Sunday, December 19, 2010
On the down side, the school day is long. Tessa comes home from school tired and drained more than I feel is to be expected. I would be in favour of a reduced school day because of the opportunity cost to students of time spent on schoolwork, which could be spent pursuing their own study. Unfortunately, the school Tessa goes to holds the opposite view and chooses to extend the school day to 7 hours plus approx 1+hrs/day of homework plus homework in the holidays. In my view, a school issuing homework for the long, summer break is saying to students, we don't trust you to make good choices about how you spend your own time, and the work we come up with is more important and valuable than your other activities.
Homeschooling parents sometimes worry about whether their children are keeping up academically with school children of the same age. I can offer some reassurance: I believe it would be difficult for any homeschooling child to make less progress in maths than Tessa has made this year. This is greatly frustrating as Tessa has always loved maths, especially geometry. I wonder if maths is particularly well-suited to a mix of one-on-one instruction and independent exploration, progressing at the pace of the individual learner, because maths is so much about grasping new concepts, exploring them so as to fully comprehend them, and then building on them with further new concepts.
Tessa's school began the year teaching French as a second language but failed to secure a replacement French teacher when the first one left so switched to Spanish, after a break during which there was no foreign language teaching. Now, just as Tessa has reached a point in Spanish where she is beginning to really enjoy it, the school has decided that Mandarin would be a better language to teach and is hoping to offer Mandarin rather than Spanish next year. The year before Tessa joined the school, her classmates were taught Italian.
If different Montessorians were asked to list the principles of a Montessori education in order of importance, the lists would probably vary. To me, freedom (with responsibility) is the most important element of a Montessori education. Sadly, there has been almost no freedom of choice for Tessa and her classmates in their schoolwork this year. I believe the students would get a superior education if they were allowed to choose their own subjects and topics for study, and study those topics in their own ways.
But, on the plus side, Tessa has had the privilege of being part of a community of wonderful people: two classroom teachers and an outdoor education teacher, and 14 students aged from 11 to 15. I feel grateful to have had these lovely people in my daughter's life. The school has made it a priority to build a strong sense of community; the year started with a camp, another camp took place in the middle of the year, and the class holds a community meeting each week to discuss issues and make decisions together.
The students are expected to take a lot of responsibility for organising some of their activities. This has given rise to great learning experiences, including creating a menu plan with shopping list for the class's second camp; designing, pricing, constructing and maintaining a hen-house; all aspects of running various fundraisers; and holding a presentation of their work at the end of each term, at which the teachers keep very much in the background.
Tessa has had to venture out of her comfort zone on a few occasions, interracting with different people in the community: interviewing a local resident about the history of our suburb; discussing purchases with staff at the local hardware store; visiting residents in a retirement home.
Despite the down sides, Tessa wishes to return to school for another year, so we will be trying to make the most of the positives, and to support Tessa to minimise her involvement in optional school extras and do her homework efficiently, to free up a little time to pursue her own interests.
Wednesday, August 26, 2009
My first thoughts were to provide school work relating to the trip (e.g. journal, foreign language work): it seems a little crazy to travel across the world and then spend time doing algebra problems etc. In the end, we put together a mixture of activities relating to the trip and ordinary school work so that Josiah can do what he feels like at the time.
Keep a journal
Ideas to write about:
- How is your climbing training going?
- What training have you been doing?
- What climbing have you seen?
- How is the team?
- Where have you been?
- What did you do there?
- What did you see?
- What are your thoughts about the country you are in? About the people, the landscape, the buildings, streets, vehicles, food, language, anything else.
- How are your attempts to use German / French going?
Keep a record of words and phrases that you learn and their meanings, in the languages of each country you visit.
In the phrase book of the language of the country where you are at present, find a useful phrase. Write it down and practise it. [We bought German and French phrase books before Josiah left. He and Tessa had fun with them.]
Keep a record of what you spend. Add 3.5% to every purchase made with the Prezzy Card.
Notice prices and convert them to NZ dollars when you are shopping:
1 Euro ≈ NZ$2
1 Swiss Franc ≈ NZ$1.30
Read Gamma Maths [photocopied pages]. Practice each new problem type as you go.
