Mar 252016
 
This year's math curriculum .... a little worse for wear!

This year’s math curriculum …. a little worse for wear!

Despite all of the messy bits of March, including a monster cold that has overtaken all of us this week, we can claim victory on one to do list item . . . . WE FINISHED MATH!!!

For us, math is the most time consuming part of our homeschool schedule. The curriculum we are using has to be taught individually to each child. My eldest does 5th grade math, my second daughter completed 3rd grade math and my preschooler is making progress on his Pre-K/kindergarten math.

In general, the math curriculum is the one we struggle the most to finish each year. It is always a dash to the finish in June, with a lot of crunch time at the end. It is so stressful. Up until I got sick with flu and pneumonia in November, we had been doing so well to stay on track with the math. Then we didn’t do math for almost a month! When December rolled around, we doubled up and did twice the lessons each day so that we could finish the first half by Christmas and even proudly displayed our completed math books for Santa.

Celebrating Christmas and the halfway point in our math studies!

Celebrating Christmas and the halfway point in our math studies!

After Christmas, we had ski class to look forward to on Fridays so we knew we were going to miss math at least once a week. So, we kept going with the two lessons a day. There was often a lot of grumbling but here we are at the end of March ALL DONE!

Fifth grade math was the first year where math began to get hard for me as a teacher. There were several story problems I had to Google to find out how to solve them. Fortunately, many other parents had the same problem and there are many supremely mathematically skilled people on the Internet who are willing to give answers and excellent explanations! Singapore Math likes to throw in tricks from time to time and the problems I was getting stuck on were usually of the type where you thought you didn’t have enough information to solve the problem until you saw some hidden trick or pattern. People who are great at math have genius skills in seeing hidden patterns.

As a quick summary of what we learned this year.

3rd Grade Math = 681 pages plus 1 ½ notebooks worth of scratch paper

  • Multiplying up to the 10 times tables (I have noticed this is a huge difference between US and foreign math curricula. In the US we tend to go up to 12 because we often need to know 12 times when we measure in feet. In other countries, 12 is less important, because their measurement systems are based on multiples of 10, so going up to 10 is enough. They have tricks for multiplying above 10 that they use instead of memorizing the 11 and 12 times tables.)
  • Adding, Subtracting, Multiplying and Dividing Numbers in the Thousands
  • Long division
  • Measurements in US and International Units (inches, feet, yards, cm, m, kg, lb, oz, etc.)
  • Money – Adding, subtracting, multiplying and dividing
  • Fractions
  • Telling time to the minute
  • Geometry – identifying right angles, calculating area, perimeter and volume
  • Story problems may require as many as 4 steps
One organizing trick for homeschool math papers that only took me about 4 years to learn is that if you can do all of the assignments, teaching and scratch paper in one composition book, you have a lot fewer papers to keep track of.  So, it takes a little time to copy down the math problems into the notebook but in the end makes a clean, neat record that is easy to store.

One organizing trick for homeschool math papers that only took me about 4 years to learn is that if you can do all of the assignments, teaching and scratch paper in one composition book, you have a lot fewer papers to keep track of. So, it takes a little time to copy down the math problems into the notebook but in the end makes a clean, neat record that is easy to store.

5th Grade Math – 621 pages! Plus 1 ½ notebooks worth of scratch paper

  • Multiplying and dividing by 2-digit numbers
  • Adding, subtracting, *multiplying and *dividing fractions
  • Order of operations – i.e. parentheses first, then multiplication and division left to right then addition and subtraction left to right
  • Perimeter, Area, Volume
  • Equivalent Ratios
  • Adding, subtracting, multiplying and dividing decimals
  • *Converting fractions to percentages
  • *Geometry – finding unknown angles in complex diagrams using principles of isosceles and equilateral triangles, parallelograms, rhombuses and trapezoids
  • Calculating averages – finding average, median and mode
  • Interpreting pie charts and line graphs
  • *Beginning Algebraic expressions, graphing equations
  • Story problems may require numerous steps, sometimes as many as 7 calculations!

