I have had many ask me about this so I thought the best way to do this would be to take each subject and break it down into little chunks and layout our outline for our upcoming year.
I am hoping to outline each subject, for our home studies, over this summer to explain our style of learning and how and why it works so well in our home.
Math and enjoyment were two words, you would have not heard spoken, in the same sentence in our home a year or two ago. We had a tough time working through all the textbook programs. They occasionally made us crazy. I am sure some have been where we found ourselves.
I researched and observed how the boys learned. I posted on many e-groups about what programs are best for certain kinds of learning styles.. I felt like I had tried to do my very best to find math the that would match their learning needs and abilities.
Most times, I found I liked something in each of the programs we attempted, AND also there was something new we would bring away from each of the math programs we tried. There was only one problem, it wasnt learning math~ for the most part it was learning more and more about the way they process information how math is taught in a rather different way then other subjects and yet it "could" be taught similiarly if only we had the "right program".
I remember how much we were struggling. The boys were doing "ok" and yet, math was such a chore they would dread having to do their math pages and for the most part information was just not being retained as much as I would have wanted. I soon realized we were dealing with learning disabilities and on top of that, the boys had a great deal of math anxiety they had acquired over a few years.
It is hard to say how it happened but my feeling is over the years in the classrooms, it was hard for them to retain the foundations they needed to move further along in their math learning. Teaching styles most certainly played a role along with a sinking feeling of inadequacy that kept growing.
Math needed to "happen", afterall it is needed almost daily. Math is all around us and I needed to find a way to break these math barriers and struggles but how was I going to do that?
I decided to back way up and look at homeschooling methods and learning styles (multiple intelligences etc.. ) I read books about teaching children to their strengths ( "Your Child's Strengths") by Jenifer Fox.
It really opened my eyes to the needs of the boys and why I had such a hard time in school as well.
UPDATED INFORMATION: Simply Charlotte just had an interesting article in their newsletter called Choosing a Homeschool Math Curriculum. You can find a copy here: http://simplycharlottemason.com/2009/07/02/choosing-a-homeschool-math-curriculum/
I posted on a homeschooling group about my struggles with find a math program for my boys. That was when I had gotten an email from Carlita Boyles, a homeschool mother, Special Education Teacher of more than 20 years experience, and author of a new Home School Math Program: Math On the Level. ( and a review by Cathy Duffy: http://www.cathyduffyreviews.com/math/math-on-the-level.htm )
More Math On the Level Reviews from Homeschool Math: http://www.homeschoolmath.net/curriculum_reviews/math-on-the-level.php
** You can learn more about MOTL from the E Group, Math on the Level yahoo group you will find helpful supportive people and Carlita offers wonderful support, advice and encouragement along the way. **
It is a maturation based, math program that is like no other math program I had ever seen before.
Using Teaching Guides for the math concepts and a concept chart and seqence chart it allows the learner to work at their own pace and allows for consistency, which we often look for in a mastery program and yet also blends a kind of spiral mastery through the 5- a day math review sheets.
We began using this program and my boys immediately started to enjoy the short lessons and the hands on activities and real life scenarios we brought to our learning math at home.
This program is our Spine for math learning at our home. The program runs up until 8th grade or through Pre-Algerbra, whichever comes first.
We also now have started using a bit of workbooks again for days when we might just want to reinforce lessons learned or for the summer where we want to keep skills learned sharp. For this, my boys overwhelmingly chose Alpha Omega Horizons. It is a workbook based, spiral mastery math program that is very colorful and chocked full of colorful pictures, puzzles and drill problems for concepts.
This was not a first choice in the beginning, they had alot of trouble with these books, mostly because it appeared quite overwhelming to them with all the color and so many problems on a page.
This kind of program is not for children who do not like alot of color or get concerned when there are too many problems on a page.
In my opinion, Horizons is for the more confident child who enjoys math practice and math puzzles.
What Math looks like in our home:
The boys have Math Binders each with dividers in them.
DIVIDER ONE: Titled: 5- A Days: this is their math practice page ( see above photo) I use for concepts I have already taught to them and that they are ready to practice, on their own until mastery takes place. A concept is reviewed for how ever long it takes until mastery is evident, then this particular concept is moved to the less frequent practice, perhaps every two or three weeks, then once a month, then every 2 months. Generally, when I teach a new concept this will go on a daily review on our 5 a days, perhaps for a week or so then I look to see it it can be moved to being reviewed a bit less, depending on their understanding. ( This helps build mastery and keep the mastery when children having memory struggles as my boys often do.) I keep all their 5 a days in this one divider for approximately one month to be able to go back and look at their progress. The old 5 a day sheets are placed in a folder and filed away.
