“Old Math” vs. “New Math”

About one month ago I was going crazy trying to help my twelve year old daughter with a probability math homework problem.  I became quite disappointed in myself because I am an educator and I just couldn’t quickly figure out this problem.  As a parent, I did my best to help her come up with ways to use resources available for her to figure out the problem on her own.  Instead of getting angry at this “new math,” as some parents call it, I actually became quite excited that my daughter was doing such complex math problems, instead of the low-level computational problems I had when I was a kid.

CB106471As parents we have quite a bit of “unlearning” to do.  There has been recent efforts to strengthen the mathematics curricula in our nation’s schools from basic through more advanced levels.  Our children need to be better prepared for the 21st century.  They need to be able to combine, adapt, and use math knowledge in ways we can hardly imagine.  Business and industry leaders are looking for new employees who have good communication skills and the ability to work in a team.  As parents, we would have a very difficult time if we had to go back in time and take the math tests our children are taking in school today.  Why?  The tests we took as children tended to evaluate only low-level computational problems.  The tests today require higher-level cognitive skills and understanding.  Learning math today is much more than knowing the “facts” and number operations.

In the past, we worked through rows of problems in math textbooks.  It emphasized rote activities.  We were passive receivers of rules and procedures without knowing what the rules and formulas meant.  No one ever dared ask about the logic of what we were doing.  What mattered back then was getting the right answer.  Yes, of course, we did have word problems when we were younger, but they were really computations in disguise.  We would just turn it into a number sentence, an equation, and then follow the rules we were taught.

In classrooms today, learning math is a sense making experience.  For our children to be successful in math class, they need to be active participants in creating knowledge.  If you walk into a classroom today, you will see the whole class and small groups talking about and demonstrating how they went about solving the math problems.  The emphasis is less on getting the correct answer and more on being resourceful in finding ways of solving problems.

Some parents think we do not teach the students the pencil-and-paper shortcuts we learned when we were younger.  We DO teach them, but we just don’t rush into it.  We would rather students do things the long way first!  Why, you ask?  Our math programs must build a foundation of conceptual understanding first before the algorithms are introduced.  In other words, we have to work concretely and manipulatively first.  Students today use concrete, hands-on materials when they encounter new concepts.  Later they will learn the symbolic shortcuts we used when we were younger.  It is more important that students describe and demonstrate how they went about solving math problems instead of focusing on getting the correct answer.  Our goal is to get them thinking like mathematicians.  Today, children in math classes generally work in pairs and groups and they do a great deal of their math mentally.  Research shows that students’ working together helps with their understanding.  When you walk by a small group trying to discuss ways to figure out an answer, you hear: “I have an idea”, “Wait, wait I got a different plan”, “Let’s try your way, then my way”, and “But that does not make sense!”  During group problem-solving, teachers are actively listening to students’ reasoning which, in turn, helps them better understand the students’ thinking.  Keep in mind that there is still time in the classroom for students to work independently and teachers know how important it is to work independently.  

I understand that some parents feel quite uncomfortable helping children with their math homework.  Math homework looks different and the amount of math homework is also different.  Educators know from research that students need activities and tasks that allow for a deeper understanding of the math.  These tasks may take longer to solve and that is why fewer problems are assigned.  I see many parents upset and who want to blame the current math programs out there such as Everyday Math, Math Trailblazers, and LL Teach Communicator Mathematics because parents do not see a textbook going home which is full of rows of computational problems.  

I hope after reading my explanation of the dramatic and exciting changes in the field of mathematics, you will realize that the traditional way of teaching math is NOT what is best for our children and their future.  The methods supported by our new math standards is what will prepare children to be problem solvers, effective communicators, and team-workers.

***Please post your comments and questions.  I am currently working on a presentation for a math parent seminar which explains what to expect from 4th grade math.  I will be providing many math tips on how to best help your child in math.  I will be posting these great tips soon.  Make sure to sign-up to get my blog posts delivered directly to your email box.  Also, please bookmark and share my blog posts with other dedicated parents.


22 Comments (+add yours?)

  1. Helen Askins
    Jun 06, 2009 @ 18:22:09

    I most certainly agree with this post. My 12-year-old’s math teacher actually had a “Math 101 for Parents” to teach us parents the same methods she was teaching our children so that we could help them with their homework. In this “class” she showed us the exact procedures of solving math as she was instructing our children and we could ask questions and such. Of course, it did take some getting used to, because almost all of us (myself included) kept wanting to revert back to our “old school” ways in solving the problems. I kept wanting to take those shortcuts that were taught to me back in the day! My daughter and I “practice” her math instructions at the grocery store all the time. We both use paper to come up with the total cost of our purchase, including the tax. More times than I’d like to admit, she has come up with the correct amount, while I did not! Her computations on the paper were more than mine (because I used the shortcuts), and she took a little bit longer to come to her solution, but she was RIGHT and I was WRONG! She’s even caught mistakes that I have made in my direct selling business! Remarkable! I’ve always been a stickler for learning new things, so the “new way” of learning math was quite exciting and interesting for me!