*indicates concepts not taught in our local school system for 5th grade

The scratch paper also serves as a medium of expression for boredom and frustration!

The scratch paper also serves as a medium of expression for boredom and frustration!

The geometry and algebra in the fifth grade stunned me. My husband and I didn’t learn any of this until about 7th grade or so. I checked around with other smart parents and they say the same. We are pushing down so much material to the younger grades. My kids so far are handling it well but I consider them “above average” (a la Lake Wobegon). I hope there aren’t too many children out there who think they are no good at math when really they might just do better on the older, more relaxed schedule.

When I compare the curriculum we are using to the concepts taught in our local school district, it seems we map fairly closely up until the end of 3rd grade. Beginning in the 4th grade, Singapore Math seems to push about 1 grade higher than the school district. Many of the concepts listed for 5th grade math we covered in 4th grade.

I read an article recently praising the Finnish mathematical system for being less pressured. Yet, when I cross-referenced the Finnish standards with what we learned they seemed to be right on track with us for 5th grade math. So, perhaps the Finns slow down sometime after 5th grade but up until then I wouldn’t call their math education programs “relaxed.”

So, what now that we are “finished” with math? We will keep reviewing some things until we take our standardized tests for the year but we are moving on to focus on a kids JavaScript computer programming book. I know nothing about JavaScript but I am learning as we go.

Does our math experience compare to yours? What do you remember about your own math education? Please share in the comments.

Done!  I will be glad to store these books away.  One less thing to have to keep track of.

Done! I will be glad to store these books away. One less thing to have to keep track of.

 Posted by on March 25, 2016 General Tagged with: ,
Oct 132014
 
Heading outside for art lessons.

Heading outside for art lessons.

Each year that I homeschool, I learn a lot about being a good teacher. In these early years, I feel that I improve as a teacher by at least 30% each year over the previous year. Most of what I have to learn has to do with time management, setting the right expectations and child behavior patterns–all great organizing lessons. Each year, I try to learn from the mistakes of previous years and try something just a little bit different.

Last year, we focused in hard on the core subjects of math and language arts. We did well in these areas but I felt like we fell down on a couple of subjects, like art, music, and history. So, this year, I made the decision to start each school day with our weakest subjects and save language arts and math for last.

Below is a quick run-down of our typical school day this fall and our goals for the year.

Art

2014-10-13-artisticpursuits We start our days with an art lesson. While this sounds “fun,” this art curriculum is really quite serious. The ARTistic Pursuits Elementary 4-5 Book One focuses on the fundamentals of drawing. We are training ourselves to see like artists and learning the elements of art that make for more interesting compositions. So far, we are learning about looking for shapes, capturing details and learning about how and when to use shading. It is really a lot of hard mental work. It is kind of a struggle to get excited about teaching these lessons but we are all excited about how much we have learned so far.

 

Goal: Be able to draw with more detail and sophistication and identify simple drawing techniques in other artists’ work.

Still life with kitchen tools

Still life with kitchen tools

Drawing of Audobon owls

Drawing of Audobon owls

First drawing of an LPS toy

First drawing of an LPS toy

Drawing of the same toy about 3 weeks later in our lessons.

Drawing of the same toy about 3 weeks later in our lessons.

Still life of fruit and vegetables.

Still life of fruit and vegetables.



Music

Screenshot from simplymusiconline.com lesson.

Screenshot from simplymusiconline.com lesson.

Because last year, we kept “forgetting” to do our piano lessons, this year, I built it into the school curriculum. Over the summer, I received an email notice from the Homeschool Buyer’s Coop about an Australian piano lesson curriculum taught completely online. For a onetime fee of $60, you could buy a lifetime subscription to the website simplymusiconline.com. This method of learning emphasizes playing songs rather than learning music theory. You watch the videos online for a quick lesson and then spend the rest of your week practicing on your own. Rather than practice 30 minutes per day per child, we practice only about 10-15 minutes per child. So far, my children are enjoying these lessons and they have both learned two songs already and will spontaneously practice them when they pass by the piano.

