REVIEW POST: Primary Grade Challenge Math - Zaccaro

(UPDATE 10/28/14: We have added Upper Elementary Challenge Math to our repertoire and couldn't be happier :) See the associated Montessori Trail post.)


Legoboy has another New Love:

Challenge Math by Zaccaro

We are starting with this one - covering grades 1-4 for "gifted children".

I ended up purchasing the entire of books in this series for several reasons:

1. looking for a good set of word problems to review earlier concepts
2. Montessori math and geometry do not align with any other available curriculum (I group the Montessori-inspired curricula options somewhere in the middle)
3. Something just didn't sit right with me concerning the other options. They are useful; I will not say don't use them (especially if they are working great for you! Keep going with what works!) - but there was a mis-match for our family, my principles and my understanding of Montessori. 
4. This set of books (there are several in the series) are designed for gifted children - children of younger ages who have particular gifts that correspond with typically older children. 
5. I wanted to review them for the sake of other families looking for a resource to fill a similar need. 
6. This series also includes some of those allegedly missing concepts, perfectly tying them into the included album pages (associating money with decimal fractions, converting into percents, etc. (NOTE: Please do not flame me in comments regarding missing concepts - I've covered this topic before, I am not saying Montessori is wrong, and I'm not saying the concepts aren't there - I am fully trained, I know where the concepts are and where they fit in. Comments of a flaming nature will be removed. I'm done with flaming when I speak peacefully. Thank you for speaking respectfully.)

Word Problems: 

     A few people have shared a few solutions to the dearth of word problems - and the lack of time to create their own (and my lack of time to create my own!) for each and every concept. Especially in a sporadic co-op/tutoring, mostly homeschooled by himself situation, there just aren't classmates around to pull up the caliber - and I am one person unable to cover everything (stop laughing!). ;) 

Montessori Mathematics and Geometry Studies: 

     Montessori math and geometry use hands-on materials to bring the children to the point of abstraction. In some areas, it seems that the children hold on to the materials longer than their public school counterparts, but once they release the materials, they are almost always ahead in conceptual understanding. Where we have children not able to apply the concepts, we have a situation where the adult likely didn't assure the child was working with appropriately challenging work and likely didn't ensure there were appropriate real life word problems and experiences available. 

Not sitting right: 

     What is about the other options that didn't sit right? I think because they are geared towards public school curriculum, several of the options have already been re-written to correspond to Common Core (the dumbing down of our country's children), and I just don't want to participate. 

     In addition, I really wanted something that more closely resembled Montessori. Life of Fred is a great complement to Montessori elementary mathematics but there are few word problems. 

     I think this is my main thing - I don't want to dig into 4th grade books to find word problems to give to a 1st grader, just to find math skills that fit.  

Young Age - Older Work: 

     Isn't that the mis-match of Montessori to other expectations again? 

Perhaps my reason are the same thing over and over - with different words: I wanted something that better corresponds what we are doing as compared to constantly tweaking, reading, adjusting, pulling "7th grade" materials for a 2nd grader who isn't "special" in that way, but simply has been given the tools to go deep with his understanding.... I was (and am!) tired of tweaking already!!!!

What we are using: 

     Legoboy is 1st year upper elementary, or 4th year elementary - and I would NOT say he is gifted in this way. However, he has received the keys provided through Montessori throughout his life. As a "4th grader", we started with the primary level book to review past concepts - kind of catch up in the word problem category. We did great for 1st-3rd grade, but I'm done tweaking (have I said that yet!?) and I have to be done looking too. 

Legoboy loves it! He is actually working out the math in his head or on paper as needed, then he challenges me with it. Even with Life of Fred, I have to "encourage" him to record any work, or answer out loud. He just wants to read the story (although he can do the math in the books). 

How it is set up: 

Each chapter contains some background/how-to-solve information on a particular topic - most is review for Legoboy, some is new or said in a new way. Then there are 4 pages of problems - 1-2 page(s) for each "level". The chapters can be done in any order, but easier concepts are towards the beginning. Chapters can cover a variety of topics but are generally somewhat grouped together.

