Homeschool Summary – Feb 2015

Waaaah.  Where did the month go.  I think this is a refrain I’m going to keep repeating month after month.

This month we took a week off to celebrate Chinese New Year in Southern California.  It was a much needed break as I found myself losing momentum.  I’m noticing that I lose momentum after about 6 weeks of schooling.  Things are also crazy because I started school again.  There never seems to be enough time after downtime for research and making materials.

In general schooling is going well for Thumper, not so well for Astroboy, whom I’m neglecting. Personally, I’m struggling in striking a balance in:

  • Chores vs School.  After awhile of doing school it feels like the home is like a Star Trek Starship, slowly losing its integrity.  The clothes pile up on the sofa, various knick knacks on the mantle, things go unvacuum and unmopped.  I’ve learned over the last year, the general unkemptness of the house unconsciously bothers me and I start feeling unorganized.  What I haven’t figured out yet is the schedule to fit that in and also how to get the kids to help with it.
  • Fieldtrips/Outtings vs School.  When we have too many scheduled activities like going to Library story time on Mondays or Homeschool Library on Wednesdays or playdates in the morning or appointments to go to, it disrupts my flow.  I really need that 3 hour work period for myself, not for the kids.  I need to have long periods of activity, rather than going to multiple places one morning. But staying home all day except for swimming makes the kids go crazy.
  • “work” vs “non-work”.  Really all activities the kids are involved in are WORK.  But it is so hard to get rid of the mindset that non-academic work is work.  When we spend an hour outside gardening, I get anxious and think, “But we didn’t do school today!” I also sometimes feel like the kids don’t get enough exercise, especially Astroboy because all we manage is 1/2 – 1 hr of play during swim practice. Sometimes when I’m tired or sleepy we go eat or sleep instead.

I made one big change this month which was to wake the kids up at 8:00am. We get an extra half hour for stuff like cleaning and chores and gardening. And somehow this makes us really have a 2.5-3 hour work period.

We also didn’t go to swimming because the kids got sick for a week. Wow, never realize how much of a time suck swimming is. Without swimming and an earlier schedule the kids and I manage to go out and take walks in the afternoon. I will need to ponder what to do about this schedule.

In general I feel like I’m veering toward too much math and language again. I know I need to make two changes. One is to not prep while the kids are working and the other is to go back to planning my own schedule and a presentation schedule.

IMG_5022Fieldtrips: We took a field trip to California Academy of Sciences and also toured Acme Bread, visited LA for Chinese New Year.

Thumper is doing much better in the Work Plan front.  I forget to ask her sometimes how she likes her work plan.  But in general, she’s got the routine down.  I made a few more changes to the work plan routine by using our wall school calendar and also reorganizing our index cards.  It’s still a work in progress.  But there are some days when I’m taking a nap and she’s just following her plan, working.

Astroboy wants me to be with him still.  I know part of the problem is the unavailability of age appropriate classroom materials.



Math:   Multiples, common multiples, 4 digit x 2 digit multiplication, distributive & commutative laws of multiplication, factors, 4 digits / 2 digit division.  Though we covered the concepts she’s not doing on in all of them yet.   The materials/presentations used were: Commutative & Distributive Laws of Multiplication (Presentations 1, 2, 3, 4), Multiples (Presentation 1 & 2), Factors (Presentation 1), Large Bead Frame (Presentation 1 & 2 up to 2 digits), Long Division Racks and Tubes (Presentation 1 & 2).  I’m partly doing this to practice for my math and partly I know she can be introduced to the concepts.  We will most likely come back again to review when we actually do the work in this area.
Work-wise: She’s pretty much done with addition memorization up to 9.  We’re going to review the higher numbers before we move onto subtraction.  She is working on 4 digit x 2 digit multiplication as well.
We barely did any English this month other than listening to audio books (Wizard of Oz), Radio Lab, being read the BFG.  English handwriting, we’re connecting letters together.
For Sagebooks, we are now on Lesson 17 of Sage book Series 4 (Pink).  For handwriting, we are done with basic stroke names.  Wow, it is so much faster now when I tell her how to write something, I can use the stroke names!  I’m now asking that she read to me 15 minutes a day at a minimum.  We’re going through a lot of the Hsin Yi Yoyo/Baobao reader books and the Sagebooks Idioms book. One thing I realized ice I started having her read was the importance if building her vocabulary. Because she definitely uses her reading skills of guessing and using illustrations as clues. But she can’t so it when she doesn’t know enough words to guess. I changed our workplan so I have to read to her daily.I read the following books. These are about 1-4th grade level books I think.
Social Science and science:
We’re charting the growth of a seed.  We finished studying the history of money.  We must have read through 5-10 books on the subject and they all say the same thing.  So I finally learned how to say barter in Chinese, 以物易物.
We toured Acme bread bakery.  If I can get my acts together, we will try and grow some yeast.
The science kit we got as a gift for Valentine’s day, Thumper spent a day using to grow some colored crystals.

