Math Archives - A Waldorf Journey https://oldsite.awaldorfjourney.com/category/math/ experiences, resources and advice from a Waldorf teacher on the journey Tue, 10 Mar 2020 19:55:06 +0000 en-US hourly 1 https://wordpress.org/?v=6.7.1 https://oldsite.awaldorfjourney.com/wp-content/uploads/2021/03/cropped-profile-photo-32x32.png Math Archives - A Waldorf Journey https://oldsite.awaldorfjourney.com/category/math/ 32 32 Developmental Math in Waldorf Grade 3 https://oldsite.awaldorfjourney.com/2020/03/developmental-math-in-waldorf-grade-3/?utm_source=rss&utm_medium=rss&utm_campaign=developmental-math-in-waldorf-grade-3 https://oldsite.awaldorfjourney.com/2020/03/developmental-math-in-waldorf-grade-3/#respond Tue, 10 Mar 2020 19:54:59 +0000 https://www.awaldorfjourney.com/?p=20544 The 3rd graders and I are working hard on our class play at the moment, which has been taking up more of our morning lesson time than I’d like. I don’t typically schedule a dedicated play block — I’ve found that students get a little out of themselves if we focus entirely on the play […]

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The 3rd graders and I are working hard on our class play at the moment, which has been taking up more of our morning lesson time than I’d like. I don’t typically schedule a dedicated play block — I’ve found that students get a little out of themselves if we focus entirely on the play — but it is difficult to get some hard-hitting academic work done.

(By the way, if you’re looking for a play for 1st or 2nd grade, I’ve got you covered.)

So, I’ve set aside our usual language arts/composition rhythm and instead we’re doing lots of math practice. Math practice is actually a really good complement to the outward energy of working on the play.

As we work on beefing up those arithmetic skills, some thoughts and questions are occurring to me.

Number Sense vs. Using the Algorithm

I was really careful last year to introduce addition and subtraction of large numbers without teaching them the tool of stacking the numbers. They still recognized that they were adding the place value columns (every time we solved I said, “1 ten plus 4 tens equals how many tens?” Just to reinforce the place values.) But we kept the problems horizontal so they wouldn’t be encouraged to think of 20 + 30 as 0 + 0 and 2 + 3.

This approach was recommended by Jamie York, as well as my favorite math resource. I wrote a blog post all about my approach to 2nd grade math here. (There are actually quite a few 2nd grade math posts. Check the 2nd grade archives.) I’ve also got a pretty thorough curriculum guide for that first 2nd grade math block.

But towards the end of 2nd grade, and then into 3rd grade, we’ve been stacking the numbers. I still remind them that we’re adding 10’s (not 1’s) when we’re working in that second column, but I know that many of them forget. I also occasionally slip in a problem that is WAY easier if they think about the value of the numbers, rather than using the algorithm. For example, just try solving 1000 – 999 using regrouping — it is HARD! So now whenever they stumble across a problem that is difficult, they take a step back and look at the VALUE of the numbers. That makes it SO much easier.

It’s also occurring to me that rounding off and using approximation is a handy skill for this work. If before we solve the problem, they round off the numbers and get an approximate answer, they might be able to identify if they’ve made a big mistake.

Using Pictures

I’ve got several students who draw little pictures to figure out their problems. I see little tally marks with circles around them putting them into groups. I have been really encouraging my students to use any tools that make sense to them, which I think is a good approach, but I think that some of them are overlooking other tools because they get stuck with what they know.

For example, we’ve been practicing large multiplication problems like 9824 X 2. As he goes through multiplying the 2, he draws little marks on the paper, counting them as he goes. I’ve been reminding him that he also knows how to count by 2’s, which is an easier and faster way, if you ask me, but he keeps going with the little marks.

I can’t imagine telling them not to use the tools they’ve found, but I’m pushing myself to come up with different kinds of problems or formats that will encourage them to use other tools. Also, ultimately, I want them to have those times tables memorized so it’ll just be automatic.

Enlivened Math Practice

I have to confess that the math practice we’ve been doing is pretty straightforward — without much imagination or creativity. But honestly, I think this is the best way to give them the practice that they need.