Goal: Complete the Level 1 curriculum and learn approximately 11 songs. We hope to perform the songs in an end of year recital perhaps for one of our older neighbors.

2014-10-13-piano1 2014-10-13-piano2



History

Balloon globes

Balloon globes

2014-10-13-chartingtheworld

World geography is the theme for this year’s history lessons. We spent September learning about principles of geography and now are taking an around the world virtual tour. We will be visiting each of the continents and spending a few days in select countries. We created a “passport” that we complete for each country as well as an art project representing each country. We are making liberal use of our library card and our local library system has been amazing in terms of providing wonderful books for us to use.

Goal: Gain an appreciation that the world is a large and complex place as well as respect for different cultures and peoples.

One of our recent stacks of books from the library on Africa.  Our library has a terrific collection of both reference books and fiction from each country.

One of our recent stacks of books from the library on Africa. Our library has a terrific collection of both reference books and fiction from each country.

Example "passport" pages.

Example “passport” pages.

Our Congo art project: interpretations of Luba fertility sculptures.

Our Congo art project: interpretations of Luba fertility sculptures.

Our Ethiopian art project: paper mache interpretation of the guinea fowl found in their folk art.

Our Ethiopian art project: paper mache interpretation of the guinea fowl found in their folk art.



Science

2014-10-13-ancientcomputing 2014-10-13-eyewitnesscomputer 2014-10-13-nyscience

Computer science is our focus for science this year. We started off with some introductory books on computer science, including the history of “computing.” We have now progressed to the K-8 Into to Computer Science Course at learn.code.org. This is an amazing curriculum available to anyone completely free of charge. They provide all the lesson plans for the “offline” activities. My children, however, look forward to the “online” lessons where you get to practice coding through a series of interactive games. The first one we did was based on the games Angry Birds and Plants Versus Zombies. Each lesson is introduced by a video starring computer science greats like Bill Gates and Mark Zuckerberg, telling the children in simple terms what they are about to learn. This really is an amazing gift to U.S. schoolchildren and I hope that every school will someday take advantage of it. In addition to our computer science lessons, we are also doing a few pages per day from the study guide for the New York 4th grade science exam to prepare ourselves for end-of-year science testing.

Goal: Have at least a general idea of how one might write a computer program, including some of the language elements and logical constructs.

Screenshot from one of the online lessons at learn.code.org.

Screenshot from one of the online lessons at learn.code.org.



Spanish

2014-10-13-spanishnow I looked long and hard for a Spanish curriculum I wanted to use. There is a lack of intermediate and advanced language curricula for elementary school students. It is also hard to find affordable programs. I finally settled on the Barron’s Spanish Now! curriculum that includes a workbook and companion CDs. This year, we are trying to focus more on speaking Spanish. I liked that this curriculum seems to have a lot of repetition in the exercises. You use variations of the same phrases over and over and over. The curriculum is probably designed for at least a junior high – adult student. We adjust it by doing only one page per day. The curriculum is similar to what we used last year where there is a story and worksheet pages to follow. We repeat the story every day and do the worksheet page. The CDs are great because they allow us to hear the correct pronunciation of words and also provide oral exercises. The curriculum also teaches Spanish grammar, like masculine and feminine, plurals, etc. So far, my children are handling this curriculum beautifully.

Goal: Improve Spanish vocabulary and understanding. Be able to respond to simple questions in speech and writing with at least a few routine Spanish phrases like “Es posible . . . “ or “Es necesario . . . .”



Language Arts

2014-10-13-commoncorela-4 2014-10-13-commoncorela-2 2014-10-13-vocab-4 2014-10-13-spelling-4

2014-10-13-pshipwriting

We are continuing with the Brave Writer language arts curriculum, graduating to The Arrow curriculum. This curriculum uses longer chapter books and provides copywork passages and literary elements for each book. Ideally, you complete one book per month. There also is a companion Partnership Writing curriculum containing several creative writing projects which you would also complete roughly one per month. My only complaint with the Arrow and Partnership Writing curricula so far is that it does not come with any sort of daily schedule or monthly lesson plan as to when to do what. There is a general guide in the Partnership Writing curriculum but it doesn’t cover basics like how many chapters are you supposed to read in a week to make sure you finish the book by the end of the month. I am having to figure that out on my own. In addition to the Brave Writer curriculum, we are continuing with the Common Core Language Arts 4 Today test prep books as well as a vocabulary and spelling workbook. This is also our year to learn cursive writing, which my children have been waiting for!