Create maths practice problems from the list. [Josiah and Tessa each have a list of types of maths problem to practice, from which they choose three types each week; they create their own examples.] Write the date in the table each time you do a problem. [Photocopied pages of problems from earlier chapters of Gamma Maths also supplied.]
[Rod and Staff's Building Christian English series.]
Take notes and/or use a highlighter while reading.
Science [Pages photocopied from Real Science for Kids Chemistry Level II.]
History [Pages photocopied from Kingfisher History Encyclopedia.]
Penguin Guide to Punctuation.
Monday, August 24, 2009
I need to have more discipline about the structure of our days too. One of the great strengths of homeschooling is the flexibility it allows to follow the children's interests and timing. But with flexibility comes a need for self discipline; otherwise nothing gets done at all. The kids and I have always preferred to have a schedule but we are (I am) not very good at sticking to it.
Saturday, August 01, 2009
Thursday, April 30, 2009
It is the first week of the second term. After a very busy two weeks' "holiday", which included a climbing trip away, work for the kids' climbing club, a visit from one of my lovely nieces and none of the gardening I had planned, I am enjoying getting back into our "school" routine. It's been raining all week, one of those weeks when I truly appreciate the homeschool lifestyle: it's so much nicer to be snuggled up on the couch reading together than having to go out to school and to work.
We are continuing much as before. Tessa found the quantity of independent reading she was doing in the first term onerous so she is rejoining Josiah and me for history work rather than continuing on her own, and may do the same for language.
I suspect I am clinging to my language plan in the face of evidence that it is not working well for Tessa. We are reading through R L Trask's Penguin Guide to Punctuation, an outstanding resource. The explanations are clear and detailed, with lots of examples throughout. But Tessa wants to be doing. She would rather do punctuation activities than read about punctuation. I have been creating a language worksheet for the kids every week to enable them to practice what we have read about, but Tessa is unimpressed. I've had another look at the Montessori Research and Development Punctuation manual and will make use of some of those activities but they only cover a few uses of punctuation. Over the holidays, I purchased Rod and Staff's Grade 6 English textbook, Progressing with Courage from the Building Christian English Series, which is recommended in The Well-Trained Mind. It looks good. Maybe I should give Tessa the choice to finish the Penguin Guide to Punctuation now and then move on to Progressing with Courage, or leave the Penguin Guide to Punctuation till she is older and start on Progressing with Courage immediately.
The indoor climbing competition season is just getting underway and will keep us very busy for the next two terms, attending out-of-town competitions, helping to run a competition at our home gym, and the kids training hard. I have never yet succeeded in keeping basic routines going when life gets really busy or when I get sick. I have this hope that Josiah and Tessa will carry on tidying their bedrooms and doing their daily chores when I don't manage to check up on them. But sadly they are happy to suspend normal practice at the first hint that I am doing so. I am trying to simplify my expectations of the kids so that even in busy times it will be easy for me to ensure that the basics get done. I don't mean that I am cutting back on my expectations, just that I am organising them differently to make them easier to check:
- Morning routine: tidy bedroom (not entirely - just check for clothes, dishes and rubbish); clear the work table in the living room. Must be done by 11am.
- Chores and whiteboard. Must be done by 9pm. The whiteboard is stuck on our fridge and is where I note any extra tasks the kids need to do, e.g. if I notice they have left something outside, rather than interrupt whatever they are doing to insist it be dealth with right away, I just write it on the whiteboard.
- Weekly task list of independent school work. I need to work out an appropriate deadline for this and negotiate the consequences of failing to meet the deadline. Some weekends, Josiah has still had half his independent work to do and has only done it at all because I've nagged him all weekend. The last week of term, neither Josiah nor Tessa did all their independent work.
Another expectation we have of Josiah and Tessa is that they leave the kitchen and dining table clean after they make themselves a snack. Sometimes they clean up without being reminded but often they wander off leaving a mess or do half the job. It's a hard one to police because often I don't notice the mess till a considerable period after the event, and often there is conflict about who is responsible. It's impressive how strenuously each will deny the possibility that they could be responsible for crumbs or spilt milk on the kitchen bench.