I’ve found a few resources that use the answers to the problems to give fill-in-the-blank letters that give an answer to a riddle, which my students really love and they do get a lot out of doing problems this way. But they get more out of solving problems that I have created. When I’m creating them, I can design the problems so they get increasingly difficult and practice the specific type of problem they’re ready for.

For example, yesterday my students were surprisingly baffled by the 0 in the problem 2305 X 5. So many raised their hands saying, “What do I do here? Is it 5?” I had to go back and say, “You’ve got 5 groups and there are 0 in each group. What do you have?” “Zero?” They replied, questioningly.

You can bet that there are more zeroes on today’s practice page. So, they get the right kinds of problems at the right time. But no fun riddles. Sorry kids.

(Want to download an example of our math practice? Scroll to the bottom of this page.)

Correcting Your Mistakes

We’ve been starting every math practice period by going over the page from the day before. I correct their papers and then we quickly go through each problem in class. It’s remarkable to hear them blurt out, “Oh! Ms. Floyd-Preston, I added instead of subtracted! That’s all!” Or, “I just forgot to carry the one!” Then they want me to re-correct their papers when they make the changes.

But I just love it when they discover their mistakes! I’m so convinced that this is the way to eliminate those little mistakes.

Moses parts the sea.

But for now, they’re still making a LOT of those little errors. Each day, I’ve got maybe one student who gets them all right, but the others have lots of little arithmetic or process mistakes.

I guess the solution is to just keep practicing, making mistakes, noticing them and learning from them. Oh gosh, math as a metaphor for life!

If you’re interested in seeing an example of the math practice pages we’ve been doing, you can download the pdf here. I’ve been loving my iPad and Apple Pencil for this. Typed math practice pages just don’t work and I love that I can save all of these pages in digital format.

I’d love to hear if you’ve got similar questions about teaching math, or if you’ve got resource suggestions. Math is not my area of expertise and though I love teaching it, I do often feel like I’m figuring it out along the way.

But then, I guess that’s the way of Waldorf teaching. I’ll let all you 3rd grade teachers of the future know when I’ve got it all figured out.

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Waldorf Grade 3 Update https://oldsite.awaldorfjourney.com/2019/11/waldorf-grade-3-update/?utm_source=rss&utm_medium=rss&utm_campaign=waldorf-grade-3-update https://oldsite.awaldorfjourney.com/2019/11/waldorf-grade-3-update/#comments Tue, 19 Nov 2019 20:16:52 +0000 https://www.awaldorfjourney.com/?p=18656 I sat down to write this week and realized that I’m having so many thoughts about the work that I’m doing with the 3rd graders, I can’t help but make this post a bit of a catch-all. Here are some of my most recent random thoughts. Hard-Working Waldorf Teachers First of all, I have to […]

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I sat down to write this week and realized that I’m having so many thoughts about the work that I’m doing with the 3rd graders, I can’t help but make this post a bit of a catch-all. Here are some of my most recent random thoughts.

Hard-Working Waldorf Teachers

First of all, I have to thank all of you for your gestures of support in response to my last post. I love the work that we do and I want the rest of the world to recognize the amazing things that Waldorf teachers around the world are doing.

You all gave me some hope that recognition is coming and that our work is appreciated. I hope you’ll all keep fighting the good fight and advocate for the respect (and compensation) you deserve. I’m so grateful for the support of my colleagues and class parents and it’s nice to know there is such a strong community of teachers following along here, as well.

What block are we in? Writing or math?

During this last week before the American Thanksgiving holiday, we’re back in our Hebrew legends. Multiplication and division review is the official content of the block, so we’re doing lots of math practice, but these stories are so great, I can’t help but work with them.

I’ve actually worked with the content of the block in a unique way this time, inspired by the stories we’re hearing. Though we’re mostly studying math, I think it’s important that we continue to write. And some of the stories are so great that it would be a shame to skip over writing up a retelling.

This year, I’ve been giving my students a composition assignment every week, usually on Tuesdays. (I wrote another blog post about our composition rhythm here.) This rhythm works really well for us for a couple of reasons.