Practical Life
We made 發糕. She has learned how to make her own cup of hot drink using the water hotpot. I’m starting to get offers for hot tea. (Horray!).

She is slowly developing the habit of cleaning up after lunch and putting items away after she comes home. This is a big point of contention between us. I try hard not to get too mad since I know it’s my own bad habits she picked up.



Language: Sagebook Blue Series Book 2 lesson 10. It looks like we get about half way through a book each month. Partly because I don’t force him to read everyday. When I get anxious we step on it for a few days and progress through half a book.

Math:  No progress.

Practical Life: Cutting. Maze. Window washing. Dish washing. Lacing.  Ciaohu

Astroboy loves mazes for some reason. I finally caved and bought him a Kumon one so I don’t have to keep looking for new ones for him to do or say he doesn’t like.

Once in a blue moon he’ll go and wash dishes after lunch. I don’t force him. It makes me happy when he does. I do require the children out their dishes away. This sometimes is a power struggle and he’s starting to say no more often.

IMG_4874One day he got bored and I got my Ciaohu 3D puzzle blocks out for him.  He’s been pulling it out every few days to work on them.

Sensorial. Geometric shapes cabinet 1-2.  Colors

This is just an introduction to the geometric shapes.  We also spent a day playing with the Science Kit we got.  He spent a lot of time mixing colors.

In general Astroyboy’s problem is his inability to do anything by himself unless it’s practical life. I feel like I I think about it really hard I would know what to do. But my brain is pulled in 5000 directions I don’t want to stop and think about it yet.  I really need to get my act together and help him in the classroom.  With me needing to teach her Chinese characters, read to her, being read to, somehow it takes up a lot of time in the day.

There are actually other things we do in life other than school that’s interesting to me, like our gardening, which is really coming along.  And trying to figure out a chore system.  I feel like, because we try to garden every day, even if it’s just to water the plants, the kids are finally getting some hands-on exposure to botany somehow, even if it’s not in the classroom.


Celebrating Chinese New Year

I was not really enthusiastic about celebrating Chinese New Year in the classroom this year.  Other than making red envelopes, it just seems like all other activities we traditionally do (writing calligraphy to put on doors, making 發糕, hanging laterns) are “traditional” and yet almost peripheral in how CNY is celebrated, props for the main event. I really wanted to experience the “festivities” part of CNY again like I did last year in Taiwan.  So I took the kids down to LA.  Thursday was CNY.   Tuesday afternoon, we went to my mom’s temple and the kids got red envelopes from the monks.  None of us expected it so it was a very happy surprise.  Thumper was super enthusiastic about how much money she received.  She got really really good at saying her Happy Chinese New Years in Chinese, learned how to use two hands to receive her red envelope, how not to open it up on the spot or talk about it in a loud voice.  She couldn’t wait though and asked to hide under a table to count her money. The main displayWednesday night, we went to Xi Lai Temple because my mom said it gets really crowded on CNY.   I think it’s one of the largest temple on the West Cost.   That night, we looked at all the displays they had out on the courtyard, and read about the theme of the display: “三陽和諧”  It’s apparently a slight change from the traditional saying of “三陽開泰” because the theme is harmony.  I got to explain to Thumper why we have sayings that use the zodiac names(陽 and 羊 are pronounced the same and we’re in the year of the Goat 羊 this year).  We spent some time looking at all the different Buddhhas and various Taoist statues. Continue reading

