Did You Learn Math This Way? UPDATED

UPDATED: Thank you readers for your comments, please keep them coming.

The method illustrated in first video I posted may be helpful to learn the concept, but for practical application, I don’t see it as effective. I could see the benefit of teaching one approach and then teaching others methods to allow the child to determine which works best. Have her solve problems with 2 digits, move to 3, then 4 and so on. The child will likely come to the conclusion that the TERC method would be problematic for large numbers. There is no one size fits all approach to learning. The child in the video has a great attitude; she’s patient and determined to solve the problem. She is fortunate to have a willing parent. What happens when you have a tired or frustrated child? Do you think this will work with children with short attention spans, tired children / tired parents? What bothered me in the video, the child says she is not allowed to use stacking in school. How is that critical thinking?

Below is another video, the parent is demonstrating different methods to solve equations. (I don’t know if the books she shows in the video are used in NC. I’ll have to search the NCDPI site for the current list of math books).

Some of you have correctly pointed out TERC (aka “Investigations) is not a requirement for CCSS, however, it can be applied. From the TERC site, Investigations and the Common Core State Standards

Investigations and the Common Core State Standards is designed to support teachers and schools that use Investigations in implementing The Common Core State Standards for Mathematics (CCSS). These companion materials, available from Pearson in hard copy or as individual page downloads via Successnet, are designed for use in conjunction with the curriculum units (copyright 2008 or later) at each grade level, K-5. Investigations and the Common Core State Standards includes everything needed to support teachers as they implement Investigations and the CCSS in their classrooms.* (Much more at the link for those interested in learning more).

And from the Pearson site

“The Standards for Mathematical Practice are deeply embedded in Investigations. They promote active thinking and learning. Investigations for the Common Core helps you teach all Standards for Mathematical Content.”

Initial post:

Parents of young children, this video is especially for you. I hope this will encourage you to pick up the phone and call or write an email to your state rep and voice your concerns. Please share this with other parents.  How much whiteboard space would be needed to add $17 trillion? (sorry, I digress but could not help myself). As I learn more, I will be writing more about TERC.

The unintended consequences of the TERC Investigations Math Curriculum

 

http://youtu.be/1YLlX61o8fg

Here’s a quick overview from Bill Quirk’s post TERC Hand-On Math: A Snapshot View

Developed by TERC, with funding from the National Science Foundation (NSF),  Investigations in Number, Data, and Space  purports to be “a complete K-5 mathematics curriculum that supports all students as they learn to think mathematically.The NSF is now spending millions to promote implementation of the TERC program.  School Boards find it difficult to say no. They rationalize: “it’s just a different way to teach elementary math, and the NSF backs it, so how bad can it be?”

This program is very bad because it omits standard computational methods, standard formulas, and standard terminology.  TERC says this is now obsolete, due to the power of $5 calculators.  They claim their program moves “beyond arithmetic” to offer “significant math,” including important ideas from probability, statistics, 3-D geometry, and number theory.

But math is a vertically-structured knowledge domain.  Learning more advanced math isn’t possible without first mastering traditional pencil-and-paper arithmetic. This truth is clearly demonstrated by the shallow details of the TERC fifth grade program.  Their most advanced “Investigations” offer probability without multiplying fractions, statistics without the arithmetic mean, 3-D geometry without formulas for volume, and number theory without prime numbers.

Key points:

TERC Omits All Standard Computational Methods

TERC Omits Standard Formulas

TERC Omits Standard Terminology

Bill Quirk has a detailed analysis TERC Hands-On Math: The Truth is in the Details, I haven’t studied it enough but wanted to pass it along to our readers.

And for those who want to dig in on the TERC site

 

 

This article was posted in Blog, Video by NC Citizen on July 9, 2013 at 9:44 am.

Comments (30)

  • I’m just floored! I think I’ve just answered the “If my kids are in school to learn all day, why do they come home with 3 hours of homework a night?” question. What a load of bunk!

    Anastasia McCarter
    Anastasia McCarter Jul 09, 2013 at 11:49
  • My son will be going into 4th grade. We pulled him out to start homeschooling him this year. I gave him an assessment test in math to see where we needed to start with our curriculum.
    We have to start all the way back at 1st grade math because he cannot do large number addition. the most he can do easily is 2, sometimes 3 numbers. Any more than that and he gets confused.
    I agree with the statement at the end of the video that it doesn’t transfer over from 1-2 number addition to being able to do 3,4,5 number addition.