  1. I have a support teacher dedicated to our class every Tuesday during main lesson.
  2. I have found that we need to do composition assignments early in the week so we have time to review them and put the final versions in our main lesson books.
  3. Tuesdays are generally good days for the 3rd graders. Mondays and Fridays can be rough, but Tuesday is pretty good. And doing the hard work of writing a composition helps make it go more smoothly.

So, to make the composition process go more smoothly, I make sure to tell a good, rich story on Monday. When my students have those strong images in their minds, they have no problem writing. There have been times that I have tried to force a writing assignment about a story that did not live very strongly for my students, usually because I was not prepared to tell it, and it never goes well.

I’ve also found that because my students are so squirrelly and restless on Mondays, it’s a perfect day for a good long story. They usually settle right in and listen, building images as I tell.

But during a math block?

Well, yes. This rhythm is working so well for us, it just feels right to let the math rest on Tuesdays and do a composition instead. It’s a solid part of our weekly rhythm that works really well. I’m sticking with it.

Over the summer, when I planned the year, I had intended to alternate language arts and math. When we were in a math block, our daily practice period would be dedicated to language arts, and vice versa. This seems like a good rhythm, and it also worked well, but I’m just loving our Tuesday composition days that I’m rethinking it.

So, here we are on a Tuesday, just finished writing a composition, and during our skills class we’ll do math. Tomorrow we’ll practice math during main lesson, put our compositions into our main lesson books for bookwork, and then do some phonics work during practice class.

I admit it is a little odd to switch back and forth, but a good rhythm is worth its weight in gold!

Hebrew Legends Resource

Have I mentioned the resource that I’m using for most of these stories? I am LOVING Pearl Buck’s Story Bible. It breaks down the stories from the Tanakh into just the right length for a good main lesson story. It also brings rich images and language. At the beginning of the year I was pulling from a few different resources, but these days I’m just going straight from The Story Bible.

Classroom Management

I don’t know about you, but for me classroom management is a constant work in progress. Just when I think I’ve got it all figured out, I see something different and feel inspired to try something new.

Lately my thoughts are about just how much management I’m doing. The thing is, ultimately, I want my students to manage themselves. I mean, I can certainly keep them in line and direct the will of the group, but how much of that should I be doing?

How much can I turn the management of the group over to the students themselves? And if I do it, will they be successful? I’ve got lots of tricks up my sleeve, but lately I’m thinking that I need to keep my sleeves down a bit and let them do the heavy lifting.

My goal is to have a classroom full of students that hold themselves (not each other!) accountable for doing the right thing. And maybe pumping the breaks on my management is the way to make that happen.

Just some food for thought. What do you think? Leave a note in the comments.

Free Classroom Management Workshop

Finally, I’m getting ready to run my free classroom management workshop again in January. If you missed it last time around, you should definitely sign up this time. I go through three of my favorite classroom management strategies and give you tips for implementing them in your classroom. And it’s completely free.

Just click here to get to the sign-up page and I’ll notify you when the workshop is live.

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Practice Makes Progress | Practicing Skills in Waldorf Grade 3 https://oldsite.awaldorfjourney.com/2019/10/practice-makes-progress-practicing-skills-in-waldorf-grade-3/?utm_source=rss&utm_medium=rss&utm_campaign=practice-makes-progress-practicing-skills-in-waldorf-grade-3 https://oldsite.awaldorfjourney.com/2019/10/practice-makes-progress-practicing-skills-in-waldorf-grade-3/#comments Wed, 02 Oct 2019 01:15:29 +0000 https://www.awaldorfjourney.com/?p=17846 If you’ve been reading the blog for awhile, you know that I started out my Waldorf journey as a middle school teacher. In fact, I took three classes through the upper grades before teaching the lower grades. Now that I’m in 3rd grade with my 4th(!) class, the first one I’ve taken from the beginning, […]

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If you’ve been reading the blog for awhile, you know that I started out my Waldorf journey as a middle school teacher. In fact, I took three classes through the upper grades before teaching the lower grades.

This was my 8th grade class the morning after the 2016 election. Read a post about that morning here.