Thursday, March 19, 2009
Websites with Montessori printables for downloadMontessori Materials
Montessori Material Makers
My Montessori printables
Fraction circlesFraction circles: whole to sixths
Fraction circles: sevenths to twelfths
Print onto coloured card and cut out.
Grid paper in Montessori hierarchical coloursGrid paper in Montessori hierarchical colours
This is a grid, colour-coded in the Montessori hierarchical colours, for children to record addition, multiplication, subtraction and division calculations on.
Montessori decimal fraction boardDecimal fraction board - file 1
Decimal fraction board - file 2
To make the decimal fraction board, print both files onto card. Cut the right hand margin from the first file. Glue the files together so that the right hand edge of the first file lines up with the left hand border of the table on the second file. Laminate.
A variation on the Montessori decimal checker boardA variation on the Montessori decimal checker board
This is a miniature, more abstract version of the Montessori decimal checker board. By the time I introduced multiplication of decimals to my son, he was moving very quickly from the concrete to the abstract on new maths concepts. I did not want to spend a lot of time making a decimal checker board for him to use maybe twice, so I made this quicker variation.
How to usePlease note: these instructions will only make sense to people familiar with the Montessori decimal checker board. To learn about how decimal numbers are taught in the Montessori curriculum, see a Montessori manual such as Montessori Research and Development's Decimal Manual.
- Write the multiplicand horizontally along the centre of the checker board and write the multiplier vertically down the centre of the checker board (or vice versa).
- Work out the product in each square of the checker board as you do when using the basic checker board: one row at a time, always starting at the right and moving to the left. Write each product in its square.
- Just as with the basic checker board, any product greater than nine needs to be rearranged: the tens removed and one unit for every ten placed in the square to the left. Obviously digits written in pencil can't be “removed” and “placed” as straightforwardly as bead bars can. The best way to get around this will depend on the individual child. The rearranged forms of the products could be worked out on a fresh copy of the decimal checker board, with the child referring back to the initial copy each step of the way.
Or the products could be erased one at a time and rewritten in their rearranged forms. Or, as my son chose, the products could be written in their rearranged forms initially.
- Finally, just as with the basic checker board, all the tens need to be swept together and added up, all the ones swept together and added up, all the tenths swept together and added up, and so on. In my decimal checker board, the row above the centre line is the base row. Squares above that row should be swept diagonally down and to the left; squares below the base line should be swept diagonally up and to the right. Of course once again figures written in pencil cannot be “swept” as easily as bead bars can. My son did the addition in his head, writing the result at the bottom of the page one digit at a time. Some children may wish to write the addition problem out on a sheet of grid paper to work out. Or the decimal checker board could be cut into rows, the rows realigned and then added together.
The prerequisites for this work are the same as for the Montessori decimal checker board: the child needs to be comfortable with addition and subtraction of decimal numbers and multiplication of decimal numbers by whole numbers, and needs to have had an introduction to multiplication of decimal numbers by decimal numbers to the extent that they have worked out:
0.1 x 0.1
0.1 x 0.01
0.1 x 0.001
0.1 x 0.0001
0.01 x 0.1
0.01 x 0.01
0.01 x 0.001
0.01 x 0.0001
0.001 x 0.1
0.001 x 0.01
0.001 x 0.001
0.001 x 0.0001
In fact, some children may enjoy filling out a blank copy of my variation of the decimal checker board before beginning work with it.
Some children may appreciate the extra cues that would be provided by a colour-coded decimal checker board in Montessori hierarchical colours. An editable version of my decimal checker board is available for anyone who would like to add colours. If you make a coloured version and would like to share it with others, please leave a comment; I am happy to host or link to a coloured version.
Manuals for ages 3-6Discovery of the Child - Maria Montessori.
The Montessori Method - Maria Montessori.
Teaching Montessori in the Home: the Preschool Years - Elizabeth Hainstock.
Basic Montessori: Learning Activities for Under-fives - David Gettman.
Shu-Chen Jenny Yen's online Montessori albums.
Don Jenning's online Montessori albums at the Montessori Teachers Collective.
Montessori World Educational Institute online Montessori albums.