Workplan 2014/2015 – Take 2


It’s been two months since I implemented our work plan routine.  Though it improved things, I still disliked how we went about it.  In my ideal scenario, a child creates their work plan on Monday, then look through it daily to create a todo list.  All this done without much much of my input except maybe for me to look it over and “approve”.   Of course, this is why I got into trouble.  I typically have big lofty ideas in my head of a super autonomous child, and then get frustrated when they don’t get there due to my limited guidance.  Then I get into this infinite loop of nagging to get them to get there, them resisting, and me nagging some more.

It occurred to me recently that the Work Plan is part of the 3 stages of work; where you take out the material, work on it, and then put it away.  This is one of those reasons why I like the philosophy, that it isn’t about just being able to master a concept like doing laundry for children or being able to add.  Instead it says it’s equally important to plan and know what it is you want to do, execute it, and clean up.  All important soft skills.

Work plan Fall 2014

Our work plan by the end of December composed of three parts.

  1. Weekly Work Plan
    The weekly work plan has 4 major areas, each with individual threads.  For example, Language has reading, writing, handwriting, etc.  Areas that need to be done daily are highlighted in yellow.  Some parts are filled in by me Sunday night and others are done by Thumper during our planning session.  For example, she writes down herself the 3 letters she will work on in handwriting weekly.  The weekly work plan is filled out once a week at the beginning of the week.
  2. Weekly Work Record
    The work record has little rectangles where Thumper records down what she has done.  She sometimes draws, sometimes writes in zhuyin, sometimes English, sometimes Chinese. There is an indirect component here in that she will learn how to write some Chinese characters since they’re typed in the Work plan by me.
  3. Index Card system
    The index cards are where the individual work unit, the todo list so to speak, is written down.  She is supposed to look at the Weekly work plan daily to decide on what she wants to do, pull out the equivalent cards and sort them in the order she wants to do them.

From my discussion with my trainer, my understanding is that while there is an overall guideline in what a child needs to accomplish, imposed by the threads listed in the work plan and in my case, highlighted threads to be done daily, the freedom of choice comes in two forms:

  • how much work they want to do per thread, decided after discussion with me.
  • for each work goal, how much work they want to do every work period to reach that goal, this can be from no work to some to all work.

So for example, we write down she does 8 problems in subtraction this week, and she is to decide on how many problems she will work on each work period.

One problem with this work plan was that very very often she will put off the items she said she will do and she won’t do them.  For example, the fraction equivalency work.  It got left on the work plan week after week because she always left it.  Some days we were out all day on Friday and this would not get done.  Other days, she runs out of time by the end of the Friday work period.  There were no consequences unlike a school.  Home life just gets in the way and I can’t be consistent.

Work plan Spring 2015

Spring '15 Master Contract

Spring ’15 Master Contract

Wanting this semester to be different, I dragged Thumper into a meeting on our first day of Spring semester.  She hates these meetings because she just wants to dive into work.  I asked her what she wanted to study this semester and her goals in the different subjects and I wrote it all down into a Master Contract.  I told her this is our contract for what she wants to learn this semester.  It’s a way for her and me to remember what she wants to learn so that I can help her find material.  Even asked her to sign her name and everything.  This is how I learned that she wanted to know more about where money came from and how money is different between the U.S. and Taiwan.

That same week, I read Montessori Homeschooling‘s post about how you need to discuss the work plan with your child.  And I had to whack myself on the forehead.  As usual, I know of the concept, but I’d forgotten how important this is in the planning of a child’s work.  I chalk this up to my anxiety that we can’t cover everything we need to cover if I let Thumper choose.  Because every week I would see the work she hadn’t finish and in order to make her finish, I would put it on the work plan again.  It isn’t that we didn’t discuss the work plan together, but she wasn’t really asked what she wanted to learn and what she liked or didn’t like about some work.  That was the piece I was missing.