Now that I’m in 3rd grade with my 4th(!) class, the first one I’ve taken from the beginning, I am realizing a whole other side to teaching in a Waldorf school.

Here’s the thing, in the upper grades, you don’t have to work as much on skill development. The students already have the basics of reading, writing and doing math figured out. They need to practice, yes, but they don’t need you to guide them through that practice in a step-by-step way. You set them with challenges and turn them loose.

In the upper grades, you want to encourage them to think. The teacher creates an environment that fosters creative thinking, problem-solving and imagination. We set the stage and then watch and see what comes to life.

The lower grades are totally different. I mean, imagination is still key. It is how we keep our students engaged and inspired. But every single day they are learning new skills and this is really big, important work! The teacher needs to get into the student’s mindset to figure out exactly what step is the next, most logical one on the path.

Figuring out the puzzle of unlocking those skills is one of the things I love most about being a teacher.

But it isn’t easy.

One of my 3rd graders stirring the biodynamic preparation as part of our Michaelmas celebration.

When my students are focused, not chatting or distracted and giving me their full attention, I can usually see, in the moment, what to say and do to help them take the next step in their learning.

When I’m not stressed out about holding their attention or worried that I’m going to lose them in the next step, I can usually follow my intuition in the right direction.

But this ideal situation doesn’t present itself without effort. It takes a lot of hard work to make sure that students are eager and receptive for those big lessons.

Luckily, there are things we teachers can do to make those golden moments happen more often. We all have our secret tricks of the trade, and mine is rhythm.

After talking to a colleague last week, I took a minute to reflect on my daily classroom rhythm. I realized that our days are SO full of rhythm that so much of what we do seems to happen automatically.

  • We always sing our morning greeting song after the handshake.
  • We always take out our composition books after playing the flute.
  • We always begin our bookwork time with crayons open and books closed.

When I thought about it, I realized that our daily rhythm is exactly the same for the first 45 minutes of our day.

Long-time mentor Else Gottgens would shudder to hear this. She always encouraged teachers to get to the new and interesting content as quickly as possible in the lesson.

But here’s the thing I’ve realized. Though the rhythm is the same, the content is not. We play a new flute song, solve different problems in our composition books and create new and interesting main lesson pages. This is the new and interesting content. But the rhythm holds us steady and keeps us going. Kids know what to expect and can anticipate the next step. They feel more confident and their teacher can focus on the hard work of identifying the next step, rather than endlessly managing behavior.

What does this have to do with practicing skills?

Rhythm is my not-so-secret strategy for creating an environment that fosters practice.

What we’re doing in 3rd grade this year is a perfect example. There are a few different rhythms we hold in our class that allow for daily skills practice. Our dictation rhythm is just one of them.

Dictation

One of my favorite rhythms this year, is something that I’ve also used with students in the upper grades. In fact, I found this rhythm really great in grades 4-6. It is designed to give my students practice with spelling, vocabulary and the mechanics of writing. This is how it’s working in 3rd grade.

  1. I write a composition at the beginning of the week. Usually it is about the first story of the week. I try to include any vocabulary, spelling words or phonics rules that we’ll be working with that week. The composition includes about 4 sentences (one for each day of the week) that work together to create a cohesive whole.
  2. Each day of the week, Monday-Thursday, after our flute practice, the students take out their composition books and write the date at the top. I dictate the sentence for that day and students write it down in their books, making their best guess at spelling.
  3. After they’ve had a chance to write it, I write it on the chalkboard, asking volunteers to help with spellings, making note of punctuation and anything else that presents itself. If I’ve done a good job of thinking through the skills we’re practicing that week, there is lots to talk about. Often an impromptu lesson arises. So far this year we’ve noticed things like the Oxford comma, capitalization rules, when and how to use quotation marks and the different pronunciations of the “ea” vowel team. As we go through, students self-correct their dictations in their composition books. Each day we add to the composition on the board, leaving the sentences up throughout the week.
  4. On Friday, the students have a complete composition on the board that they then put in their main lesson books. In the upper grades, the dictation is given as a quiz on Fridays. It gets scored and recorded on their end-of-block report.