Goals: Improve patience for longer chapter books. Improve reading comprehension and vocabulary. Continue progress in creative writing.



Math

2014-10-13-singmath-2a 2014-10-13-singmath-2b 2014-10-13-singmath-4a 2014-10-13-singmath-4b

We are continuing on with the Singapore Math curriculum, levels 2A/2B and 4A/4B. The only change I made this year was that I didn’t order the teacher’s manual for the books this year. In past years, I found that I hardly referred to it. There is so much to complete already between the daily assigned textbook and workbook pages that I didn’t need any other teaching activities to supplement. The only downside is that I don’t get an answer key without the teacher’s manual but the math is still simple enough at this age that we don’t really need it.

Goals: Complete each curriculum. The second grade curriculum requires addition with carrying and subtraction with borrowing as well as simple multiplying and dividing by 2, 3, 4, 5 and 10. The fourth grade curriculum requires multiplying by 2-digit numbers, adding and subtracting fractions, adding, subtracting, multiplying and dividing decimals and calculating area and perimeter.



Preschool

Another twist this year is that I have one more student added to my homeschool, my preschool-age son! I am still trying to find a curriculum that works for him. I initially planned out a lot of fun crafts but after trying a few with him learned that his dexterity is still quite limited (although he loves painting with a brush) and that he has more enthusiasm for reading, games and playing outside. We are also doing some socialization learning for him through a sports class (more on this in a future post). Formal schooling isn’t necessary for him at this stage so I am not worried about doing a lot but am trying to keep him engaged in reading and learning in general. He always seems to end up in the middle of the girls lessons, whether “helping” them paint or accompanying them during their piano lessons so he is also learning quite a bit by osmosis as well.

This is the most ambitious homeschool schedule we have attempted yet! It has taken several weeks to feel comfortable with it but it is finally starting to settle into a groove.

 Posted by on October 13, 2014 General Tagged with: , , , , , , , ,
Sep 242014
 
Sometimes little brother joins the homeschool action . . . especially if it involves Danny and the Dinosaur!

Sometimes little brother joins the homeschool action . . . especially if it involves Danny and the Dinosaur!

Last fall, I gave a peek inside our homeschool classroom, showing a little about what we were learning. It was my first year homeschooling two children at the same time, one in kindergarten and the other in third grade.

I am pleased to report that in general, our year was a success! Teaching two at a time didn’t pose as many challenges as I anticipated. With the exception of math, I generally taught all subjects concurrently to both children. I generally taught at the third grade level and assumed that my younger daughter would probably not pick up all of it and we would adjust as needed. To my surprise, she generally kept right on pace with her older sister!

While I went into teaching third grade completely oblivious to its importance, I learned later on that third grade is a high stakes year for most kids. Time magazine calls it “the single most important year of an individual’s academic career.” Researchers can predict the likelihood of high school graduation based on how well a child reads in third grade. As a result, many states will hold children back if they are not reading on level by third grade. The common maxim is that before third grade, you are “learning to read” but that once you hit third grade you must “read to learn.”

Reading ability was not a concern for us but I must say that in general, our homeschool ramped up for third grade. We tried to teach more material and more complex material. It was challenging at times but we stuck with it.

With apologies for length, here is the subject-by-subject breakdown of our homeschool year:

Math

2014-09-24-singaporemath1a 2014-09-24-singaporemath3a 2014-09-24-commoncoremath1 2014-09-24-commoncoremath3

We continued using the Singapore Math curriculum we have been using for the past several years. This was the first year we completed the full curriculum on time by the end of the year and I was thrilled with that progress.