The Monday after, for our weekly meeting, I made some changes to our work plan meeting.  Of course, the devil’s in the details.  She’s not at a point where she will willingly go and plan her day or her week.  Maybe because it’s still a lot of what Mama Lao-shi dictates.  Though I’m slowly trying to change that.  But I think another reason is because I haven’t broken down the steps on how to plan for her.  So this is the habit part I’m trying to establish with her right now.


Weekly Calendar

Weekly Calendar

Each Monday, we start with our Weekly Calendar.  This is a new “calendar” I put out so she has an idea of the major outings, commitments we have this week.  For example, the fact that we have to go swimming daily, or that we have library time on monday or a playdate on Friday.  She is to write that down.  She also writes down when I will make certain presentations.  This part is actually for me so that I do not put off doing new presentations.

We then work on our Weekly Plan.

Old Work Plan

Old Weekly Work Plan

New Work Plan

New Weekly Work Plan














  1. First we look through all that she did last week.  As we go through each thread, we check against her Work Record to see if she’d reached her goal.  We discuss if the goal was too much or if she did not like the work.  However, we add all the work she did not finish last week into this week’s additional work.  I’m quite adamant about this as I want her to be able to plan ahead on what she wants to do, rather using procrastination as a way to not finish.  For example, she had agreed in our Master Contract that she would learn 12 Chinese characters a week.  If she doesn’t finish, we add those words to the words she has to learn this week.
  2. We then go through this weeks’ Weekly Plan and fill in the blanks.  Usually I’ve already worked on this plan on Sunday to fill in parts I really want her to continue on.  For example, the Sagebook work or Sight words.  Otherwise I’m hoping as this semester progresses, she works more on more on planning her week herself.  We re-discuss as we go through how much work she wants to do per week, if her idea of how many units of work is too much or too little, etc.I filled in spots that are more complicated to write, since she’s not writing much yet.  I’m so thankful that I read the post.  Ultimately I like it much more when she plans her own work and having an in depth conversation about it help us toward that goal, as compared with me telling her what needs to be done and having her write it down.  I think it also helped that she’s done this for 3 months already and has an idea of her work progression.Having the Weekly Calendar also changes how much work we will put on our Weekly Plan. This planning part really is nebulous and requires some more advanced planning skills. Because there are no rules. You kind of have to have a feel of how much work you’re able to accomplish each week. I’m really hoping after practicing awhile, she gets this.

I’ve made two more changes to our weekly plan.  And much like What Did We Do All Day, I’m allowing items to span two weeks as I find that the longer items like research and writing don’t ever get done otherwise.  This is now highlighted in green.  I just kind of have to figure out how to denote this is the second week.  Another change I made this semester was to put EVERYTHING she needs/wants to do during the day into work plan or daily plan.  This includes feeding Pudding, folding laundry, new project ideas she comes up with during the day, even Reflex Math.  Otherwise she never does them.

Everyday, we work on our Daily Plan the minute we come into the classroom.IMG_4827

  1. Look through her list of cards from yesterday and pull out the index cards she did not finish.  These are her first items to do today.  She is not allowed to move these items to the back.
  2. Look through her Weekly Work plan and pull out ONE CARD that is her project of the day.  This is so that she definitely works on long projects or things that interest her first, ala, Getting Things Done.
  3. Look through her Weekly Work Plan and pull out index card of work she wants to do.  She of course has to pull out cards in the highlighted yellow thread.  This is usually where I try to gently remind her that an item needs to be done since she doesn’t have a long term view of the week yet.
  4. She then looks through and sorts the index cards in the order she wants to do them.
  5. She looks through our Weekly Calendar to see what plans we have today.  I check her ordered cards with her and we may take off a few items at the back of the todo list due to our plans.
  6. After she finishes one work, she is to write them down onto her Work Record Log.
Work Record Log

Work Record Log


The last week or two, I’ve actually been “making” her to finish her unfinished work by the end of the day.  More about this when I discuss Time Management in another post.  I don’t want to make her do things.  But I’m still contemplating what it means to work in general.