The four core books we will be using are the following: 

1. Primary Challenge Math - grades 1-4: Includes chapters on Sequences, Problem-solving, Money, Percents, Algebraic Thinking, Negative Numbers, Logic, Ratios, Probability, Measurements, Fractions, Division. This book includes topics that Montessori has in upper elementary. Guess what? That tells me it is likely to trust a child's abilities and correspond well. I am NOT disappointed. 
2. Upper Elementary Challenge Math - grades 3-5 (this is available for pre-order, shipping in April)
3. Challenge Math - grades 4-9: Includes chapters on Astronomy, Algebra, Problem Solving, Percents, Fractions, Decimals, Ratio & Proportions, Physics, Statistics, Probability, Metric System, Perimeters, Area, Volumes, Trigonometry, Calculus
4. Real World Algebra - grades 4-9: Includes chapters on Language of Algebra, Geometry and Algebra, Proportions and Algebra, Physics, Levers, Pythagorean Theorem, Percents and Algebra, Simultaneous Equations, Algebra and Money

We also have the following that at first skim have been great: 

• Becoming a Problem Solving Genius: A Handbook of Math Strategies
• 10 Things All Future Mathematicians and Scientists Must Know (but are rarely taught)
• 25 Real Life Math Investigations That Will Astound Teachers and Students
• Scammed by Statistics: How we are lied to, cheated and manipulated by statistics and why you should care

I am working on something of a correlation between the AMI mathematics album and these books - slowly creating a correlation. I will share this on the Keys of the Universe Discussion Community in Excel format and will likely post it on this blog at some point in pdf format (this will happen faster if those who are interested, let me know - I'll prioritize it ;) ). 

Sample - Chapter 4 - On Money

 

 

Work Plan - Balancing Freedom and Responsibility

One more work plan post - then I promise to start posting about our journals :)


MBT over at What DID We Do All Day? has put up some posts that have generated quite a hubbub of conversation. (what would we all do if MBT shut down her computer??? ;) )

Part of the conversation in the comments on the posts, as well as private e-mails with individuals, have revealed a few more questions....

The main one being - how controlling are these work plans?

The answer is... Follow the Child.

I'm not very creative on that one, huh? ;)


What follows are totally random thoughts as I sort through e-mails, past blog posts on work plans, the current ones with their ensuing conversations, and questions raised in elementary training.

I will try to organize these thoughts, but in case I run out of time, I wanted them out of my head at least! ;)



Here's the thing - I personally homeschool and I personally chose Montessori (whether school or homeschool) because I want to live in a structured environment that can handle spontaneity. Thus, I have chosen to Montessori homeschool so that we can live out moments like this:

LEGOS!!!!! Yes, we really LIKE our UPS man here! 

His goofy smile - when he's the MOST excited!
Um. The work plan is out the window for the *rest* of the day!
Although he'll still do his daily stuff at some point. 

Structure: For a child just starting out, you'll provide as much structure as they need to assure that all subject areas are being covered in some manner at some point - the details are up to YOU, your environment, your child.

Individualized: Every subject every day is unrealistic and does not provide near enough depth. But however you rotate through a week or a month, or work in blocks - no-one can plan that out ahead of time for a child unknown to them; hence work-plans that are already set up for "February cover these things" - are most likely not going to work because your child might be ahead or behind in varying subjects.


Freedom and Responsibility: We want the child to still continue to choose their own work and not be locked into this work plan/contract dictating their every move and interest. HOWEVER, it should also be built according to their needs as well as their interests, which in elementary don't just always correspond.
3rd year elementary example: Legoboy needs more work in decimal fractions; but is much more interested in history (it's always history around here!) - thus our work plan balances "this specific presentation in decimal fractions on Tuesday or Wednesday"; "enough follow-up to truly master the concept" (this can't be checked off until it is mastered); "possible new presentation if ready"; and what he tells me are the next things he plans to do in history for the week - "I'd like to look for books on the Vikings at the library" - "I would like to look up more information about the evidence for monasteries in North America before Columbus arrived". These are specific, but also child-led.)

Responsibility with freedom. Freedom with responsibility. 


THE BASIC DEFINITION: Essentially, we are at first taking their primary level "morning planning in my head" that they did, and putting it on paper or some other visual format. We are not DICTATING at this point as much as getting them visually organized.

Work Plan as External Order: Remember at the second plane of development, they have internalized the order they've had around them during the primary years, for good or bad, and an elementary child is outwardly "messier" than the primary child. THUS, the work plan is one place to have that outward order in place. Something to show the order that is in their minds.

Plus there are simply expectations of elementary children we just didn't have for primary children (local educational requirements and the like).


