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I can see students that are not developmentally ready to do what I am teaching. They need more engaging activities that will build on their level of understanding of number concepts.

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The idea that number sense develops in such an early age struck me. And how crucial it is to engage children in meaningful conversations with numbers to build on their number sense.
Another important thing to remember for me, is that the Kindergarteners come in with varying exposure to numbers and the less exposure and exploration time they have will have a great impact on their understanding and success in later years as well.

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I agree the article puts things in perspective when understanding student math  levels coming into kindergarten. Their lack of skills could be inexperience with numbers , not intelligence .

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I was amazed about how early children start developing number sense. Although my own children are now grown, I did reflect on things "How many can I have, mommy?"did start fairly early.
The other thing that came to mind is how do non-school age children. Single child or the oldest child in a family could be at a disadvantage going into school.
I like that this article allows math to be an exploration, not a drill

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1. I thought the parent talk with children is so vitally important and it shows in students ability to gain number sense at a young age.
2. I was interested to see the number concepts of doubles and doubles plus one at pre-k and K grade level. I teach the GO Math first grade curriculum and doubles and doubles plus one is one of the areas of instruction.

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The success a student has in mathematics is dependent upon skills learned at a very young age. A student needs to be given opportunities to deduce and reason with numbers and is not to be expected to memorize if he/she is going to develop a strong number sense. Language plays a strong role in developing number sense and we should educate and encourage this type of language to be used at home during every day situations to strengthen the skill.

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I also was thinking about my 3 year old as I read this. She LOVES to count and picked up on it very naturally. She can count to 20. What she struggles with is the VNR...just looking at the objects and knowing how many without counting 1,2,3, etc.

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1. One important point I took away from the article is that young children can not be pushed ahead of their developmental readiness. Even simple adding of 0 or 1 can be too advanced for some children in kindergarten. This is really important for teachers to know, especially with how fast our math curriculum is paced sometimes!

2. There are so many different ways that children develop number sense. It feels really overwhelming to think about it all. It is very important for teachers and parents to understand and help the child learn and practice.

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I agree that some people seem to be born with an innate ability for number sense. However, this article makes me wonder if that ability were fostered in the pre-school years, would more of the population seem to be able to gain that ability?
Cindy McKibben

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I wonder about where it talked about research supporting children at risk for academic failure not working with the easiest sums until even first or second grade. That was surprising for me.  How are those students granted access to grade-level curriculum then?
I took away information from a comment in response to research questions 2 & 3. The article talked about the importance of creating meaningful dialogue surrounding collections and numbers. I understand and agree, but never thought of it in the language that was suggested. The example was to ask the child how many feet does she have, and then ask how many shoes will she need, etc. My take-away was when they were saying the child will need two shoes, NOT ONE. Or the child may have one cookie, NOT TWO. I hadn't thought about labeling what it isn't.

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I gained a lot of insight from reading this article.  My first take away was how sometimes kids are just not developmentally ready to do what we are teaching.  Sometimes we get into the routine of what we have to teach and not focusing on if this is what is best for the students.
My second major take away was about how essential fact fluency is.  I have always knows it is important but the examples in the article were an excellent reminder of keeping myself in check.  A lot of times the program that we teach doesn't meet the needs of each student.  I think this article reminded me to step back and look at fluency, number relationships, and keep in check what is purposeful.
-Michelle P

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I could relate with what you said about some students coming to school already behind where they could possibly be.  I agree with the article saying different kids learn at different rates and I have seen that first hand.  But it is hard when they are all in a class and at such different levels but that is part of our job as educators.  It just reminds me how important what we do is especially for those kids that need that little extra help.
-Michelle P.

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Erin I agree with you. I have a 2 year old at home. We are working on counting with 1:1 correspondence. We use toys, snacks, books, anything around the house. She is also working on this skill at her daycare. No way are we pushing her or forcing her to work on her numeracy. But it is something that she enjoys.

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I agree with you on both your point of interest. I have a number of 2nd and 3rd graders that still cont on their fingers. I wil also be using the stategy of labeling groups by wha they are not.

Bonnie

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Numeracy Article

After reading this article one take away I have is parents need to talk with their children at a very young age to help them begin developing a number sense early on. Another scary point is: If children come to school without that ability they are already behind and need interventions.

Another take away is that the activities we use with our young children should not include flash cards and worksheets. They need to be playing with numbers, set of objects, recognizing which group of objects is larger or who has more. When I would count with my children I never made a point of saying this is 2 not 1 when looking at a group of two objects. I will be doing this with my grandchildren for sure.

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There is SO much I am still learning as well. So many of the programs schools use assume some skills already in place to be successful and don't address them, or don't address precious skills in older grades.
Erin Arno

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I think the most important take away from the article came at the very end, "Early instruction does not mean imposing knowledge on preschoolers, drilling them with flashcards, or otherwise having them memorize by rote arithmetic facts. Fostering number sense and fact fluency both should focus on helping children discover patterns and relations and encouraging their invention of reasoning strategies."
Also, the statement that early numeracy instruction as young as 2 or 3 years old does make sense, but not in a worksheet sense, but in a development of number awareness around them, which would mostly have to come from parents and daily caregivers.

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I found it very interesting the children as young as 18 months can start constructing an understanding of number sense. However, recognizing that a child must be developmentally ready and not rushed into learning math facts is critical to further their mathematic knowledge in the future. I also found it interesting that if a child develops verbal number recognition early on they will be more likely to recognize the purpose of object counting. A meaningful understanding of object counting can lead to determining efficient counting strategies and applying them to problems. In turn creating opportunities to discover patterns and relations within math problems.