The hard part for me right now is knowing how much work a child typically can do in a three hour work period.  For example, I can tell you for 3-6, 1-3 work is probably all some children can do.  The rest they’re socializing, moving around, eating snack, doing their chosen work again and again, etc.  I don’t know what it is for the 6-9 child.  If I know this part, then I would be able to help Thumper plan her week better.  Maybe it is time to do some detailed observations.

The work planning part gets better and better each day.  It’s really hard for impatient me to wait for a habit to form.  I have to constantly remind myself to remember how much more independent she is now compared with last semester.


Sagebook Progress Week 5


Things got a little crazy after we started on Sagebooks.  I started researching on teaching stroke orders, character layout, character components, and then started school.  Yikes, it’s already been 5 weeks since we started on Sage.

For Thumper, as we wrote in our January monthly summary, we have spent this week and last week reviewing.  I think we’re losing momentum a bit because of our scheduling issues.  I have not actually had time to review the characters she doesn’t know with her.  She has just been reading the treasure boxes and also this week started on the idioms.  On our work plan, I basically gave her a daily item she needs to do, which is to read Chinese for 10 minutes to me.  She can choose books from the Little Bears series, the idioms, the Sagebook Readers, or the Sagebook Treasure boxes, any of the first 3 levels.

Thumper actually loves the idioms books.  I say so because as a child who does not want to read and seldom repeats work twice, she asked to read the same idioms book (book 3) 2 days in a row both with me and by herself.  Astroboy also wanted me to read it to him.  The books themselves really require an adult to be there to explain the concept to them.  My kids are not going to be able to start making sentences with these idioms without some examples from me.  Unfortunately I’m slightly rusty on them myself and the Sage ones don’t come with examples, so I don’t even know if my examples are proper.  But whatever, she loves the “jokes” part included after each idioms intro, even though that also requires some explaining.

Anyways, yes she doesn’t remember some characters, but I’m still amazed at how she can remember the strange conceptual ones that are not nouns.  There’s nothing to hang these on other than the intro we had 3 at a time, and composing and writing down a sentence.  We didn’t even bother with reading the reader books much this time around as we were jumping around the books in this series since she knew about 60% of them already.   I super envy young kids’ memory ability.

As for Astroboy, we kind of started on book 2 of Blue Series.  I’m kind of neglecting him because of my obsession to create materials for Thumper.  So I think I formally introduced 6 characters total in 2 weeks?  However, seeing his sister reading the Treasure book one day really spurred him on (because she read the whole book).  Just that one day, he wanted to read the WHOLE book.  We spent maybe an hour on it.  I could not dissuade him.  So at least he’s seen all of them.  After about character #10-#12, he started getting confused on all of them.

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Multiples, Common Multiples, Commutative Laws of Multiplication 倍數, 公倍數

Age: 7.5

Presentations: Multiples: Concept and Language of Multiples, Multiples: Common Multiples, Commutative Law of Multiplication: A Number x a Number, Commutative Law of Multiplication: A Sum x a Number

Last week, I did 3-4 math presentations related to multiplication.  I believe this is called 現買現賣 in Chinese.  I basically practiced on Thumper what I’d learned in class.  Partly because my teacher said these presentations should be done as soon as possible in Elementary, maybe the first few weeks/months of school?

I skipped the Wooden Hierarchical Material because I just don’t have time to make the material and while Thumper needs a review and could really use the visual, she’s been exposed to the concept already.  Instead, we did the following presentations:

  • Multiples: Concept and Language of Multiples
  • Multiples: Common Multiples
  • Commutative Law of Multiplication: A Number x a Number
  • Commutative Law of Multiplication: A Sum x a Number

These four are just part of two different write-ups.  But it seems that these are the most basic ones that can be grouped together because they require no writing from the child whatsoever.  After what my teacher said about working with the math manipulatives without writing, I’m now not as confused about what I’m supposed to be doing with these presentations.  As I dive into the materials, I can see that these same concepts in multiplication are reviewed over and over again, each time getting more abstract, so I don’t need to stay with work with one material for too long if it seems like Thumper gets it.  I would know she doesn’t get it when she’s stuck at understanding how to use a material.  For this reason, I did not “make” her to take out the beads again and try it herself at a later date after she said she wasn’t interested.