My kindergartner blew through the kindergarten math books and then proceeded to blow through the first grade math books ahead of schedule.

My third grader had a bigger challenge ahead of her. Third grade is the year to learn the multiplication tables. Memorization of math facts is not something that comes easily to her but she is very good at adding numbers in her head. So, for example, rather than memorizing 8 x 4 = 32, she often had to count, 8, 16, 24, 32. I did not feel it necessary to emphasize speed at this stage so we just made it through the year with the counting method. On the plus side, with the concept of multiplication firmly in her head, she could calculate answers to questions beyond the scope of the course, such as 20 x 5. She also gradually began to memorize the facts after calculating them so many times.

We learned that there are many ways to teach third grade math. In our local public school, it appears they require students to memorize up through the 12 times tables and the corresponding division facts and then answer story problems based on these facts.

Other math curricula have different approaches. With Singapore Math, after we had learned the 2, 3, 4 and 5 times tables, we then had to learn how to multiply ANY number by 2, 3, 4 or 5, such as 55 x 5 or 555 x 5, by learning how to carry numbers in multiplication. Next, we had to learn long division so that we could divide any number by 2, 3, 4, or 5, including remainders. After we had learned all of that, then we progressed to learning the 6 times and higher times tables up through 10. Singapore Math (and it seems more commonly in Asian math curricula) emphasizes breadth of concepts whereas U.S. math seems to emphasize memorization of facts first and then teaches concepts like long division later on.

Comparison of public school and Singapore Math teaching methods for third grade.

Comparison of public school and Singapore Math teaching methods for third grade.

The only challenge for us with this mismatch in strategies is that U.S. standardized testing frequently has questions requiring rote memorization of the 11 and 12 times tables, which we didn’t properly learn. My daughter had to work a little harder to answer those questions but generally did fine using her counting method.

We also used the Common Core Math workbooks to prepare for standardized testing. In general, the math in these books was easier than the Singapore Math curriculum but helped us prepare for the format of many test questions. We found the Common Core Math to be a fairly accurate guide for each grade level of testing.

Language Arts

Brave Writer: The Writer's Jungle and The Wand.

Brave Writer: The Writer’s Jungle and The Wand.

We used Julie Bogart’s Language Arts program called The Wand. The curriculum was developed in conjunction with Rita Cevasco, an expert on childhood language learning. There were 10 months in the curriculum. Each month we read 2 books. Each book was read 10 times before moving on to the next selection. Daily lessons included learning of complex phonics such as c’s that sound like s’s, the –tch letter team and unusual vowel combinations. A brief history of the English language was also included. We learned about Latin, Greek and other language roots. We copied quotes out of the assigned book and did dictation. At first, I couldn’t imagine teaching some of this to a kindergartner and third grader but I pressed on. This curriculum took me a lot of time to plan in advance and to create my own worksheets to go with the material. I was not a big fan of it at first due to the time commitment.

However, about mid-way through the year an amazing transformation happened in my children. I started getting spontaneous writing! My girls would write me notes or comic strips or all kinds of things without being asked! I realized that some of the more tedious parts of this program, like the spelling practice, were very important in building their confidence in writing. Now that they knew how to spell many words properly, they were happy to write things. They also were more willing to take chances on guessing at spelling, since they had a background in the different phonics and an understanding of when certain spellings are used. So, this curriculum was an amazing success and I would recommend it to anyone willing to put in the time.

One quirk about this language program for us, however, was that it appeared that Rita Cevasco might be a Brit. A few of the phonics lessons ended up requiring some modification because they didn’t make sense to an American speaker of English. Brits pronounce certain vowels differently than Americans. For example, the word “aunt” has a short “a” sound in American English but a short “o” sound in British English. The adjustments were minor, however, and as avid PBS watchers we found the differences more amusing than frustrating.

2014-09-24-commoncorelangarts1 2014-09-24-commoncorelangarts3 To prepare for standardized testing, we also used the Daily Language Review books for first and third grade. These books ask questions about grammar, punctuation, reading comprehension and other common testing subjects. The third grade edition also required several short writing projects, which was a good supplement to The Wand curriculum.