    Missy
    Missy Jul 09, 2013 at 13:21
  • I can understand this if the student is just learning about Base 10 and learning what numbers are and how to break them down into 1,000 100, 10 and ones. But, when doing a simple addition story problem…good heavens, get it done already. I’m totally against Common Core!!

    Beth
    Beth Jul 09, 2013 at 13:22
  • That was the single dumbest thing I have ever been privy to.

    8 minutes of nonsense to not even come up with the right answer! Good grief. A case for homeschooling!

    Kathy
    Kathy Jul 09, 2013 at 15:07
  • I am a math major who could not get a teaching job at a local high school do to the rough economy causing too much competition for an AC. I worked as a tutor in the schools for three years after my bachelors (I’m now finishing my doctorate) and HATED trying to help middle schoolers with math. Not be side of the kid or the questions at all, but because of stuff like this. They are being taught to solve everything with pictures. Even algebra problems had to be solved in picture form! It is ridiculous and making math even more difficult than it should be for kids who would already be struggling without these crazy requirements! Math is working with numbers, not being an artist! A question that would take 2 minutes to solve mathematically would take 20 min to solve with pictures. Then, I even had teachers saying the correct answers to the students’ questions were wrong. Sense when is -400 a larger value than 20? I’m most afraid that even the teachers are getting to this point. SO so SO sad!!!

    Fed
    Fed Jul 09, 2013 at 17:02
  • This upsets me or stuff like this does.

    We are homeschooling our daughter for the 1st time, who is in the 2nd grade. Even though she is at the top of her class and considered to be 4th grade level for math in a public school system and 5th grade for reading…I am seeing her math skills are completely different than the way I was taught. She doesn’t do stacking equations at all. I think we are going to have to start back to square one. I am so disturbed.

    Rachel
    Rachel Jul 09, 2013 at 17:13
  • I teach 6th grade math, where the weakness of “methods” like lattice and fair share (for division) really become apparent. Thank you for understanding that this is coming from district and state mandates, not from teachers!

    Mary
    Mary Jul 09, 2013 at 17:21
  • I am not a math person but this frustration and lack of love for math has inspired me to spend a decade developing a new introduction to math. After children understand the concepts, I find number sliders are an easy, quick way to solve problems!
    http://arithmeticvillage.com/

    Kimberly Moore
    Kimberly Moore Jul 09, 2013 at 17:57
  • Wow that was painful to watch!! More examples of the dumbing down of America! I wanted to scream and I wasn’t the Mom having to sit there patiently. Personally, I would be observing in the classroom immediately and if that is really the nonsense they are teaching as math, then that would be my child’s last day in public school. People question why we are falling so far behind other nations academically — here’s your answer!! The Department of Education is not in the business of real education anymore. We are beginning homeschooling our 3 boys this fall but we never experienced that level of nonsensical “teaching”. I hope and pray that Common Core becomes obsolete in all 50 states. The sooner the better.

    Rebecca
    Rebecca Jul 09, 2013 at 18:40
  • I use to be a 2nd grade teacher in the public school system 15 years ago. Yuck. We had to teach investigations and I thought it was the worst curriculum ever. The poor kids I taught had no idea what I was trying to teach. Thank God I pulled my kid out homeschooled her for the last 6 years of her schooling. She is a National Merit Scholar – 2011

    c
    c Jul 09, 2013 at 19:11
  • Um, not understanding the reasoning behind something does not automatically make it wrong. Kids should be taught stacking as well, but this form is to help them visualize, or make concrete, an abstract idea. Many young children suffer in real world applications of math because they can’t solidify it in their minds and this does that.

    Kiko
    Kiko Jul 09, 2013 at 21:47
  • I remember using yellow cubes when I was in grade … 2? Maybe in kindergarten. We had the singles, the line, the 10X10 and the cube. I’m 30, though, so obviously we did the normal lining things up math (who knew all these “styles” had names?!). I’m not sure what concept our teacher was teaching us–I know the cubes came later than the others, and that was probably multiplication. I can see using this as ONE type of way, to show a concept, but there would be no Mad-Minutes with this method! (I know,I know, apparently Mad-Minutes are not a good anymore, but I did love them, and Around the World’. Ha!