The Language of Multiples presentations are about defining what a multiple is.  Like, 2,4,6,8. You lay out the short bead chains, label them, skip count for the experience and then give a definition.  This lesson took Thumper all of 5 minutes.  Astroboy was the one who actually counted for her and laid the number labels down on the rug, since he likes to count.

I laid out the short bead chains, have the child label them, and for each number say something like, “有幾個5在10裏面?(How many 5s are in 10.  剛剛好有兩個五在十裏面,而且沒有剩下。(There are exactly 2 5s in 10 with nothing left over)…..二十五是五的倍數 (25 is a multiple of 5)”  After repeating the “nothing left over a few times” (沒有剩下), Thumper suddenly interjected and said, “Oh! What about the other numbers, do they have something left over?”  And she proceeded to try it out by skip counting numbers 4, 3, 2, 1 using the bead chain of 5 while I continued working with Astroboy in counting and labeling his bead chain of 6.  Thumper determined that for all numbers except 1, 25 is not their multiple.  I really liked this aha moment for her and I think is one of the strong arguments for using manipulatives.

I will make sure to say “nothing left over” as well taking about multiples in other lessons now.  I do want to note how it does not roll off my tongue translating the album and saying it in Chinese.  It is obviously not a daily conversation I hold with people.

Common Multiples

In the Common Multiples presentation you lay out a bunch of bead bars.  The kids find for themselves multiples that are common to each number.  For example, in the photo, she is laying out the multiples of 2 and 3 in a multiplication table format, then laying out the answer using your decanomial bead bars (bead bars #1-#10), then looking for all the common ones they have. (6, 12, etc).  I’m finding that Thumper still has a liking to moving beads around.  She got the concept pretty quick since she knows some of her multiplication tables.

Common Multiples

Sorry I don’t have photos for the rest.  I will show you my album pics instead.

Commutative Laws of Multiplication

The Commutative Laws ones shows multiplication rule that it doesn’t matter what order you put the numbers in:

  • a x b = b x a
  • (a + b) x c = c x (a + b)

In this exercise, you lay out the multiplicand (被乘數) in bead bars horizontally, the multiplier (乘數)using a gray card, then you calculate, exchanging and laying the product out vertically.  You do the same thing in reverse to show that the answers are the same.  And my favorite part is the teacher saying, “I wonder if this will work with other numbers?”  I like the invitation to exploration rather than telling the child about the property and that’s it.


Thumper really lingered on the last presentation (A Sum x a Number).  We must have spent more than an hour on this.  She just kept pulling out numbers to try even though she kind of understood the concept already after the presentation.  Similar to the previous one, you’re using bead bars for the multiplier and gray cards for the multiplicand.  And just showing that the products are the same.  (a + b) x c = c x (a + b)

Even when Astroboy and I went upstairs to have lunch she was still figuring them out.  I loved that she found the topic interesting.  I couldn’t help myself (I know I know) and told her that there is a secret in the work.  I wanted her to figure out that you can add the two numbers together in order to get the sum and then multiply them by the multiplier.

It was really neat to watch how her brain is working out new knowledge.  After the first presentation she knew that the answers are the same.  But she still wanted to figure out the answer each time for each side.  I’m not sure why that is.  She got really busy making her own multiplication tables, using the Chinese version of Nienhuis-like multiplication table sheets I made for her 3 months ago.  It was so she can look up the answer instead of calculating in her head each time.  I didn’t ask her to do that.  And in hindsight I could have pointed her to the multiplication chart, which is a Montessori material.  But I just let her explore as she wanted.

She did figure out the secret to the “presentation”; that you can add the numbers together first.  Though this week I found out that you don’t really want them to figure this out because your’e teaching commutative law.  oops!)