InfoMontessori's online Montessori albums.
Manuals for ages 6-12The Advanced Montessori Method volume II (also called The Elementary Materials) - Maria Montessori.
Teaching Montessori in the Home: the School Years - Elizabeth Hainstock.
Don Jenning's online Montessori albums at the Montessori Teachers Collective.
Division by a 2-or-3-Digit Divisor: a Montessori-Style Teaching Manual - Lisia Grocott.
Montessori Research and Development Montessori manuals available for purchase. I recommend the Montessori Research and Development manuals reservedly. Montessori homeschooling with my children, I have used the Decimals, Fractions, Maths, Geometry and Language manuals for 9-12. Both children have thoroughly enjoyed the maths and geometry activities. I do not believe there is a better programme available, Montessori or other, for teaching elementary maths. However, the Montessori Research and Development manuals I purchased in about 2003 are riddled with errors. Many of the activities are explained poorly and required modifying before I could present them to my children.
The prepared environment and the role of the teacherIn my opinion, the prepared environment is the base of a Montessori education. It is through the environment that the adult helper attempts to meet each child's individual, changing needs. The environment is clean, orderly and attractive. To begin with, the adult entices the child to work, through presenting and re-presenting a variety of activities, waiting patiently for the day when one of the activities will “call” to the child, and the child's concentration will be caught.
When that happens, the adult must quietly step back. The adult's role now is to protect that fragile concentration from interruption, for in the early stages, if it is broken, days or even one or two weeks might pass before the child's concentration is caught again. Even a friendly “How are things going?” or an awareness of being observed might be enough to shatter the child's concentration.
The child begins to make choices based not on surface appeal and whatever catches their eye but based on a deep inner desire to explore certain activities. The adult's role is to observe and consider, changing the environment and making new presentations and re-presentations based on the child's needs. The child will not be in this perfect state of knowing his or her own needs all the time; sometimes children will be slaves to whims. The adult must learn to distinguish between indiscriminate choices and the choices that stem from a genuine inner need.
Trust the childI think the hardest task of a Montessori teacher or parent is to trust that children will educate themselves if allowed to follow their own interests as described above. According to Maria Montessori, there should be no compulsion. Children are invited and enticed to work, not coerced.
RespectClosely tied to trust in the child is a great respect for the child. Not only are children treated with respect in all interactions, but their concentration is also respected. Adults do not interrupt a child who is absorbed in work, and children are taught to avoid doing so too.
Children's ability to care for themselves and the environment is respected. It has been observed that children derive enjoyment and a sense of pride and self worth from being able to look after themselves and their environment. To that end, presentations of practical life activities are made and children are premitted to do as much for themselves as they are capable of and as they want to.
The principle of respect encompasses every aspect of a Montessori environment. As well as respect between people, there is also respect for the things in the environment and for everything in the wider environment of the world. The Montessori materials are treated with care.
"Help me to help myself"It is acknowledged that help can be a hindrance: when a child is capable, but only just, of doing up the buttons on a jacket and is trying hard to do so, it would be quickest to take over and do the task oneself, but that is not what the child wants, nor is it actually helpful to the child.
If a child completes a task or activity, ignorant of some sort of error, the child is not corrected. Instead the adult makes a note to re-present that activity at a later time.
The materialsMaria Montessori created a set of apparatus from which children can discover for themselves, and then practise, many different concepts. Even complicated mathematical concepts such as calculating cube roots are presented concretely with physical apparatus so that through seeing and building for themselves, children can reach their own understanding of each concept.
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Friday, March 13, 2009
Our "free choice" days are proving a hit although they are a little chaotic with both kids wanting my attention at the same time, and with other activities interfering because our weeks have been busy. Josiah is spending most of each free choice day working on a science fair project, studying how much prey spiders catch in their webs. Tessa, with her free choice days, has started a blog and learned to crochet, among other things.
Tessa is enjoying working more independently. To begin with she took notes of all her independent work, but she found that tiring and is now taking some notes and meeting with me to discuss the rest, so that I get feedback on her learning.
I am very impressed with Real Science-4-Kids Chemistry II. I wish there was a Real Science-4-Kids Physics II.