 

Science

2014-09-24-giantscience For our science curriculum, we used the School Zone Giant Science book. I liked it because it was colorful and included fun activities such as word searches and simple experiments in addition to reading the text and answering questions. Hands down, the experiments were my children’s favorite. The book covered a wide variety of topics from weather to plants but the main focus was on animals. We learned about insects and ocean life, lizards, snakes and mammals. Animals are a natural hook to science for most children and this book understood that well. I was surprised at how many animal facts were new to me!

 

Spanish

2014-09-24-readandunderstandspanish Our goal for Spanish last year was to find some way to move beyond the stereotypical memorization of numbers, colors, days of the week and a few vocabulary words that is the default elementary foreign language curriculum. We found the Read and Understand Spanish series which is designed primarily for bilingual classrooms. We started off doing once a week Spanish lessons reading the story of the week and completing the 4 worksheet pages. That was not giving us good results as the children were exhausted with Spanish by the end of the lesson and weren’t retaining much.

We switched to shorter daily Spanish lessons with repetition of the story each day and completion of 1 worksheet per day. The worksheets required a combination of writing, cut and paste exercises, word searches and drawings. Coincidentally, many of the stories complemented our other learning in other subjects. Story topics included Jane Goodall, spiders, and fictional stories about children having birthday parties.

Foreign language is one of the most difficult subjects to teach in my experience. While we made progress in terms of learning to understand Spanish phrases and sentences (as opposed to just one random word here and there), my children do not “speak” Spanish to any measurable extent. The lack of immediate progress can be frustrating. However, I do notice subtle progress, particularly in my third grader. She seems to understand more and more and occasionally will write Spanish words herself before I have the chance to spell them out for her. Both girls made good progress learning to write down spelled words in the Spanish alphabet, which is particularly confusing because the Spanish “e” sounds like the English “a” and the Spanish “i” sounds like the English “e.”

In general, I liked this curriculum and would consider using it again.

Handwriting

2014-09-24-smartkidswhohatetowrite 2014-09-24-handwritingwithouttears One of the areas that needed attention last year was handwriting. One of my children had a dysgraphia resulting in frequent letter reversals. We began the year with Dianne Craft’s figure 8 handwriting program and did that daily for the recommended 6 months. I used the program for both my girls. I wouldn’t say that the program was an immediate magic bullet for dysgraphia but it did seem to help. After using the program, the reversals seemed far less frequent.

After 6 months, we moved on to worksheets from the Handwriting Without Tears program that I had picked up used at a homeschool conference. The biggest benefit I received from this text was learning from their suggestions about how to format a handwriting practice page for maximum results.

About three quarters of the way through the year, I realized that I was wasting a lot of time using pre-printed handwriting practice worksheets. I was missing out on the opportunity to use handwriting as a reinforcement for our other learning. So, I began to create my own handwriting practice worksheets using our spelling words. This approach worked very well and I have continued the practice.

Both girls made significant strides in handwriting. Today, the dysgraphia issues are almost non-existent and all the hard work we put in seems to be paying off.

Art

2014-09-24-artisticpursuits I thought I was going to love my art curriculum but I found myself struggling to want to use it. I found it hard to get excited about many of the art projects we were doing and my children did too. After a while, we found ourselves not using it. For me, it was the extra effort required to look ahead and gather all the needed supplies (on top of all the other learning we were doing) and also the lack of excitement from the children when they were doing the assignments. These weren’t like craft projects. They required focus, attention to detail and appreciation of art history. My children seemed to rush through them in 5 minutes, although they did enjoy them and were proud of their work. I am disappointed that I didn’t do more with art and wish I had finished the curriculum. Fundamentally, I think it is a good curriculum but you need to approach it with some of the same seriousness you would use when teaching a subject like math or science.

