Katie, I didn’t know if it would be easier to put all my questions from this Module on Early Number in the same place or to spread them out throughout the blog postings. So, I’ve done both. Here they are all grouped together, but you will also find them throughout the postings. Let me know which one was more useful and I will go with that next time 🙂

– Even though there seem to be some differences in opinion with pacing and children’s development of math understandings, both Piaget and Montessori believe that manipulatives are necessary to make the learning concrete and more understandable. What did you note as significant differences or similarities?

– When viewing/listening to Dr. Higgin’s PP on Early Number Concepts, I really enjoyed exploring that website that she directed us to http://illuminations.nctm.org/Activity.aspx?id=3565 I think this would be a great activity to bring up on the Mimio board or Smart board and have students take turns coming up to play. I loved this! And have bookmarked this to use when I’m in a classroom. I also felt the idea of using red/yellow counters dumped from a cup over and over is very useful. As children record this information for the same number over and over again, it really drives home the idea that this “number” is really made up of other numbers. What did you find most useful from this presentation? And how did you do with our 1st grade activities with counters?

– In the Erikson Videos, I really enjoyed watching “Parts and Whole.” I think that young girl was just guessing and not interested/engaged at the beginning when asked how many bears had run away. But, then when it became a “game” and the girl wanted to figure out “who was missing” she shined. What was the video that you related to the most or learn the most from?

– When examining the Common Core Standards for Mathematics, I believe that the early number concepts (that we are learning are so important for beginning students) are present in the standards. And, I have seen many teachers using this scaffolding of mathematics understanding in the school. What have you seen in the younger grades lately? Have you seen teachers building understanding or just teaching rote counting and number memorization?

– In the TCM Teaching Number article, you said that you thought some of this was too complex for such young students. I disagree. I think that teaching children the meaning of “3” and showing relationships and building connections seems simple. Are you just talking about how they discussed the process? Because, if so, I agree …. you wouldn’t say to Kinders “We are going to learn that the orthographic symbol 3 represents more than just a number, or a group of items, or a word …..” Some of their wording was truly complex and confusing. What are your thoughts now?

Hi Annette,

I’m glad that I saw this after only posting one response rather than posting in each of them and you having the same response in each one!!! I like the idea of posting all the questions in one post as it’s easier to find them all (obviously haha) and I can start doing the same.

1. I think the obvious similarities between the two were that both focus on “hands-on” activities and are child-directed. One key difference is that Piaget learning is also teacher-directed and Montessori focuses on self correction and individual learning.

2. I really liked them because I thought that they were a good means of introducing counting and simple addition/subtraction to students but I was thinking as I was doing the activities that I would have loved if there had been a way to adjust the difficulty of the math used so that these activities could be used for higher level students. There were a lot of fun for entry level math students but I feel like they could be fun for higher level math (grades 2 and 3) if the difficulty could be adjusted to suit their math needs.

3. The bears one was actually my favorite because I noticed that, whether she may have been guessing or thrown off by the introduction of multiple factors (different colored bears), she did a great job figuring out how many when she was only presented with bears of a single color (yellow). I’m not sure if there may have been a connection between the two but still thought it was interesting.

4. I haven’t had experience working with the younger grades quite yet (I start my field experience on Monday) but, the 5th grade class that I was in last semester followed the standards pretty closely, though very few inquiry-based activities were incorporated into the lesson. It was pretty straightforward math.

5. I was meaning the way that they presented teaching the meaning of “3”. I definitely believe that children would be able to understand how numbers are related or connected but presenting it as “3 and three are not really the number but … kind of is” is a little advanced. It’s a little existential…

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