Meetings and Nuances: Most of the nuances of the work plan/contract - no matter the format you choose - is going to be in your meeting/discussion. The children should know they have these requirements but they should also be verbalizing their mental plans with you so those things can be noted. They should also have enough freedom to learn the consequences for their work choices - the good, the bad, and the ugly!
(I worked hard Monday through Wednesday - I have Thursday and Friday as light days; vs. I slacked off Monday and Tuesday, and now Wed/Thurs/Fri are going to be harder ---- these sorts of things should be worked out in a loving manner with the adults involved, so that lesson is learned but spirits aren't quelled - best done in homeschools ;) ).



Type of Requirements: The requirements can be vague (something in "math - squaring") or very specific (Math - squaring/cubing - Game 3A) - and usually a combination of both. I might have 2 presentations to give to my son in history this week, but he is expected to do something more with it of his own choosing; or he is expected to follow-up with a previous presentation.

Verbally discuss the plan for the day/week: We can ask the child to plan his day - not everything needs a particular time, but to say, "When do you plan to work on Game 3A? Let's plan a time so I can make sure I am available to show you." Now, this could be "after I am done with XYZ" or it could be "Tuesday at 1 pm or so, when the baby is down for nap".

Working beyond the plan/contract: Then the child is expected to find additional work to do - again, this needs to be emphasized within the environmental set-up, which includes the conversations and nuances with the adult. That just because they have done one bead chain, doesn't stop them from doing much more.


Work plans should match the child: My problem with reading and seeing such examples as a child NOT doing another bead chain because they've already "checked it off" - is that those are the children who have the wrong kind of work plan for their needs. They need something that will set them off to do MORE work, while assuring they have a base minimum of variety. There is a clear mis-match AND the adult has not set up the proper environment.

MBT has a neat system where if her boys work heavily with something, they could see it disappear off their plan for the rest of the week. In terms of a written work plan, such as the one I posted yesterday, if there are 5 boxes to checkmark, they could mark off all 5 in one day! (in which case, I might ask for something to be followed up later in the week or to move on to the next presentation in that sequence, just to keep things going).

Routine check-ins: Hence, in the beginning we want to check in throughout the day; then at least daily. As homeschooling parents, unless we have very large families or lots of other commitments, we will probably touch base every day; in schools or those with very large families/commitments, it might be touching base with each child 2-3 times a week. At least through lower elementary and possibly into upper elementary; older children might do a longer-span work plan and officially check in with it once a week. Throughout all of that, you are still going to be involved, so it's not like you don't know what they are doing  and can offer guidance along the way.



Areas of Interest are included or not - usually both: A child should also be working in his areas of interests - perhaps those are planned in (once your daily stuff is done, you work on your own items; or you work on your own project for the morning and the afternoon is the required stuff; or you don't have to say anything; OR if there is something your child needs, such as a trip to the library, you write that on the work plan - "Thursday morning: library").


Daily requirements???
Depending on your work plan style, yes a child could foreseeably do nothing but math on Monday, nothing but language on Tuesday, etc. And if that works for the child - GREAT!

But typically we do have a very tiny number of items that are daily (but are also generic - just something that meets my definition of real work (see yesterday's post) must done in these areas each and every day) - in our home, it is daily math skills, piano, tae-kwon-do practice, drawing, and Latin practice.


Our Montessori, spontaneous, work-plan organized crazy thing we call life: 
Back to those Legos above? It was mid-morning when they'd arrived; he had already done some of his daily stuff, and started on a project in history. I let him spend 20 minutes or so exploring the box and its contents, long enough to decide he really wanted to set everything else aside for at least a few hours. He then spent some time cleaning things up he'd gotten out; then finishing up a few chores so he wouldn't have to stop to do them later. He made himself some lunch to have on hand so he could keep building. Then he DELVED right in!

He had time to spend with it; then made some proper plans so he could spend longer with it; executed those plans; and had one HAPPY day!

I attribute almost all of that to Montessori and a good deal of it to the process of working with an adaptable work plan and journal system that taught him those skills of organization, planning, follow-through, consequences (he could work for 4 hours on those legos, but then be hungry and grumpy, having "missed" lunch - so he prepared ahead of time (I would have made him something at the proper time, but HE thought to make his own food for himself and not "burden" someone else with the task of waiting on him - thoughtfulness! Now, I did have to bring him water later - he'd forgotten to get that ;) )) - and again:

Freedom and Responsibility in action. 