If I go with what my teacher said, I would probably just ask her next week during our planning session to see if she wants to try working them again without me.  We are obviously a bit in this presentation, but it was still fun for Thumper.  I think you can start this at 6+, depending on what the child knows.

All in all a really good week on the math front.  Really glad I decided to splurge and take that math class.

Multiples in Chinese

Here are the vocabulary I needed to look up in order to present.  Chinese is much easier to understand new math terms because I don’t have to know Latin.

  • Multiples – 倍數
  • Common Multiples – 公倍數
  • Multiplier – 乘數
  • Multiplicand – 被乘數 (literally means the number being multiplied)

Some Montessori Math questions answered

Just had my first class tonight on Montessori Elementary Math.  I have to say, other than the cost factor, Montessori Math really is the way to go for a homeschool math curriculum.  I did a mapping of Common Core vs Montessori Math presentations and for most of the presentations Montessori does math about 2-3 years before Common Core.  Now it doesn’t mean it’s forced on the children, it’s just that since the curriculum is already there for the 3-6 year olds, it kind of naturally progresses faster.  Of course, not all children progress at this level either.  But you do get introduced to a lot of abstract concepts early due to the concrete materials. I need to do a brain dump before I forget all the answers I got tonight to my pesky homeschooling problems I’ve been having the last few months.  Some of the answers made me go “D’oh! I knew that! <sigh>”

  1. How come the kid(s) just work on a material for a bit, or none at all after my presentation? Apparently very normal for elementary kids.  The 3-6 child likes repetition in work.  The 6-9 gets a concept and then is ready to move on.  You want to really invoke their interest in anything you present and tweak it in different ways in order for them to work on it.  I can ask the child to work with the materials but I don’t need to have any written equations, goals for them to explore, etc.  I now feel so much better that when I presented the Least Common Denominator it took 10 minutes and then we were kind of done.
  2. My trainer really advocated for the child to NOT do writing if they don’t want to or need to.  To have the child really work on concrete materials as is.  This explains so much why I did not see any written paper work in my presentations and yet I keep seeing it online in blogs.  And she’s talking about this even for the early elementary kids (1st graders).  If the child’s hand isn’t ready to do a lot of writing, as evidenced by all the wriggly writings, then there’s no reason to have them write.  The emphasis is really on the concrete materials.  And I’m reminded of the recent arithmetic book I read from the Life of Fred guy about how you really need the child to work in the concrete level as deeply as possible before moving on to abstract.  He says abstraction doesn’t start till 12.  I don’t know if it’s true but he’s basing this on Piaget’s theories.  But the take away is just really concrete, manipulative materials as much as possible and it’ll translate so much easier to abstract when it’s time.  Otherwise it shows up 3-4 years down the line when the child is working in the abstract and now doesn’t get it.  I’ve heard that for sure from public school teachers.
  3. Going back to point #1.  Tonight I saw a lot of 10-15 minute presentations on multiplication.  My question when I saw these presentations was, that’s it?  It appears that the beginning presentations (we haven’t gotten to the abstract parts yet) contains ideas that the child would have worked on in 3-6 but now they’re formal presentation.   So I can totally try this out with Thumper this week!
  4. I also learned that I want to make sure to have introduced the concept of multiples before fraction.  Oops.  Thank goodness we stopped at equivalence.
  5. Lastly, I was all set to poo poo the multiplication presentations (common multiples, commutative and distributive laws) at the beginning of my album, thinking “Why does Thumper need it if she already is learning her multiplication table?”  But apparently a lot of these presentations contain a lot of indirect preparation for geometry!
  6. Continuing with point #2 and #5, it was pointed out to me that you don’t want to give the child hints.  For example, you could point out to the child that 3 x 5 is the same as 5 x 3.  Basically telling them what a commutative law is.  But once you do, then the child doesn’t want to do your concrete material work.  And now you’ve missed the chance for them to play with math so to speak.  Oops!
  7. For the Great Lesson on Story of Numbers, apparently you don’t need to present them all at once.  You can just do 1 poster at a time every few days.  And most importantly, this Great Lesson doesn’t contain a lot of information precisely because it’s only there to arouse the child’s interest.  You can do the whole sequence maybe in 3rd grade.  That’s why it doesn’t have the whole history of numbers and the charts are a bit limited in information.
  8. I also learned that you might need 2 decanomial boxes instead of 1 because in the common multiplier layouts it doesn’t have enough otherwise.
  9. When I asked about the Fraction Charts, I was asked, “Why not have the children make it?”  It’s always so weird to ask questions that have been confounding me for awhile because the answer always takes me in another direction and suddenly the question itself, and my obsession with the right answer, seems so unimportant