    Karissa
    Karissa Jul 09, 2013 at 22:41
  • I am totally against this. I understand that a great understanding of base ten is a great foundation for math…however this is a very sloppy approach. I am a former K teacher and my husband is/has taught upper elementary as well as middle, and high school (math, health and P.E.). We are facing our oldest child entering kindergarten in the fall. We are considering homeschool. Our one major drawback is that in the state of NC, he loses his services for Autism if we do elect to homeschool. So either way, I feel like we are up against a wall…he is going to lose out in one way or another…

    Kelly
    Kelly Jul 09, 2013 at 23:37
  • Teaching the Common Core Standards to students is not synonymous with using the TERC math program for teaching.

    Linda
    Linda Jul 10, 2013 at 7:49
  • This is CGI Math (Cognitive Guided Instruction). “Stacking” teaches the child nothing. It’s just a bunch of unrelated numbers to her. She did well to remember to carry the tens digit (most forget to because they don’t know what it is or why to do it). Typically, as seen here, stacking is used because we are only concerned with the end result, not with the child’s understanding and arrival to the answer. However, she was able to explain what these colossal numbers mean and how they are related to each other using CGI math. Does it take a long time? Yes. Are we impatient? Yes. Would other children in the class notice the wrong answer and call her on it? Yes. Other children in a CGI classroom would be free to speak up and help her out with the ones department. So you have kids paying attention and actively participating because they have a voice in the learning process as well. I remember stacking. It was boring. Thousands and thousands of endless algorithms. And no one caring whether I understood or not.

    Jason
    Jason Jul 10, 2013 at 10:11
  • This is not a new idea linked directly to Common Core. As an elementary school teacher with 12 years of experience in grades 1,2,3,5, and ELL, any teacher worth his or her salt uses a variety of methods to show these concepts. As adults who were never shown these methods surely they must seem superflous and exacerbating, however, believe it or not, some children benefit from “seeing” these numbers. If the teacher did “not allow” stacking, hopefully it was only for a particular lesson or unit designed specifically to show understanding of our base 10 place value system (an extremely difficult and abstract concept for many children). It is relatively common knowledge (or should be) that no curriculum is complete and common sense must be applied to be sure our children are being taught what they need, i.e. large number addition and subtraction, along with other concepts mentioned in the article. Ifitse public school teacher (so graciously unnamed in the video)forbade the use of stacking for more than that, then, yes, I disagree with his/her methods, but I still don’t believe you can pin it directly on Common Core. Background knowledge of number sense with actual manipulatives, along with drawing out the numbers, and stacking should have all been included in the instruction of these concepts. Not every child learns the same way! Having taught prior to Common Core, I can honestly say that I’ve never felt that it’s intent was to create a dumbed-down product. In an educational world where the emphasis has been to create a proficient standardized test-taker, in place of an educated, knowledge-applying, contributing citizen, it actually seems to be a move back to actually having children think and apply knowledge, instead of only being able to find and regurgitate information.

    D. Elliott
    D. Elliott Jul 10, 2013 at 11:20
  • What a wonderful mom to patiently let her daughter discover the problem with what the school is teaching her. I taught my kids math before kindergarten and it was numbers – not pictures. They loved it and when my oldest got to kindergarten she was so disappointed by the way they taught math that she asked if she could keep learning at home… that is why I started to homeschool her. (She is now in college and still loves and excels in math!)

    Nisha
    Nisha Jul 10, 2013 at 11:42
  • I actually taught the TERC program a decade ago. This does not represent it at all. Everyday Math and Terc both use the manipulatives of the cube and the square, rod and :bits: I hated in everyday math they actually gave them names that had nothing to do with it like bits and skinny. It is to teach the understanding of our number system the base ten. I do not like the common core but TERC has nothing to do with it. It has been around along time and is actually one of the better math programs I have seen. When I taught with it my students learned and understood what they were doing it was not just memorization like when I was a child. I think it is great that your school is using it. Most schools I know are pulling away and using Singapore math instead.