 

History

2014-09-24-littlehistory 2014-09-24-earth-lifeofplanet 2014-09-24-earlypeople

History was another area where we didn’t quite meet the expectations we had for ourselves. Our goal was to give the children a broad concept of what history is, how old the earth is and how old people are.  My husband did most of the history reading to the children. The year started out well but gradually as we all got busier and busier history just seemed to slip through the cracks. It was also a hard lesson for both me and my husband to learn that it is quite difficult for young children to listen to the non-fiction books we had selected. Many teachers prefer historical fiction for this age group and I can see why. With history at this age, it seems to be an “exposure” subject where children may not absorb it fully the first or second time but with each exposure they start to appreciate more and more. As a teacher, it is hard to stay motivated when your students are staring at you blankly or fidgeting and hoping you will finish soon!

Overall, I think we can call our school year a success.  We attempted more subjects than ever before and learned a lot about teaching strategies for this young age group.  Repetition is key for these young learners.  Going over and over and over a concept seems to really drive comprehension.

In my next post, how we fared with standardized testing this year.

 Posted by on September 24, 2014 General Tagged with: , , , , , , , ,
Sep 192013
 
Singapore Math's kindergarten worksheet, asking kids to add and subtract with a number line.

Singapore Math’s kindergarten worksheet, asking kids to add and subtract with a number line.

If there is one homeschool subject that seems to strike fear in parents’ hearts, it is math. Fortunately, if you start with the younger grades, kindergarten math is a great way to build confidence. Can you count? Can you do simple addition and subtraction? Wow! Great! You can teach kindergarten math! First grade math is similarly simple. Things start to heat up in the second grade, however, and by third grade, you will find that your own math skills start to get tested.

Whatever anxieties math may raise in all of us, I got an important lesson recently in how vitally important math is for preparing a student for the business world. I was chatting with someone recently who is probably the most entrepreneurial minded person I have ever met. He earned his living buying and selling small businesses and spoke of running up to 8 business at one time as though it was nothing special. I asked him a few questions about how he learned these business skills and the first thing that came to mind was that he loved math as a kid. He completed high school math while still in elementary school. Hearing this made me think differently about the best businesspeople I have met. It seems true that good businesspeople think in numbers. They readily translate complex situations into numbers and start running calculations (even subconsciously) on how to achieve a desired result. So, when we talk about wanting to develop a nation of entrepreneurs, what we might really be saying is that we need all children to be better at math than ever before.

When I first started teaching math to my eldest daughter, we were using a prepackaged kindergarten math curriculum. We had to complete a certain number of lessons and pages every day. The math curriculum we used was thorough but repetitive. My daughter generally did well in math as a kindergartner and she didn’t need to practice counting out 10 or 20 objects for 5 worksheets in a row. It was hard to hold her attention with this curriculum.

When first grade rolled around, the math curriculum was one of the first things I knew we wanted to change. I went looking for recommendations by visiting the websites for some of the best private schools in Washington, D.C. I wanted to know what curriculum those schools were using. It was during this research that I learned about Singapore Math.

Singapore Math is a math curriculum that, not surprisingly, originates from Singapore. It was developed by a group of educators to serve as a sort of national curriculum for Singapore schools. The curriculum has since been imported to the United States (because English is one of the national languages of Singapore) and has been modified to fit U.S. educational guidelines, especially for the State of California. There is even a version of the curriculum specifically for homeschooling parents. There are still a few Singapore-isms in the U.S. versions, however. The pictures used in the lower grade curricula of unusual fruits and toys have led to funny conversations with my daughters questioning “What is that thing?” Some of the international names in the story problems are giving us an education in diversity as well.

It is hard for a math curriculum to distinguish itself from others but Singapore Math is a distinctive approach. The curriculum is clearly written by people who have a deep understanding of math and who think creatively about math. For example, if you are teaching a kindergartner about counting, the curriculum will emphasize that it is important to learn to count not only in a forward direction but also backwards in descending order and in random segments of numbers. When learning second grade fractions, the curriculum doesn’t just stick to circles and squares but gets into more complicated shapes like these:

Singapore Math's mind-stretching fraction exercises for second grade.

Singapore Math’s mind-stretching fraction exercises for second grade.