There is also the thing against timed math.  But that is one area I disagree with because I feel it kind of depends on how you do it.  We can just give them a stack of multiplication flash cards and have them practice and why do we need to know our facts fast?  I think with me learning math in Chinese I see this in a philosophy difference.  One focuses on understanding math concepts and the other is a bit more on memorization.  One helps when you want to do advance work, the other helps in day to day life.  I advocate both because you need both.   And for me I see multiplication table being much easier to memorize in Chinese to begin with so why not?

Chinese Characters by Grade Level

One of the anxieties for me is wondering if the kids are hitting “grade level” in their Chinese characters knowledge.  In the past teachers have refused to tell me, citing reasons like, “They may know it today during the assessment but not know it tomorrow.”  Or, “They may recognize a character but not know how to write it or use it.”  While this is very true, and in fact it’s a problem I see daily with Astroboy, I generally hate it when people don’t want to give me estimates.  THERE IS ALWAYS A RANGE!  Seriously.  Because obviously my child doesn’t know 10000 characters (is there even that many in Chinese?), nor do they know 1000 (it would take longer than 2 years for most children).  To me, it also illustrates the distrust between parents and teachers.  Somehow I’m going to take this info and try to whip my kids into learning more characters faster or accuse them for not knowing enough.  Okay, I will stop ranting now. There is a list published in a research paper of number of characters children will be presented for reading and writing by each grade level in Taiwan.  This is expected number of characters to be introduced.  It does not mean your child will know this many.  But it gives you a good general idea of where your child is vs a child in Taiwan.  Or plan your curriculum.

 Grade Level  Reading (characters / words)  Writing (characters / words)
 1st grade  400 / 600   300 / 400
 2nd grade  800 / 1200   600 / 800
 3rd grade  1200 / 1800   900 / 1200
 4th grade   1600 / 2400  1200 / 1600
 5th grade   2000 / 3000  1500 / 2400
 6th grade   2400 / 3600   1800 / 3000

There is a character vs word component because knowing a character is only half way, since characters are usually used to compose words; e.g. two characters combined.  For each writing level, you’re expected to be able to make a sentence with said character, know when this character should be used.  The same knowledge applies to words you can write. I hear the standards are different in China.  You know a lot more characters by the end of first grade.  But no time to research that right now.  For me, it’s difficult enough in the U.S. to learn this many for each grade level.  No need to feel even more anxious by comparing to China. This website lists frequency character coverage.  I don’t know if it’s based on Traditional or Simplified Chinese though.  Anyways, using this chart we have:

  • 400 = 70%
  • 800 = 85%
  • 1200 = 91%
  • 1600 = 95%
  • 2000 = 97%
  • 2400 = 98%

Looking at this table, it seems that you should be able to read pretty well after 3rd grade.  I’m assuming after 4th or 5th grade, you’ve seen enough characters to really be able to guess at the meaning and pronunciation of new characters you don’t know. For the Sagebooks, this means that it only takes you to 1st grade level and we really need another 500-700 to reach 3rd grade level.  For us, IF we get through the Sagebooks by the end of May like I planned, we’re on track for first grade level.  I guess I better get started on planning what to do with the second 500 characters!   If I want to reach 300 character writing proficiency, we also need to cover up to the Orange Series in Sagebooks.  This means about 20 characters a week.  I’m not sure it is doable.  Though technically Thumper already knows how to write a lot of these characters already.  I just want her to be able to write it properly.