DIVIDER TWO: Titled: Teaching Time : - this is where we might work out concepts using our Teaching Guides from MOTL, while working on a wipeboard I will introduce a concept and then we will work either with manipulatives, games, cooking, chalk, shaving cream etc.. whatever it takes to help bring the concept into a real life scenario. The boys will save any teaching concept practice pages so we can refer back to these when we need to. (These pages might be something I might have pulled off the internet for a more visual idea for the concept or it might contain theirs or my little writings as I would teach or they would attempt concepts on their own. I thought it important to save this information because much of it was in their own writing and for them it is a sort of "math language" if you will, a way for them to go back the next day and see visually what was thought out on paper. )
The boys also have a compostition book which we keep in the side pocket of the binder. This is called their Math Journal. I had started this math journal when we first began homeschooling, (now three years ago), gosh time sure goes by fast. We keep the SAME journal until we finish it to the end. I do not change the journals year to year with new notebooks as I feel that especially in math consistency and review is key in creating relationships and connections between concepts and can very beneficial.
DIVIDER THREE: Titled: Concepts Practice: - (this may seem a bit redundant from our second divider, but not really here is why) this is usually oak tag sheets of paper where they have used their notebooking skills to practice concepts like money, time or basic geometry. Creating lapbook folds for information once it has been learned and cutting and pasting it to the pages for kind of change for them. This section would include notebooking pages on money (see my profile in homeschool launch, below) It is a fun, different way to practice concepts that have been taught and is a wonderful way to review the information as well. (again, always finding ways for consistency and review). :)
DIVIDER FOUR: Titled: Lapbooks: - we keep the back of the bindders for their on-going lapbooks that are under construction. We currently have one being worked on for Multiplication, and one for Fractions. This will be worked on as they move through the concepts in the areas. ( My older son is not as likely to work on Lapbooks as my younger child, more because of personal preference, but this year we may make up some mini-offices he enjoys these for reference instead of flipping through his notebook pages).
We do not hurry to finish these kind of lapbooks since they are used as a reference. For example, if they are working fractions.. they will keep adding more and more information about fractions (ie., equivalent fractions, improper fractions, mixed fractions, adding, subtracting, multiplying, dividing.. etc.. ) You can clearly see how a lapbook at this magnitude could last a year, if not more depending on the skills and how they are mastered.
We work MOTL three times per week with the other two days for their workbooks. This allows me some time for gathering resources for the next lessons or perhaps practicing on the computer with internet games or videos. We also play games with math that help reinforce skills.
Most days we will begin our math by opening up our binders and the boys will review over what they did yesterday, just as a refresher and they will explain things verbally as they read through, this is helpful to me to see at what place we need to pick back up at.
Some resources for some of these things are:
5 A Day Worksheet (sample) ** I recently had an idea as I made my way to get more of my 5 a day worksheets copied. ( I usually do about 300 or 400 at a time, because this is for two boys and this lasts me quite a while).
I decided to make about 500 copies at one time and have them paint binding glue on my stack of worksheets so I have it made into a "tablet" of 5 a days. This is much easier to work from and I can rip off the worksheets as I need them and it is much easier to store. :)
(example of our 5 a day worksheet is in the above picture, near beginning of post). Notice the "notes" section, this is where we may practice or re-teach something just a bit more or show a connection with yet another concept to see if they can understand it, they almost always can. I have found this to help them see a bigger picture for my right brained learners, it also stretches them to a higher level of thinking and learning.
The 5 a days are helpful in a few different ways; (1) they reinforce concepts already taught. Nothing on our 5 a day is going to be something new to them that they have never seen or tried to do. This exercise replaces the countless time and effort that goes into those dreaded worksheets that can be so redundant. (2) they help my boys remember multiple concepts at one time (3) the 5 - a days also allows for review in areas of trouble. When the boys finish their 5 a days, we correct them together. Then they go over areas that might be a problem (4) one more advantage, is that on non-teaching days if there are appointments and things happening at home, I can confidently give them their 5 a days to do for review and these are great short lessons for their math for that day.