  2. Dee
    Jun 06, 2009 @ 18:25:58

    Alicia, I too am an educator of math. I taught high school math for over 17 years and am currently teaching at a community college.

    You are correct about how important it is for students to learn to work together. The best part about them working on math problems in small groups in my opinion, is that all too often students are afraid to ask questions in class for fear of appearing dumb, so they never get the answers they need to be successful in mastering a skill.

    But when students work in small groups, they are much more likely to ask questions of their peers; and then the peer(s) who are able to answer the question not only help the other student learn the subject better, but they reinforce their own understanding of it.


  3. Alicia Vilas
    Jun 06, 2009 @ 18:35:02

    Dee, I agree about small group work. It is very hard to convince some of my fourth graders to not worry about their wrong answers and just participate. I try to praise the ones who participate, even if they get the wrong answer.

    Helen, you need to tell me more about this “math 101 for parents”. I need to do a math workshop for parents on Thursday. Any ideas?


  4. lisa schnettler
    Jun 07, 2009 @ 00:00:53

    My son is in the first grade and at first I was taken aback by the “style” of the math homework. I have to admit, it threw me that he didn’t come home with 50 of one type of question one night. and then 50 of a slightly different type the next.

    But I can see that they are teaching the concepts in a way that makes it “stick” more than the rote memorization ever did. And by having different types of questions mixed together on a page each night, you don’t encounter the problem that I personally had of not remembering in June what you learned in February.

    With everything intermingled and interconnected, I think the level of understanding is deeper and longer lasting.

    I think the visceral reactions I have heard from some parents re: the “new math” stems a bit from fear of anything new AND the weakness that most people have in math thanks to the old way we learned it. Many are honestly intimidated by Math, uncomfortable with it. And feeling at a loss in front of your child is not something any parent enjoys. But that doesn’t make the “new” math “bad”


    • Alicia Vilas
      Jun 07, 2009 @ 09:24:12

      Hi Lisa. I did notice that Everyday Math tends to give many different type of questions for HW so that a student does remember what was learned earlier in the year.

      I will be presenting a parent math seminar in a few days. Hopefully I will make some parents a bit more comfortable with math. I plan to stress the use of the parent math guides sent home during the year and the free online tutoring service for kids in JC.


  5. Karim
    Jun 07, 2009 @ 02:34:20

    If you are around 35+ like me we learned Math, using the traditional model, considering that we need our children to be:
    * Able to work in groups
    * Learn to solve a problem in different ways
    * Use the highest levels of Bloom’s
    It is very important that our own children learn to use math in a real life situation to be have meaning, I love Math and I think sometimes we focus so much in the question and we don’ t pay to much attention to the real problem… I love and agree with this article but at the same time I think that we need to be realistic with our children and teaching them at early age how to:
    * Invest money,
    * Save money
    * Manage a checking account/savings
    * Introduce the concepts of rate and APR,,, so far it’s incredible that a lot of educators still can manage their accounts correctly too… and they graduate from college… Is this a problem of Math or Common sense?

    Too crazy!!!


    • Alicia Vilas
      Jun 07, 2009 @ 09:29:57

      Wow, how young are the students in your district when they are learning about investing money and managing a savings account? I teach 4th grade and do not cover that at all. What is the name of the math program?

      LOL…that is crazy. You are correct though. If those educators must teach those concepts, they must fully understand those concepts.


  6. Karim
    Jun 07, 2009 @ 02:37:27

    I mean some educators can’t ….


  7. Arlene Slobodin
    Jun 07, 2009 @ 08:29:24

    Alicia, my whole teaching carer has been about students working together and discussing and proving their work in math. We can’t get inside our students’ heads to see how they were thinking and the process(es) they used to solve something. By doing this, you can more readily see where a student ‘went wrong’ and explain it to them. It also allows the rest of the class to see when there is more than one way to solve a problem. Praising those students who take a chance, even though their answer may not be correct is important. i stress this a lot at the beg. of school. My class sees that I give a treat to a student with a ‘wrong’ answer and they’re confused. i explain that they didn’t want to answer, but took the chance. Their ‘wrong’ answer is something we all learn from. The hands start going up like crazy, right or wrong. Another strategy I use is there is nothing that is hard, easy yes, hard no. The word is challenging! Hard implies ‘I’ll never get it’. When something is challenging, there is always the window of ‘getting it’ and they do!!
    We never discussed when we were young, discussion is imperative, sharing is imperative. When a student can explain their work, you know they truly understand it. This has worked from first graders all the way up.