    Danielle
    Danielle Jul 10, 2013 at 12:03
  • My kids were all complaining about how hard cursive is. I didn’t understand why they thought simply connecting the letters was hard until I saw my son print. He had learned to drawn the letters in backwards order! The way I learned was you draw letters from left to right, just like you read them so in cursive, you simply don’t pick up the pencil. You know that “Hooked on Phonics” program that helps kids read? Know what “phonics” is? It’s what we call “sounding out the letters.” American kids aren’t dumb, they just are being taught to do everything the hard way!

    Diane
    Diane Jul 10, 2013 at 12:19
  • I think making a connection between visual and numeric data is great for stimulating both hemispheres. Also, this teaches how to plan out your approach. While it does not seem as easy as learning to simply add them up, this teaches students to use their brains to figure things out instead of just “Do steps 1-8 over and over again until you memorize it”.

    brian
    brian Jul 10, 2013 at 13:56
  • The attitude that the majority of these comments are taking is exactly the reason that we need math education reform in America. Ideas like “get it done already” are completely unhelpful; learning math should not be about being able to plug numbers into formulas that students have memorized–that’s not a helpful life skill in the least. BUT, critical thinking, reasoning, etc. are invaluable. Understanding WHY you are doing what you are doing is invaluable. And even though this girl gets the question wrong, at least in splitting the numbers into hundreds, thousands, and so on she is beginning to understand why we add the way we do.

    People think math is boring because it’s just numbers and formulas, but it’s so much more than that. And at least this system gives some hint towards that.

    E.
    E. Jul 10, 2013 at 14:47
  • I am not an expert in pedagogy but I am a physicist, and in my opinion, what this little girl is doing is beautiful. She isn’t just plodding through a formula like a robot with no understanding of what she is doing. Instead, she is developing a tangible connection to otherwise abstract concepts. This is something I am just now beginning to do. She will be far better off in life building these connections at this age than people like me who were taught to memorize and regurgitate.

    Hannah
    Hannah Jul 10, 2013 at 15:31
  • In response to these last few comments, there is merit in learning not just to plug stuff into formulas but in learning why the formulas work, but methods like this should only be used to teach the concept behind the formula. Calculus is a great example, when taking the derivative you could just learn the derivative rules, and not really learn why they work and thus never be better than mediocre at Calculus, or you could be taught the limiting process originally used to develop the derivative rules and understand why they work, or even use Archimedes original method of exhaustion. But once they learn the rules, why should anyone be forced to continue using the archaic and relatively complicated limiting process and risk making a mistake, a mistake which could end up causing the system to fail catastrophically, when they can just use the derivative rules.

    Learning the concept is good, but it is good for learning not doing. This method they are learning is eerily reminiscent of the Egyptian numeral system, albeit even simpler and less useful (the Egyptians could at least multiply with their numeral system), why should we be taking thousands of years of advances in mathematics and throw them out?

    Brian
    Brian Jul 10, 2013 at 20:18
  • As an instructor of teacher candidates at a SUNY college, I am saddened by the short-sightedness of most of the comments I see here. I am not a big advocate for mandated curricula; however, the techniques presented by the Seattle reporter in the first video each have as much (or more) merit than the traditional algorithms for promoting a true understanding of concepts, and developing problem solving and organizational skills that are needed in all subject areas.

    I know many adults and college students who have a fear of mathematics. Mostly, to the layperson, “mathematics” means ARITHMETIC. Many of the students I teach are terrified when I tell them that, for much of the semester, calculators will not be allowed. If (as seems to be the consensus in the comments) our traditional algorithms are THE BEST THING EVER, why are so many scared to use them? Why do so many people consistently get even fairly simple problems wrong, or take way too much time doing one problem when they have to do arithmetic by hand? Why can’t my college students multiply 30×60 without setting up and performing the traditional algorithm, or quickly see that 18×20 is just twice 18×10? Somewhere we have failed to instill any number sense, even in students who graduate with fairly good grades throughout elementary and high school.

    The traditional algorithms we learned in U.S. public schools (up until about the 1990s) work and are efficient and effective for SOME students. I have international students in my college classes who have NOT been taught to use these same algorithms, and they are often much more willing than the American students to consider the merits of alternate techniques. But, once my college students play with these alternate methods a bit, so many of them say, “Oh, my gosh! Why wasn’t I taught to do it this way in elementary school?”