Math Journals - when the boys use their math journals it is usually during a math story or during perhaps review time. Never during teaching time.(Gosh, I just cannot stress this enough). For us, I found it too hard for them to try to grasp something and then try to "take notes" or as we call it do their "math journaling". Math journals are for when we know something and want to write it down.. it also is when we perhaps realize a connection to something, much like my post about the book Even Steven and Odd Todd and we found a connection between even/odd numbers and dividing. (see blog archive)
Here is a link on math notebooking: http://www.squidoo.com/math-notebooking
this might help some also. :)
Our math journals are also used for "teach me" time. This is how and where I see what they have learned.
It is where, I may ask them to tell me about how many ways we can show one dollar. Or how do we show and create an equivalent fraction. With no help they will go through and teach me with a wipe board, I will have a few problems written ( an oral test of sorts) and they will go through each and "teach me", for I believe when we can teach another person we have an understanding and have fairly mastered the concept. :) Here there is very little use for tests.
We also use games in lieu of tests. ( aside from Uno, Yahtzee, Monopoloy, Dominoes, Bingo for Facts, etc.. ) ( also instead of tests we will use written narration exercises which work much better). It works really well~ here are a few we have tried;
List of Interactive Math Games
Making Math More Fun - sign up for Teresa's free newsletter and games, they're
Kids Math Games
Mrs. Kelly's 6th grade math
Math games for kids
Times Attack, for multiplication facts, a real favorite for them. :)
To create my own board games: Ready Made Game Boards
Love to Know - Printable
I had also tried making up some games for studying math facts;
Math Ball: We purchased a foam ball about the size of a basketball or so and with permanent marker wrote numbers 1-10 all over it. Then divided the numbers with lines so they had their own "space" on the ball.
We throw the ball back and forth and whichever his thumb and index finger lands on he creates a math fact for it and says it and answers it. We throw it back and forth and I do it too so he is "hearing " the facts also. :)
We also use Math Ball for skip counting each throw is where we will sequentially call out he next number that we are skip counting by.
We use twister for the facts too, we spin and I will say a fact and they have to call out the answer before they can move and advance their step in the game... they love it.. :) they end up laughing and exhausted.. lol :)
SKIP COUNTING LADDER:
We were practicing skip counting and to move away from all the charts we decided to head out side and draw a tall ladder with steps . We wrote out the numbers for the 2's and then another ladder for the 3's etc.. for my older son he wrote out the 8's and 7's, (ones that gave him trouble). The jumped and yelled out the numbers and then we made it harder they couldnt step on a line.. then they had to use no ladder.. it was a quick fun way to practice.
* I dont think I ever realized the emphasis of movement with learning something as I did with this.. the next day we decided to review our skip counting.. my youngest started back on the 3's for his 5 a days and when he did I saw him get up and look up and march like he was in the squares again... amazing.. :) *
Bringing Literature into our Math Learning:
With the help of a wonderful group called The Living Math Forum, I have begun to incorporate literature into our math learning. For subjects we are learning about I can go to the Living Math Site and look up books for specific topics of study~ I have a few planned for this year from her lists along with a few others if we have time to get to them.
List of Math Readers from Homeschool Math
ONE WORD OF CAUTION: I like books, you will get to learn this about me and my blog, there I said it :) ~ so if you like books~ your in the right place. :)
Number Stories of Long Ago
Mathematicians Are People Too
The above are on the list for read alouds.. for individual lists there would be too many to list for my younger son.. it would probably be more helpful to check out the Living Math Site reader lists (see above link) for my older son I have a few more picked out for him. Some of these were recommended on a recent webinar I listened in on with Maureen Whittman from her book "For the Love of Literature" and also her webinar recording: "Bringing Joy to Your Math and Science Lessons".
Our list grew even more:
The Number Devil
" Bringing together the surreal logic of Alice in Wonderland and the geometrical wit of Flatland, and spicing it up with his own dry humor and passion for the magical properties of numbers, hans Magnus Enzensberger deftly explains the basic concepts of math, encounters a sly, clever number devil who introduces him to the wonder of numbers; infinite numbers, prime numbers, Fibonacci numbers, numbers that mysteriously appear in triangles, and numbers that expand without end. As Robertand the reader venture deeper and deeper into this amazing dreamworld, ideas take flight and once-unfamiliar or difficult mathematical theories and principles become crystal clear.
A Los Angeles Times bestseller illustrated with whimsical full color art The Number Devil is a wonderful combination of knowledge, charm and wit that will appear to readers of all ages, from math phobics who fumble over fractions to math fanciers who can solve complex equations in their heads". ~ an excerpt from the back of the book~
Alvin and the Secret Code- Read the book to decode the message!