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I think not rushing is so important! It's really hard not to rush children ahead, because for us adults it seems so simple. We forget that it is a whole new concept for children to learn what numbers are.

-Leah

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One idea that really stuck out to me in this article is the idea that once a child understands the "counting sequence" and what each number represents, they will then be able to start at any number and know what the next number is. I have seen older elementary students who still struggle with "counting on".
Another concept that I thought was interesting is the idea of showing children "non-examples" of numbers to help them understand the boundaries of each number word. I previously taught 2-3 year olds, and I never thought to intentionally show non-examples.

-Leah

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I really liked the talk of not rushing the child into learning facts and other such skills, but still discussed the importance of having basic knowledge of numbers before entering kindergarten. It was also very interesting the concept of using appropriate methods for the child's age to begin working with numbers.

-H.Therrell

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I think the article explained very well how important to expose little ones to the world and it help them to build the number sense.  However, I think some people are born with it (lucky people)! For sure that I'm not one of them.

Tomo Pistole

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Yes, I agree with your opinion. It's very important to communicate  with kids and explore them to the world.

Tomo Pistole

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I also appreciated the part about how young children learn to visually recognize patterns and groups to help with counting. Oral counting is really hard for some of my kiddos and I definitely think part of the issue is that they missed out on some number sense knowledge during their early years.

~Kylie

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My first take away from the article was an increased awareness of the need for young children to begin developing a number sense early on and how it can impact their future mathematics.
My other take away was the importance of using developmentally appropriate tools to help foster the learning and understanding of numbers, not just utilizing flash cards or trying to have students memorize.

~Kylie

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I understand your point about having the opportunity to show the "difference" between 5 and 3, but that could be the same as showing the difference between L and M. Unless the child understands what 5 and 3 are, that has little meaning.

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I have a difficult time remembering my elementary days when I was forming my numeration skills, but I remember a class I took in college which led me to understand WHY I understood numbers the way I die.  Numbers are so much fun, and when you can SEE them they make so much more sense.  VNR makes learning math a breeze and the earlier that can be accomplished, the more fluent one can become.

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Your description of "oneness, twoness, and threeness" works for me. I like the way it adds individual importance to each group.
The idea that students may need intervention the first day they enter kindergarten and that the curriculum may not provide what the student needs is concerning.

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Reflecting back on my own early school experience in the 60s. I think I remember that I could not count or recognize numbers or letters. That may explain why I had to repeat the first grade and why I had such a difficult time with math for most of my life. My early math education lacked the rigor described Baroody when he describes a child composing and decomposing whole number to understand that it may be described in many different was. Where he describes the "concept of additive and subtractive identity" he, in my opinion, missed a prime opportunity to introduce the term "difference." By comparing groups prior to subtracting them, the child can see the difference between 5 and 3, vs,
OOOOO
OOO
the visual difference is more concrete and easier to see and internalize.

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Hi Anne,
I agree with you! In the home setting, and even pre-K setting, it seems that the exploration of small numbers is very organic and student centered. As kiddos enter first and second grade it gets much trickier to create those opportunities for exploration during the math block. (S. Artz)

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I have a little guy, who is almost 18 months, so this article was so interesting to me! My first big take away  was the importance of exposing the youngest of children to oneness, twoness, and threeness. I like how the article suggested teaching using examples and non-examples of each number.
My second take away was that many children are not ready for even the easiest of formal fact fluency until the end of kindergarten or beginning of first grade. I have felt that some of my kiddos are not ready for our fact fluency program at the beginning of the year (in first grade), and this article was really helpful in explaining what those kiddos might need to be ready for fact fluency practice. (S. Artz)

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It was eye-opening to me as well that we need to understand that not all Kindergarteners are ready to jump into the K curriculum. It is like reading, they have to have some knowledge of how numbers work before they can start putting together more ideas.

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My take aways from this article are: a deeper understanding of the sequence of skills needed for students to make connections between number, counting, cardinality, and fluency with these skills.  I think the bigger of my take aways is how important it is to recognize when students come into Kindergarten with deficient number sense and how jumping in to a program that assumes they have the skills needed will only set you and the student up for failure.
I am still struggling because there is just so much to understand about math acquisition and that I don't have that understanding yet. This article gave me a much clearer understanding of what students need to be successful in the program tasks that, to the less-trained eye like me, may seem easy enough to "show" but harder to "teach"

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It is very true, as you stated, that children will build their mathematical sense when they are ready, if they are exposed to numbers.  That is by far the best way for children to learn.  Thank you for sharing.

Anne-Marie Pender

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The greatest take away I have from this article  is the necessity to talk to children, using simple language daily to encourage learning, preferably when they are in their home setting and very young.  As shown in the examples used, children were asked how many feet they had and how many socks/shoes they must get.
Along with those little games played on a daily bases, it becomes a fun exercise between parent and child, during which time a child will begin to invent other items to count and/or discuss in mathematical terms.  When children invent their own methods of learning, the information is well integrated into the brain.
This same method can be successfully copied in a pre-k classroom, but becomes more difficult if those facts are still being acquired in the second grade setting.  Interventions have to be initiated to prevent further failure.

Anne-Marie Pender

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My first take away from this article is that number sense starts at a young age.  If students do not come into kindergarten without basic number and counting knowledge they are already in need of intervention.

The second take away I got from this article was that young children learn to visually recognize patterns and groups to aide their counting knowledge. Children need to see what numbers look like because oral counting is such an abstract idea.