.
Delete1. What are your thoughts on Innumeracy in your classroom?
ReplyDeleteOver the years I have worked with a variety of students that have struggled with math. When you sort them out a bit they fall into a couple of categories. There is the "my parents aren't good at math student" , the "I have never picked up a flashcard student", the "I don't do my homework student", and the "I don't want to show my work student." Then every now and then you get a student that it just really seems they have a true mathematical disability. I hope that some of the modeling we now do will assist in bridging the learning gap for students that legitimately struggle with math.
2. How can you relate to the answer-getting strategies used to teach math?
Modeling is very much a part of my third grade math instruction.
With modeling, one thing that we spend a lot of time on is "work space." With all the modeling (drawing), younger students need instruction not just with the math concepts, but in how to present their thinking on paper so that it can actually be communicated to someone else. Planing space, working left to right, drawing a picture (area model, tape diagram...)writing a number sentence, solving with an algorithm, and finally writing the answer in a complete sentence. You feel like celebrating every time you finish one problem!
Heidi, as I read through this article, I keep thinking about the Smartest Kids book.
DeleteHeidi~
ReplyDeleteI love your categories for struggling math students!! I feel it is difficult to reach some of these students because they are already have math innumeracy before they start. This can make math class extremely difficult, and it becomes hard to differentiate for so many students all over the board!!
I think innumeracy greatly impacts classrooms in America. When students look at a math problem and are unable to read what it says, how do we as teachers expect them to solve the problem? As a Consultant Teacher, I work closely with students working on their mathematics. I often find that students do not even know where to start with a problem because they do not understand math vocabulary or symbols. There are a lot of adults who also are unable to read math. Math is in a way its own language, and time needs to be spent understanding math vocabulary to overcome innumeracy.
ReplyDeleteThe math I see taught in high school is taught with a lot of tricks. Students do not learn the theory or basis surrounding those tricks. Unfortunately, by the time most students get to high school, they don’t want to know where the formula comes from, they just want to plug in the numbers and get the right answers. We need to start reforming mathematics education at a young age, and allow students to discover and problem solve on their own to increase their appreciation of math.
I agree with you Lori, education reform needs to begin at a young age. I think this was the problem with the "roll out" of the CCLS. I don't necessarily think the CCLS are improper, the implementation process was not well thought out.
DeleteLori,
DeleteI agree with your thoughts on starting with a good foundation. Meaning the youngest students and implementing proper roll-out strategies/trainings. I too find my students have reached the point of don't teach me why just show me how so I can be done..
Similar to how our students struggle to pass a foreign language (or are often exempt), they struggle with math because it is a lot of decoding and practice, just like Spanish and France. I am hoping that the next groups of students we get will be used to Common Core and won't have the same struggles, but I am not optimistic after hearing from the elementary and middle teachers on this blog!
DeleteI had never heard the word innumeracy before, but it makes complete sense. However, with the implementation of the CCLS, I have found that students are working more towards “sense-making” rather than answer getting. I spend more time now than ever examining the process a student used to arrive at an answer (even if the answer is incorrect). When talking with students and reflecting after a test or quiz, I am able to see that they often do have a deeper understanding of concepts, but perhaps got caught up in the language of the problem. As we have implemented the modules over the past few years, the use of models has been particularly helpful. To me, models help break down word problems and give students an avenue to communicate/demonstrate their level of understanding. As I am reading through this article, I find myself frequently thinking about a book study Heidi Topolski facilitated. The book was titled The Smartest Kids in the World…and How They Got That Way.
ReplyDeleteInnumeracy in my classroom is becoming more prevalent than ever before. This is my 15th year teaching, and I have noticed my students have slowly become more and more "innumerate?" Given that my students have varying ability in solving our math, I try as much as possible to have them learn through modeling, peer-partnering and also try to include hands-on math. For instance, if I was going to have a student put siding on our house I ask them to tell me how much siding we need. This seems to raise their attention and comprehension when it becomes visual, then I show them how I used to do it, and then we work in groups to learn strategies in estimating.
ReplyDeleteI like that you have your students visualize the siding vs. just taking the area of the wall and dividing it by the area of a drywall sheet. Even though you could get a rough answer that way you still have to battle with the layout of the wall and the size of the sheets. You have to decide the orientation of the sheets so they cover the area in the most cost effective way not just based on what the division tells you.
DeleteI truly believe more of that is needed Matt! They have to be able to see, hear and feel (experience) the math in order to give it meaning! Great example!