Questions about time ask not only what time it is but also how much time has passed and cover time shifts from a.m. to p.m. In kindergarten, students start dividing numbers into tens and ones and write numbers up to 40. Money questions involve rarely used coins like the 50 cent piece. Units on measurement and capacity require students to learn the metric system of meters, centimeters and kilograms in addition to the U.S. system of feet, inches and pounds. Based on what I learned as a child, these math standards are far more challenging.

Last year’s second grade math curriculum was the most challenging yet. The main objectives of second grade math (as we saw from the Singapore Math curriculum as well as the second grade test preparation books we used) are:

  • addition of any three digit numbers up to 1,000, including carrying tens and hundreds
  • subtraction of any three digit numbers up to 1,000, including borrowing tends and hundreds
  • multiplication of 2’s, 3’s, 4’s and 5’s
  • division by 2’s, 3’s, 4’s and 5’s
  • simple story problems involving all of the above operations
  • introduction to two-step story problems that require two different operations to reach the solution

What made the second grade Singapore Math curriculum different in this regard, however, was that it emphasized mental math strategies. For example, if you are adding 199 to a number, it tells you that you can think of adding 200 and subtracting 1 from the other number. My husband naturally thinks in math this way. He describes it as “floating memory” math because you need to be able to hold several numbers in memory before you calculate the final answer.

One of many mental math strategies taught in Singapore Math.

One of many mental math strategies taught in Singapore Math.

I never learned mental math strategies. I do everything on paper, calculator or computer, following a memorized process. So, as I am teaching my daughter, I am actually teaching myself! If you don’t naturally think this way, it is challenging to learn these mental math strategies. Observing my daughter, I have seen that she might have an initial understanding of the mental math concept and can execute the assignment for the day but then later on when she an easy opportunity to use a mental strategy, she often won’t use it and instead will use the paper method. But sometimes she will sneak in a mental math strategy and it is exciting to see her start to see the bigger picture in math.

Using Singapore Math requires that you buy in to the theory of the program and commit to teaching even through the hard spots. The typical flow of the program for us tends to be that you have a few units that are easy and flow smoothly and then you hit a really tough unit. I remember in first grade being astounded that we were basically being asked to teach all of the pluses from 1+1 to 9+9 in just a few weeks. I began to question my choice of curriculum and thought this was perhaps too ambitious. We struggled through the unit, held our breath, turned the page and found that the next units reviewed and practiced the pluses in different ways to reinforce the concept and let us relax a bit. Since we already had done the hard work of learning the pluses, the next lessons went much more smoothly. If you have a math genius on your hands, you can emphasize more of the memorization and quick recall of all these math facts. For us, we focused more on learning the process of how you solve these problems rather than memorization and quick recall.

The Singapore Math curriculum has worked for us, but it isn’t always easy. The main downside is that if you do every page and every problem (like we do), it is very hard to complete the curriculum in one year. There is a Part A and a Part B for each year. Toward the end of the year, we sometimes have to cram in extra work on weekends to get it finished and we haven’t yet finished the full year curriculum in the given school year. We always drag a bit of Part B into the fall. For example, the second grade curriculum is 633 pages with multiple questions per page. While that works out to about 3.5 pages per day in a public school 180 day school year, in practice, that is a LOT of pages to get through. You can’t always plow through the harder units at the same pace as the easier ones. Sometimes 2 pages of review questions take two hours to get through. Based on my informal comparison of public school math objectives to the Singapore Math curriculum, the public school system typically covers about half of what Singapore Math covers in a year, which is a much more realistic objective.

So, while we stick by Singapore Math because of the creative underlying approach and its high standards, I have met a lot of homeschool parents who found it just too stressful. Perhaps as we head into the upper grades and the math gets harder and harder, we might feel the same. But if we can stick with it, I feel confident that my children will have excellent math skills by any measure.

How do you feel about math? Do you think these heightened standards are appropriate for children today?

*I have no affiliation with Singapore Math.

 Posted by on September 19, 2013 General Tagged with: , ,