One more time because I LOVE this smile! 

Wednesday - and done with the WEEK!?

(I am typing this on a Wednesday)

Legoboy woke up this morning to check his work plan before getting some breakfast. He discovered that despite our busy days Mondays/Tuesdays, and other than the daily practice stuff, he is actually done with the work plan for this week.

He has some choices -

• we could go over things and see where to go deeper with work, adding a bit here and there to maintain and/or grow throughout the week
• blow off the rest of the week and just play with Legos (aka live in  heaven for a week)
• re-write a new work plan for the rest of the week
• hire himself out to Garden of Francis for the rest of the week and finish earning money towards this next tae-kwon-do belt test

recognize it? ;) He's been making all
sorts of things out of Legos lately.
Montessori things

Well, Mama has stitches in her finger and lots of orders to still work on - SO. He has committed to reviewing math every day (via Life of Fred elementary series and the Fractions book), and hiring himself out. With some Legos on breaks. 

And he had one last request: listen to more of the Maestro Classics CDs. He is studying them one at a time, just listening for now and making lists of project ideas he has on each one. He would later like to do a day for each CD to just work on his chosen projects - down the road a bit. Right now he says, "I'm just absorbing it."

Sounds good to me! Nice relaxing week - he earned it! 

Click here for our original post about Maestro Classics.

Decimal Fraction Board - when to start

Here's a question I am asked a LOT - whether this particular material or others. And most particularly those material that in reality bridge lower and upper elementary, making that "break" between the two ages within some albums cumbersome at best.

(this particular material has been asked about 5 times in the last month alone, hence I pick on this one ;) )

First "years" - definition: my numbering of "years" assumes the child will have the opportunity for a full 6 years' worth of elementary Montessori. If this is not going to be the case, then it can very roughly be considered as equivalent grade levels - in the US, a 6 year old is 1st grade; 7 year old is 2nd grade; etc. as of the beginning of the year.

When should a child start the Decimal Fraction Board?
It's really whenever the child is ready and depends on how strong was their primary and earliest lower elementary experiences. My albums have them noted as beginning between years 2 and 3 - so definitely starting in lower elementary. Year 2 if they have a very solid foundation or catch on quick; and year 3 to begin if if they needed a lot of remedial work or have teachers using albums that don't have the same foundation OR just plain don't have interest in fractions enough to get them there until year 3.
Anecdote: my son was voracious about fractions and I thought he would get to this work early - NOT SO. He took a seriously long break from all things fractions, but applied what he knew to real life, and only recently (year 3!) has come back around to fractions-study in general - and now he is starting this decimal fractions work. He had a bit of an intro to it because of a strong interest in money in years 1 and 2, but this material just wasn't cutting it for him. I backed off and now he's going at it full-force. 

With the extensions, it definitely lasts a year or a year and a half, so for most children would start in lower elementary and finish up in upper elementary (some children won't need it in upper elementary if they started in year 2 and "get it").

This is one of those works that shows how difficult it can be to delineate between lower and upper elementary ;)


Here is what my album page has for pre-requisites (the most important thing than actual age) -

Prerequisites: 

• concept of parts of numbers (fraction work); 
• knowledge of multiplication facts (esp. multiplying by ten – large bead frame, bank game); 
• familiarity with decimal system categories (golden bead, wooden hierarchical); 
• hierarchically colored beads/pegs (stamp game, pegboard, decimal system number cards, multiplication checkerboard, racks and tubes, etc. - enough of this work that the colors are intuitive to them now)

Shortly after working on this material, a few months, a year, maybe even days if you have a child for whom this material truly connects, you'll move the child on, at the right time, to the decimal fraction checkerboard:

By the time, they have the decimal fraction board, they have typically had the regular multplication checkerboard, and it is now just a matter of merging a few concepts. Wait until the child has each of the concepts down pat - or if there is a struggle, the particular type of struggle would be addressed with a synthesis - and go for it. The introductory lesson itself (just laying out the individual square of felt) will be enough to tell you if the child is ready or not. 

Thus the Decimal Fraction Checkerboard is potentially a lower elementary work as well - indeed, upper elementary prefer to use fewer beads, so introduce this work as early as is appropriate for the child in question. 

Above all else - have FUN with it!