    • Alicia Vilas
      Jun 07, 2009 @ 09:35:05

      I really do appreciate your comments Arlene. I miss the talks we had as a group when we were part of the math lesson study group in New Brunswick. Are you still in charge of a math lesson study group?

      I agree with the praising of all participation since that is how children will mainly be learning from this point on. I see the difference in understanding with the children who are passive learners vs the children who are active learners in the classroom. Those days of sitting in a classroom as quiet as a mouse while the teachers lecture are long gone!


  8. AnnMarie Estevez
    Jun 07, 2009 @ 10:43:21

    Love your blog!! Math for our children has come a long way and we do need to become more familiar with it.


    • Alicia Vilas
      Jun 07, 2009 @ 11:26:35

      Thanks. I think as long as adults speak in a positive way about math in front of children and we try to understand the changes, that should help quite a bit.

      Some children feel because their parents have problems with the math or parents had problems with math as children that they are bound to fail in math.


  9. lisa schnettler
    Jun 08, 2009 @ 15:54:10

    I definitely agree re: nothing being “too hard” and in rewarding the process of thinking through a problem or trying to solve it as much as arriving at the correct answer.


  10. Eva
    Jun 09, 2009 @ 09:29:08

    You are right on the money. Karinna is on 3rd Grade and I when I take a look at the math homework I sure don’t recall doing that kind of math on 3rd grade. And while the new math they are learning is great, I feel like she needs some help. As a parent sometimes I feel like I may be confusing her by helping her “my way” …


    • Alicia Vilas
      Jun 09, 2009 @ 19:46:23

      Hi Eva. I have noticed that children who tend to do well in math, don’t get very confused when learning it the way I teach it in the classroom (according to the math program), and then go home and their parents show them the way they were taught when they were younger. I noticed some children who struggle a bit may get confused when taught both ways at the same time. For these children I do not recommend teaching it a different way. Eventually they will be taught the shortcuts we learned.

      Try saving the parent guides that go home which explain the way the math is taught in the classroom. Which math program does Karinna use? I’ll go online and see if I could see which program they use in your district.


  11. Alicia Vilas
    Jun 09, 2009 @ 20:07:30


  12. Ana Barreiros
    Jun 09, 2009 @ 20:38:13

    It is not something unheard of whenever a student states “I don’t like math because I will never use it in the real world”. New math is a way in which students are able to make connections to everyday life. True it is difficult for parents to adjust since they were not taught math the way it is currently being taught today. However, children today reap a greater benefit since this “new math” allows for peer interaction and a variety of ways to learn or obtain an answer in math. It creates innovative challenges that promote childrens’ thinking skills. I’m not saying the old way was wrong, just more difficult because of all the memorization involved. Unless you were very good at math, majority would find themselves struggling. Hopefully, this “new math” will help those who are not math-inclined to succeed. The children should get reinforcement in math as it is taught within the school. Yes, I know this might mean frustration between parents and children. However, if you give your child a change to explain it to you, and you patiently work with him/her, then you are both bound for success at completing the assignment. Besides, it is on rare occassion that a child does not take notes which they can later use as a guide to arriving at the solution. Unfortunaly for the adults, once you have children you will re-enact your educational years. Your studying is not quite over. Even when they are in high school, you will ecnounter that many things are no longer taught in the same manner. Just be patient, and very open minded:)


  13. Angie
    Jun 11, 2009 @ 22:31:27

    Alicia, you couldn’t have said it better! Love your blog! My husband and I attended a district wide “Parent Academy” for Math when our daughter was in third grade. I have to say the majority of us, if not all were taken back by the “new math” concepts. It’s so different than how we learned math. I remember early on my daughter’s teachers recommended “not” helping with homework if “we” did not understand the methodology……good suggestion in order to avoid confusion.
    Also, to the person who wrote suggesting we teach money & finance….my daughter is in fifth grade and is in the middle of a stock market project. They had to individually research and present a stock. The class then chose the one they thought would “make $$” they were given $20,000 (fictitious, of course) to invest. They are currently tracking the stock – I’ll let you know what happens!


    • Alicia Vilas
      Jun 13, 2009 @ 10:55:10

      Angie that sounds like a great project. Do let me know what happens! I remember you mentioning the project to me.

      Good advice for parents who do not understand the math.


    Jun 14, 2009 @ 17:09:31




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