What we do... for math

We spend probably the largest portion of our school time working with numbers, taking a three pronged approach that addresses conceptual understanding, application, and numerical sense/speed.  While this structure may come across as serious or intense, it actually works to free us up quite a bit to be playful and joyful in our numbers work together.  I'll address each prong below for each of our children.

Conceptual understanding.
This is where I introduce new concepts to the children in a concrete fashion and let them explore and work towards understanding.  I do not teach concepts, but guide the children through an independent discovery process.  I find that Montessori lessons and materials fit our needs well here.

I obtained our Montessori lesson albums from the North American Montessori Center (for grades 1-6) and NAMTA (for grades 7-12).  While costly, I cannot say enough positive things about these albums.  They provide clear and thorough explanations of how best to guide the child to discover and understand for themselves the concept at hand.  If there is interest in hearing more, I can provide a detailed post in the future summarizing my full opinion of their value.

I obtained our Montessori materials from Alison's Montessori, Adena Montessori, and Montessori Outlet.  With very few exceptions, I wasted quite a bit of money here.  Most of the materials I bought could have been made at home successfully for a fraction of the cost.  I can provide a post in the future summarizing my opinions concerning which materials are a "must buy" and which can be made successfully at home (and provide directions or links explaining how this can be done), if anyone would like guidance here.

While I am prepared at the start of the week to give each child 4-5 Montessori math lessons, I follow the pace of the child (considering both their wants and needs).  This means that I will support a child's lingering on a concept for several days if there is interest (want) or I may encourage a child to linger on a concept a bit longer if I see that they are on the cusp of a breakthrough (need).   We will also skip over material or cut short lessons if there is little interest or learning occurring from the work.  When this occurs (and it does, despite my best efforts), I simply make a few notes of my observations in order to learn more about my children and where they are in their conceptual development and learning styles.  I then use these notes to determine if, when, and how we should circle back to the lesson(s) we cut short.

The atmosphere when the children are completing this work is one of focused concentration.  The kids seem quite absorbed in their work and pursue it with quiet intensity.  I step back and simply observe their process, sometimes jotting down observations as I discover more about the children and how they learn.  I do sometimes feel bored while they work (there is only so much to observe) and so also spend this time quietly preparing materials for future work, returning emails, etc.
 
Here are a few pictures taken this week of the children working independently following their Montessori lesson.   Avery is finishing up "grade 3" and Alexander is beginning "grade 7".   Do note that, for Avery, I must put the traditional Montessori "command cards" into a context for her to find math interesting.

Here is Avery's work with the checkerboard material to deepen understanding of how to use multiplication when a two digit multiplier is encountered:

Alexander using the cubing material to explore what exactly negative and fractional exponents mean.
 

Application.
This is where we get to see how useful and important math is to our engagement with the world.  This is what many call "living math".  The children pursue this application work after their Montessori lesson has been completed.  I find that this allows the child to "pull up" from their conceptual work and encourages them to continually seek linkages to what they are learning.  While a child may spend just 15-45 minutes on their Montessori work, they may linger anywhere from 30 minutes to 4 hours on applications.  The atmosphere as the children complete this work is lively, engaged, and noisy as we discuss, debate, try things out, fail, succeed, build, model, and USE math.

The books and resources I have found for Avery (grade 3) are wonderfully abundant and usually focused on a single concept.  This makes it easy to link an "application" book(s) to what she is currently conceptually learning.  Here are some of our favorites:   MathStart books with the wonderfully done MathStart Teacher's Activity Guide,  the Pythagoras series, and the Warlord series.  While we are not fans of Life of Fred for learning a new concept, we enjoy Life of Fred tremendously for applying newly learned or already mastered concepts.

While Alexander often enjoys working with Avery on her application work, he does have his own to pursue independently or to work in collaboration with me.  Resources for Alexander tend to combine several concepts at one time and use puzzles and brain teasers to challenge and dig deeper.  Here are a few we currently enjoy:  Murderous Math, Family Math the Middle School Years, and Life of Fred (with the above mentioned caveats).   Below are some pictures of the kids applying what they have learned.