    The problem, as I see it, is that the changes in our society have warranted changes in the educational system (inclusive classrooms, mandated curriculum, state & national testing, and, just the “entitlement” attitude of most students and parents.) The teachers, however, are not given adequate training or information about THE BIG PICTURE. I know how hard teachers work; so in no way am I blaming them. Change is difficult; and when you already have hours of planning, grading and paperwork to do, it is nearly impossible to find any time to do the research that could help while planning and developing the curriculum for your school.

    So, here (as quickly as I can) are my thoughts on the merits of and the successful implementation of these alternate methods:

    1. DEVELOP EARLY NUMBER SENSE: The development of number sense (size of numbers & where they are located on a number line) and operation sense (addition, subtraction, multiplication, division) through investigations of decomposition of quantities is essential to future success in arithmetic. Environments where students are encouraged to use manipulatives (thinker toys) and create charts, graphs and other types of drawings that explain their reasoning must be fostered EARLY, and THROUGHOUT their elementary school education.

    2. PREPARE TEACHERS, and START AS EARLY AS PRE-K: What has happened in U.S. schools since some time in the 1990s is that these techniques (that MUST BE started as early as Pre-K) have been pushed on teachers who, first of all, are not given the information they need to understand the big picture, and then are made to implement these strategies IN PLACE OF the traditional techniques that they feel more comfortable teaching. Also, I have seen first hand that these techniques have been put in place starting at a 4th or 5th grade level, so after five or more years of “traditional” arithmetic teaching, suddenly students (and parents, and teachers!) are thrown into this unfamiliar environment.

    3. TEACH CONCEPTS & PROCEDURES TOGETHER (in that order): One of my favorite math educators, the late John Van de Walle, had many very insightful thoughts about how children learn mathematics. He said (my paraphrase) that, teaching procedures (like traditional algorithms) before students have developed a conceptual understanding (what does “the product of two numbers” mean, for example) will very likely lead to many students who have no sense of what the size of their answers mean. So, if a student makes a serious computational error, (s)he has no sense that the answer is not even feasible for the given problem. That does NOT mean that in first or second grade a teacher should go into some long philosophical lecture about “the meaning of a product”; but that letting students use manipulatives and other modeling techniques can foster the number sense needed in order to have good judgement about the meaning and size of answers. This type of training can be done both before and in combination with traditional algorithms, which may, in fact, be faster for many students when they must do arithmetic by hand.

    4.DON’T SCARE PARENTS! Personal experience has shown me many instances when well-meaning parents feel as if they cannot help their children with their mathematics work outside of school. They claim (and, sadly, it is often true) that the teachers say, “Don’t let your parents help you. We’re not doing it THEIR way.” Again, this comes from teachers really only having the time to know a small part of the big picture for the strategies they are told to implement. Maybe what teacher should convey to the students and their parents is, “Right now we are trying the problems this way. When you are at home, play TEACHER, and explain this method to your parents. Then, maybe your parents can show you a different way. Bring that in, and when it’s time, we can look at how the two are similar.” The fact is, at some point many students will be proficient at the traditional algorithms. Using the alternate techniques with SMALL PROBLEMS to develop a conceptual understanding is a very powerful way to convince students that the traditional techniques give the same answer, and are much easier to use for LARGER PROBLEMS.
    PROVIDE PROFESSIONAL DEVELOPMENT OPPORTUNITIES: Forums where teachers, and even parents, discuss (online and in person) their concerns, questions, successes and failures with these techniques need to be a part of the school year and summer months. Teacher candidates who are coming out of colleges now should have been introduced to these techniques. If their teacher preparatory courses were good ones, these new teachers should be better equipped to see the big picture. These rookie teachers may be helpful on committees and teams that are putting together curricular plans for a school system. College and university instructors, like myself, can also provide workshops for teachers who are struggling to implement their mathematics curriculum, and for parents who would like to understand what is going on.