DeleteMatt, That is great that you have a way to show students how the math is actually useful beyond the classroom. I wish that the math we do in Algebra class could be used in real life experiences so that students could gain a better understanding, but unfortunately-much of it doesn't apply to their lives. Kyle H
DeleteI think innumeracy is one of the largest problems Americans face. AS stated in the reading many educated people cannot do simple math even properly in their jobs and every day lives. Understand economics and other financial situations is the root of our problems even at the Government and executive levels. I have students that can pass the Algebra I or even the Geometry exam but fail a test on fractions, percentages or even decimals operations. Most math in the Career and Tech classes require an understanding of 4th - 8th grade math but the students freeze and cannot regurgitate any material from those years in their education.
ReplyDeleteI have a perfect example of the answer-getting strategies that I discovered today. I was talking with a student who was correcting a homework on Algebra today. This student was presented with the question of what number is added to 3 times itself and equals 60 in so many words. He said he just thought of a number that when tripled was three fourths of 60 and then the left over was that same number which would be the other fourth. He could have simply done x + 3x = 60 then solved for x but he thought about the situation differently with the concept in mind of what algebra really is.
Sara you are absolutely right. I have the same kids with the same issues. Especially when it comes to converting fractions and recipes.
DeleteWhile I watch our students try to complete geometry and Algebra 2 homework each day, I am sometimes shocked at the basic knowledge they seem to be lacking. I watch them plug very simple calculations into their graphing calculator (such as 32/2 or 4 X 20) and they have significant trouble memorizing formulas. Even worse, they cannot apply the formulas correctly that they do have memorized, so they are pretty useless in helping them solve equations. I realize that I work with students that have learning disabilities and my experience may be skewed, but I worry about how they will be able to manage their money or keep track of things without basic knowledge of math facts.
ReplyDeleteI had some really great math teachers growing up, but I also recognize that there was some answer getting going on. With my current students, they are often in a rush to just get the homework done, without much regard to accuracy or learning the process and formulas. They then perform poorly on tests because they did not really give their homework an in depth look throughout the unit. Most of them have a negative attitude towards math at this point and are just trying to finish up their 3 math credits for graduation because they are discouraged.
1. What are your thoughts on Innumeracy in your classroom? I'm sad and frustrated at the same time. How can these kids to eleventh grade and not be able to perform simple math equations.
ReplyDelete2. How can you relate to the answer-getting strategies used to teach math?
I think it's a great concept for the classroom but can the student relate once taken out of that Environment. I see students come into class and freeze up when asked math question.
1. What are your thoughts on Innumeracy in your classroom?
ReplyDeleteI see innumeracy everyday! Students that struggle to understand positive and negative numbers, students that don’t understand fractions or that fractions and decimals can be equivalent, students that don’t understand coefficients, exponents or subscript numbers. Throughout the school year we are continually reviewing and re-teaching these topics.
2. How can you relate to the answer-getting strategies used to teach math?
I think sometimes students just want to know the “steps” to solving a problem or type of problem and as teachers we sometimes give them. I think when students memorize steps they aren’t actually learning the process necessary to complete the task just the individual components that will allow them to solve very specific problems. Once they arrive at a problem that doesn’t fit the “steps” they get frustrated.
“I, We, You” is used mostly in our classroom. When trying methods similar to “You, You’ll, We” we struggled with various behaviors and distractions. We tried creating different groups and going over expectations but it seems our students in this class struggle with working in groups. They have no problem socializing in groups they just struggle with taking about math!
Inumeracy is an issue that many of our students struggle with. Last year I taught a self-contained math class and really wanted my students to learn to be fluent in basic arithmetic. I used a great math program (Xtra Math), but soon my students were complaining that they weren't in Kindergarten. They were not able to answer the questions correctly, but still did not see the value in learning this basic math fluency. I was at a loss. I was not sure what to do. Unfortunately I scrapped the idea because of the resistance I received for several months, even after trying positive reinforcement. This confused me, because I had seen the same program work great at the Erie County Youth Detention Center where I worked as an after school tutor. I think inumeracy is a major issue that caused many of our students to struggle with at the middle and high school level. Students would be able to learn upper level concepts much easier, if they did not depend on the calculator for basic math facts.
ReplyDeleteThe answer-getting strategies is what far too many students (and teachers) focus on. One of my colleagues and I call "answer-getting" "Bulldozer math." Students just want to get the right answer, bulldoze through all the information, and get credit without actually understanding the topic. We try to slow the students down and actually understand the math and why we do certain processes. I do admit, we do focus a lot on processes rather than lengthy discussions. In particular, I think this is beneficial for the special education students in the class who need flowcharts/outlines of steps needed to answer a question. However, I know they are not truly gaining the understanding of the concept. The focus is merely passing the class, passing the test, and passing the Regents exam. Until the process changes, I do not see many teachers utilizing the discussion tactics that help students understand the content. Kyle H