Avery applying what she learned regarding geometric solids (from a few weeks past)

Alexander applying what he learned regarding fractions (from a few weeks ago)

Numerical sense/speed.
This includes the area of learning that many of us home educators (myself included) consider "drill and kill" and avoid at all costs.  In the last two years, I have circled back to this area to try and salvage what is beneficial here to my children's learning.  I do believe that lots of practice with basic math skills will lead to an instinctive numerical sense and a computational speed that increases enjoyment of mathematics.   But how to do this without killing a child's love of math?   Our answer is games.  Lots and lots of games.  If there is interest, I will write a detailed post in the future that shows the many ways we do this, but here are the resources that I find myself frequently drawing from: Family Math series and Peggy Kaye's Math Games.  For most of the games, I have the flexibility to adjust the material practiced to best fit each child.  And, lest I not forget, Scholastic has also produced some thoughtfully done workbooks that provide practice in a silly, fun way.   The atmosphere while the kids pursue this work is joyful, silly, competitive, and often loud!  Below are some pictures of the kids playing games to bolster mastery and speed.

Avery's animals ready for skip counting games.

A home made board game with practice cards made for Alexander

Fairy math class and boring books

We just wrapped up our first (partial) week of homeschool and, despite lots of worry, it went really well. By the second day, the kids worked with focus and engagement on their individual work plans. I braced myself for a few weeks of settling in to the structure that school work demands, but the kids seemed ready for the challenge.

We had some interesting milestones this week. I finally figured out how to spark Avery's interest in math and Alexander figured out for himself how to get motivated to read books that are not of his choosing.

Traditionally I have had trouble with Avery moving beyond the learning phase of a concept and into the practice phase required for mastery. She really loses interest in the work and approaches the monotany of practice with dread (if not anguish). In the past, I have tried to spice up the practice problems with personalized mystery codes she needs to crack, magic potions that she can earn that will reveal messages written in invisible ink or small prizes received once all the work is complete. While all of these efforts improved her attitude, none of them truly engaged her and created that "spark" that is the hallmark of genuinely loving learning.

So for Avery, this week marked the beginning of "Fairy Math Class" and the start of truly enjoying mathematics. Avery is an avid story teller with a rich imagination. She needs context, plot, and characters to be engaged. She is also very socially wired and prefers to have a buddy alongside her rather than work in isolation. As a result, we created "Fairy Math Class". When Avery is ready to start math each day, I call her "class" to order. I gather all 7 of her fairy figurines and sit them on a mat. While the fairies watch, I give her a traditional Montessori lesson and then guide her as she completes the first few examples of the Montessori work. Once she has the concept down, the fun begins. I tell her a story about the fairies that requires her to use the new concept and material she has learned to finish the story. Sometimes she needs to solve problems to help them and save the day (i.e., count out the correct number of beads to buy shoes for a fairy ball). Other times, she needs to solve problems to help them play a game (i.e., adding up and deciding who has the most points in a contest). The best times are when she must solve problems to play a game with the fairies (i.e., taking a fairy friend to find ladybugs I hid about the house with math problems under their wings, solving them and determining which fairy found the ladybug with the highest answer). Math has come to life for her now and she has that wonderful spark in her eye as she engages with her work. It is wonderful to see and even more fun to "play" math with her.

Alexander has had a wonderful break through in reading. He has always enjoyed reading, but has had a narrow interest in reading material. Not only has this made it hard to find enough books for him (he reads with blazing speed), but one of the best things about reading is how it can broaden our minds and expose us to so much beyond our ordinary circumstances or traditional interests. That is one of the reasons I have chosen to assign some reading this year.

Assigned reading was not at all welcomed by Alexander. When the 22 age appropriate books arrived in the mail last week, I opened the box with great excitement and poured over each title with Alexander. He absolutely did not buy my enthusiasm and actually ran into his room crying that he only had boring books and that he wanted to return to Kindergarten where there were "interesting things to read". I was a little concerned about how assigned reading was going to work. But, as I numbered and ordered the books on our classroom shelf, I discovered that Alexander simply needed an organized goal (and implied challenge) to this work. Once he saw the books numerically ordered on the bookshelf, he challenged himself to read through all of them ahead of schedule. He absolutely loves a competition, especially when it is without any external pressure. So before I could worry myself into figuring this out, he plowed through the first four books (4 weeks of reading material) in the first two days of homeschool. And, wonderfully, he discovered an interest and enjoyment of reading books that he would not normally choose for himself. This is the real blessing of reading isn't it? The journey and discovery of an amazing world beyond us. He is officially on this journey now and I am so excited for him!

And so it begins

Avery having a lesson with the golden bead material.

After much anxiety and preparation, we began our first full year of homeschool. We started with s'more waffles-- a creation the kids invented that morning. It was a wild success and really delicious (if totally messy). Next, we embarked on a treasure hunt to find the school supplies and materials we collected for the school year. The kids were completely into the hunt that took them inside and outside the house as well as down the street and into the neighborhood. They took turns opening their treasure boxes and examining all the items inside. Love that new markers and pencils delight them as much as they did me back then! They spent the rest of the day pouring over each item and getting their pencil boxes and supplies organized.