"When Slvin Fernald and his best friend, Shoie, find a secret message one day after school, they first try to break the code themselves. Then they visit a man who knows more about codes and ciphers than anyone in town; Mr. Link, a former spy. He teaches tthem what they need to know to be ace decoders and it 's a good think because soon they're in teh middle of a dangerous mystery!" ~ taken from the back of book~
The Confessions and Secrets of Howard J. Fingerhut
" Many people dream of $ucce$$, but few go after it quite like Howie Fingerhut. Throwing himslef into his "A Boy for All Seasons" lawn care business, Howie is certain he'll win the H. Marion Muckley Junior Business Person of the Year award. To maximize profits, he decides to write a how-to book chronicling his bu$ine$$ and amazing $ucce$$. Howie shares everything with reader, including the high points such as the eight foot snow drifts he is hired to shovel and the low points such as the negative numbers that keep appearing on his profit sheets. Many how-to books off er advice, shortcuts, and pep talks, The Confes$$ion$ and $ecret$ of Howard J. Fingerhut offers taht and so much more- humor, hear, and a resilient spirit". ~ an excerpt taken from the book~
Our math has most certainly changed over the past few years. I have now seen my boys eager to learn certain math concepts. We also use many, many books for learning math. I have found series that are my most favorite and they have allowed the boys to stretch their thinking in ways a textbook and workbook would not have allowed or explored.
More book lists to use for my younger son: http://mhschool.com/math/mathconnects/assets/docs/mc_lit_list.xls
Some of my favorites:
Learning Math Naturually, I think this is what got me started...
Making Math Easy by Enslow Publishing - this is an excellent series. We used this before we found MOTL and used our Math Journals. It was wonderful and my youngest enjoyed this very much.
Fractions and Decimals by Lucille Caron and Phillip St. Jacques - another excellent series these authors have several books on various math concepts.
Family Math - a great book for a fun way of learning new concepts through games and hands on learning.
Marvelous Multiplication- great activities for a broader understanding of multiplication concepts.
Math is now much more fun. We explore and learn and now are starting to explore the connection between Math and Science.
The following are more resources we use for our math learning:
Visual and Auditory Learning:
Kahn Academy- over 800+ videos for all levels of math learning
Math Playground videos
Links Learning, I have used this alot with both boys (see left tool bar for more illustrated lessons)
Worksheets/Folds/Templates/Cutouts and Activities:
Tool for Learning- this is an assortment of things I use for lapbooks, notebooking or cutouts for learning.
Math E Books by Houghton Mifflin
Johnny's Math Page
Sparkle Box, great for creating games and making lapbook and notebooking cutouts
Lesson Snips, these are helpful if I am lacking support in teaching an area and am running out of ideas:)
Soft Schools, one that I have visited often and while we may not "do" the worksheets, we may use the resources to create fun games etc
For lapbooks, I have some favorite places and groups: ;)
Love To Lapbook E
Notebooking E Group
Homeschool Helper, this gives alot of patterns for "folds" for creating our own lapbooks.
Real Life Math Learning:
Math in the Home - an assortment of lessons and activities for learning math in your home.
Math in Daily Life
Real Life Math
Real World Mathematics
Some personal thoughts. ....
As for myself, I am confident I will keep adding to this list as I find more resources that I find helpful. Our Math continues to grow and change with the boys, what looks one way this year of this Fall may look different after Christmas. Learning seems to be that way for us. We do what is best for us and I attempt to teach not to my own strengths but to my childrens strengths and their learning needs and abilities.
I hear some parents or teachers mentioning often how they "can't teach that way" or "they are not able to teach creatively", or maybe, "I'm uncomfortable not using worksheets and workbooks". I am also so intrigued by the irony of others using the "boxed curriculum" and then in the same sentence explaining they want their children to follow their own explorations in learning. - this can be done and
it might be true with some learners, but at some point looking at your child or your student and making a clear observation and assessment of how things are working is much more important than how the "I" might feel. It is your learners education not yours. Allow them to take some control of it for themselves. Sometimes we need to step out of our comfort areas for true teaching to reveal itself.
I remember feeling in the beginning, (and I have often explained it this way to others around me) that I felt as though some days with math I was on a tightrope.. just not to sure exactly which way things would go.. I was not completely in control or running the lesson, if you will and I have to say those were our most magical more successful days of teaching and learning.
Allow your child and student to explore and find ways they learn best. Don't be afraid of doing something just a bit different than others or how everyone else feels something might or should be learned. Stretch and broaden your understanding of teaching.. you will soon see the benefits as I have with my Learners at Home.
Sunday, June 28, 2009
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