    Kimberly Conti
    Kimberly Conti Jul 11, 2013 at 16:12
  • Common Core is not TERC. CCMS can be taught using a wide variety of math programs. The school I work at uses Everyday Math to teach common core. We do NOTHING like this. Our kids add large numbers easily. Common core is not a curriculum, it is a set of educational standards saying what our kids should be able to do. It is the destination for our students. You can reach the destination using many programs to get to the destination, just like I can get somewhere by bus, car, train, subway or walking!

    Lauren
    Lauren Jul 11, 2013 at 17:31
  • First of all, I would like to repeat what others have said, mostly because it is driving me bananas to see this printed everywhere….

    COMMON CORE IS A SET OF STANDARDS, BY GRADE LEVEL. THESE STANDARDS ARE USED TO MEASURE THE PARTICULAR THINGS STUDENTS IN A CERTAIN GRADE SHOULD LEARN BY THE END OF THE YEAR. COMMON CORE IS NOT A CURRICULUM. YOU CAN USE VARIOUS CURRICULUMS TO MEET THE COMMON CORE STANDARDS.

    In case any of you ever attempt teaching math concepts to young children, you should know that place value, “borrowing”, “carrying” (two really terrible terms), etc. are really difficult concepts for them to grasp. Just because you have been taught and understand the concepts (reminder, you are all adults), does not mean that they are concepts that children are able to grasp. How many of us remember hating math? How many good students struggled in math? Or, even if they were good math students, how many TRULY understood what the algorithms represented? This is not high school, or even middle school math. It is elementary school. Teaching students in this way serves as a foundation for the later skills that students will learn–and believe me, they WILL have the algorithms down before the graduate. Please inform yourself before making bold statements about mathematics programs you may not fully understand.

    Jessica
    Jessica Jul 13, 2013 at 18:39
  • Correct, CC are standards not curriculum. I never said CC standards were curriculum. However, the standards are the first step towards curriculum and assessment. Please take a couple of minutes and listen to this short video with Bill Gates commenting on CCSS. Gates is a leader in driving Common Core. He has spent millions on this effort as we have documented on this blog.

    Since that video was made, national tests have been developed so what do you think will happen to curriculum? No doubt, the curriculum will align to the national tests as Gates predicted. Many people are not aware that CCSS have been copyrighted and the owner are the National Governors Association Center for Best Practices and the Council of Chief State School Officers. Private entities own CCSS, not the states…more posts to come on that topic.

    While I am not a teacher, I am a parent and have experience working with children in both math and reading. No doubt, we all learn differently and we all excel and struggle in different subjects. I am not an advocate for one particular method for teaching math or any subject. I am opposed to a one size fits all approach. One child may thrive in the FERC method and others may struggle. I do not know if FERC is being used in NC. I remember working with my children on homework assignments. Various approaches were taught to solve problems and introduce math concepts. When my children struggled, we partnered with our teachers to work through any challenges. From the video, the mom has done the same thing and you can hear the young girl in her own words conclude the stacking method is easier. My concern is she is not allowed to use the stacking method in school. I found the video of the meteorologist helpful, she worked through various methods, showed lack of content in some math books and proposed an alternative.

    On this blog, there will be more posts on math and other subjects. Feel free to continue in the discussion. I do not claim to be an expert but I am a parent who has seen children struggle and thrive in school. Parents bring the perspective of what it’s like to sit around the kitchen table at homework time while teachers bring us the classroom experience…it should be a healthy discussion for all readers here.

    NC Citizen
    NC Citizen Jul 14, 2013 at 12:09
  • I am not in love with having to learn the common core, but this is not a demonstration of what the common actually is.

    c
    c Jul 22, 2013 at 0:02
  • Investigations is being used in my county and I can not for the life of me understand why! I understand that some children do not have a sense of base 10 which CCSS is to help facilitate; however, Investigations does not do this!

    Melanie
    Melanie Jul 30, 2013 at 12:32
  • Common Core’s Lattice Multiplication….
    ….renders underwater basket-weaving classes obsolete,

    http://tinyurl.com/LatMult

    copy paste in your browser and you’re on your way to discover how your new Common Core training wheels make you look like an idiot. But Chairman Mao would approve.

    Here’s more:
    http://tinyurl.com/JurassicT
    http://tinyurl.com/cchistrionics

    Wayne Harropson
    Wayne Harropson Sep 25, 2013 at 9:59

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