Tuesday proved to be our first true day of school. Our lessons and work period went pretty smoothly, but not perfectly. They are getting back into the swing of sitting still and focusing on things not always of their choosing and I am getting back into the swing of having patience while they settle into place. We were all pretty wiped out by the end of our work period. I have not even introduced the afternoon session yet! I think it is something we will need to work up to. After school we went to swim team. The kids swam tiredly, but rallied afterwards for play swim with their friends. They closed down the pool with energetic glee. Where do they get their energy?

Here are a few pictures so far from our week...

S'more waffles

Reading clues from the treasure hunt.

Examining the bounty.

Weekend away with Eric

Eric and I just got back from a weekend together in Tahoe. The children stayed with Emi and had a wonderful time watching movies in bed, eating "red light" foods, riding bikes in the driveway and playing games. Emi is a lot of fun!

Eric and I have been trying to have these weekends away every so often to reconnect and have focused time together. We miss the children a lot and talk about them an embarrassingly large amount of the time, but find that the hours upon hours spent just together with no responsibility to anyone or anything but each other is incredibly re-charging.

This time away was particularly great as Tahoe this time of the year is pretty "boring". The ski season has yet to begin, but it is too cold for hiking. There were hardly any other people in the entire resort that we stayed at. We loved it. We spent hours talking by fireplaces, talking over long meals, and talking while walking around. We watched two movies --a real luxury for us at this stage of life and laughed at how (just like when we lived in San Francisco before children), we talked away the evening, missed dinner, and found no restaurants open at such a late hour. Fortunately for us, the desk clerk at our hotel called the restaurants in the resort area for us and found a sushi restaurant that was open for take out for another 20 minutes. So we ran in the freezing cold to this restaurant, ordered take out and had a wonderful late night meal in our warm cozy room. I'm glad we are still able to lose track of time so easily!

We got back home the next afternoon and had a very laid back, normal evening with the kids. They seemed happy to see us, but had a wonderful content, secure feel about them.

We have a busy next two weeks ahead of us. I hope I am able to stay focused on this wonderful family that I am so blessed to have.

School holiday

I just love having the kids home due to a school holiday. Having the whole day free to spend with them. I love the hours upon hours together. There is something fabulous about having quantity--not just quality time-- together.

We excitedly planned our time together a few days in advance. (Anticipation is half the fun!) The kids wanted to start the day off pretending to feel sick and, therefore, needing to stay in their pajamas and eat a special breakfast (cinnamon rolls and icy apple juice) in Mommy's bed while watching a Max & Ruby DVD. They also needed popsicles for pretend sore throats. After that they wanted to play puppies and make a craft. Next, they wanted to go to Mimi's Cafe for lunch (we went once awhile ago and Alexander has very fond memories of their hot chocolate). The children managed to charm at least 8 people in the lobby during our 20 minute wait for a table. The way they talked, shared a chair and treated each other brought lots of "how cute!" and compliments while we waited. My favorite memory of lunch, though, was in the bathroom when Avery pulled her skirt and underpants down around her ankles as soon as she opened the door to the bathroom area, then walked half naked to a stall, shut the door on me and announced "I need privacy, please!" Privacy? After walking half naked across a bathroom full of people? I just loved that.

After that, we went back home for more play. This time they wanted to play Noah's Ark and turn the playroom into an ark. We built a little fort in the middle of the room for the people, found a play lantern, gathered snacks and a thermos of water and carried as many stuffed animals as we could find. We had fun turning the lights on and off for day and night and eating snacks in the fort. Later, we planted tulips in planters outside. And, finally, while I made dinner and cleaned up the kitchen, the kids played Clifford Games on the computer. Since Eric was not expected home until late that night, we then ate dinner, took baths, brushed teeth, put on PJs and read books in Avery's room. Alexander then watched a movie in his room while I snuggled Avery to sleep.

Once Avery was asleep, I went to Alexander's room and snuggled him up and talked a bit with him. I just love our night time conversations. Tonight, he wanted to play our "feelings game" where we take turns asking each other, "what was your most X moment?" Alexander's likes to ask me about what was my most disgusting, stinky, exciting, silly, challengiest, bravest moments that day. I usually go for variety or for things I know he felt that day. I am enjoying these talks so much. I hope we can do this for years. After I gave Alexander a few more snuggles, I went to bed, computer in hand to wait up for Eric.

While waiting, Alexander had a nightmare. While giving him snuggles and rubbing his back, he explained he "was in outer space and touched all the planets, except Uranus which was too hot, and then went to Mars where there was a dinosaur that tried to eat him." He seemed comforted when I reminded him that God made sure that all the dinosaurs were gone before He made people, but really loved it when I told him that dinosaurs are thought to have been very poor thinkers and to have had very small brains about the size of a walnut. So, if we ever saw a dinosaur, we could easily trick him. So, I said that if he has that dream again, he can shout to the dinosaur, "hey! look! a piece of cheese!" and the dinosaur would forget all about him and go look for the cheese. Alexander said he would shout, "hey! look! a T- Rex!" because he figured the dinosaur was a meat eater and would want that more. He seemed very relieved to have a plan in place for a possible encounter.

However, I apparently went too far when I next said that he could also dig a big hole and trick the dinosaur to go into it and then he would not be able to get out of the hole and bother him. Alexander did not like this idea at all. He said that would hurt the dinosaur. I love that he just wanted to not be eaten by the dinosaur, but didn't want to harm him in any way. What a loving, kind heart he has.

So that is how we spend our time together when we have quantity. I can't wait for Thanksgiving break!

So sick

Alexander woke up feeling pretty awful last night. At first he started coughing and then he started vomiting. Eric and I both went to him and soothed, changed, held, and comforted him until he fell back asleep in my arms. At some point, Eric went to snuggle up Avery who had woken up and stayed with her, peacefully asleep in his arms, the entire night. (It is so wonderful on so many different levels to have him in a job finally where he can actively and fully be apart of his children's lives). I stayed and snuggled up with Alexander and helped him throughout the night as he got sick several more times. I could tell each time frightened him, but I could also tell how comforted he was by my presence. I truly didn't mind and actually felt very blessed changing his sheets and pajamas, applying cool wash cloths and a cold "boo boo bear" to his forehead, stroking his curls just the way he likes, and rubbing his back and repeating all of this until he was better. It felt really good to be able to help him and nurture him so completely.

It is a strange thing to be thankful for. But I can't help but think about how lucky I am to be able to be with him when he needs me and not separated from him due to divorce, job travels, or illness. How blessed I am that I have the skill set to help him-- that his illness needs do not exceed my abilities or never abates as can happen with a serious condition. How fortunate I am that I could focus completely on him and not worry about job pressures tomorrow or have to race back and forth between children crying for a parent's love. How lucky I am that I have been able to spend enough time with him to know what helps and soothes and what doesn't. How relieved I am to not be so exhausted from life that I can't step back and fully appreciate the beauty and joy in nurturing a child. It is wonderful to be able to fully appreciate it. So I am very, very thankful for my sleepless night last night. It is so strange the things in life that help you appreciate how very blessed you are.

And, if you are wondering how Alexander was feeling today? Wonderful! He had the luck of feeling 100% healthy but got to stay home from school because it hadn't been 24 hours since his last symptom. And, just in case he wasn't actually feeling as good as he looked and reported, we kept things quiet. He spent the entire day in his pajamas watching movies (a real treat), drinking lots of fluids, reading books, playing games, and playing Beatles songs with Daddy on the drums. He looked very happy.

Today Avery begins her reading adventure

Dear Avery,

I just received a call from Hanna, an assistant teacher at your preschool, telling me the wonderful news that you have begun working with the moveable alphabet. You are sitting next to the large mat writing words such as "cat" and "sat". When Miss Hanna called me, I got tears in my eyes just imagining you reaching this milestone and knowing that you are officially embarking on your reading journey. It is a wonderful journey. And one that I have known would start any day now. I prepared some reading games for you awhile ago and we have been practicing "reading" for a few months now during our afternoon snacks-- and recently things have become very exciting. Three months ago, you matched simple words to pictures by sounding out the first few letters. And a month ago, you sounded out and read your first three letter phonetic words with picture clues. Last week, while taking your babies on a picnic with me, you found, sounded out and then read "on" and "us" on a sign all by yourself. And sometimes during play you will say a word and then figure out the letters that it is made of ("pirate. P! I! R! T!").

But, at school, you have seemed a little daunted and hesitant by the moveable alphabet and some of the more advanced reading games. So, your teacher and I have let you go at your own pace, knowing that you would know best when you were ready. And, today you were. Avery, I feel so excited for you and proud of you. You love looking at books and listening to stories. You love to be read to. Today you really start your journey on learning to read all by yourself. Soon you will have the freedom to read whenever you want to-- free from waiting your turn or waiting for someone to finish a chore to sit down and read. Seeing the light of recognition in your eyes as you see the letters turn into words is amazing. This must feel so very wonderful to you. I am so happy for you, sweet girl. Reading is a wonderful, life-opening journey. Congratulations!

Love,

Mommy