Why I Love This Rhythm

There are so many things I love about our daily dictation rhythm.

  • Because we do it every day, the practice is nearly automatic. Students don’t have to overcome the idea of being presented with a writing assignment before they can engage with it. They know it’s coming, they’ve done it every day, so they feel confident about being able to do it again.
  • This rhythm meets so many of our practice goals. In this activity, students practice block vocabulary, phonics rules, sight words and, importantly, commonly used words. I would rarely put words like because, about and people on a traditional spelling list (maybe once per year). But students need to practice these words regularly. This gives them the opportunity to do it. And three goals accomplished with one activity is great news for a busy teacher who doesn’t have enough time with her students to fit it all in (let alone prepare all of those lessons!)
  • The dictation is about the content that we’re learning that week so there is imaginative content for the students to connect with. This is way better than just a list of random words that meet a particular phonics rule.
  • It’s short. I don’t need to have a complete skills lesson to do this practice. I take no more than 10 minutes to dictate, correct and review our dictation. In the upper grades it takes even less time.
  • It allows me to give the students an example of well-written content without having them passively copy it from the board. Students are engaging with it and thinking about it, not just copying. I think copying from the board is one of those old Waldorf traditions that doesn’t really serve student learning. There’s always a way to have them engage and do more. I love to have my students write their own independent compositions, but the challenge of doing this is that their writing is fairly simple and uses common vocabulary. Dictation presents them with a picture of what writing can look like so they have something to aspire to.

Also, one thing to note, I don’t ever collect and review these books. I let them choose what writing to use and let them know that they are the only ones who are going to see these books. This helps them to feel comfortable taking chances with spellings and giving every word a try. They also don’t get stuck on erasing or forming each letter perfectly. I tell them pretty regularly that dictation is the time for their “fast writing” not their “beautiful writing.” If I had a group of students who tended to write sloppily, I probably wouldn’t make this distinction, but I have the opposite problem. For some of my students every letter is a work of art!

Just so you can see what a daily dictation looks like, here is a picture of one of my students’ daily pages. You can see that he likes to check off the words as we go through them, noting to himself that he got them correct (so cute). You’ll see that I also ask them to write the complete, corrected version in their books below their practice, rather than erase their mistakes and write in the corrected version. This is so helpful to me in seeing what phonics rules they need to review!

This sentence gave us so many things to discuss! The main thing we recognized was that there are three “ea” words (means, head and year), and they don’t all make the same sound. This student made some very intelligent guesses! (Oh, and, for the record, I gave them “Rosh Hashana”.)

The other thing we talked about was the word “Jewish.” Before I even considered writing anything on the board, I asked them what they tried. This was a hard word! Some students tried a G at the beginning. Other attempts we heard were “jooish” “guish” “juwish” “jooesh” and “jouish.” Every time a student shared their attempt, I acknowledged and validated something about it. “You heard the -sh at the end!” “There are many ways to make the -oo sound, you used a -u.” Speaking about it this way ensured that everyone was safe to share their attempt. It was fun collecting all of the different ways that word could be spelled!

This week we also made challah for Rosh Hashana!

You can also see that after the dictation I put a couple of math problems on the board. I have the students turn their books sideways in 3rd and 4th grade so they can use the lines to keep their columns straight. This is another rhythm that works really well for us and ensures that we get some daily math practice, no matter what.

The importance of daily practice

One other thing I’m really thinking a lot about this year is making sure that my students get practice in all of their core academic skills every day. For me this means math computation, writing and reading.

Over the summer, I planned that anytime we were in a math block, our daily skills class would be language arts focused. During language arts blocks, the skills would be math.

In practice, I’ve found there to be much more overlap and less separation than I anticipated. For example, though we are currently in a math block (measurement), we are doing a lot of writing about it. I have clearly outlined academic goals for each week of the block, and they are all math-oriented, but when it comes down to what we are doing in our lessons, there is a whole lot of both happening.

Here’s today’s main lesson, as an example.

After our daily opening and warm-up, we did our dictation (the 2nd day about Rosh Hashana) and a couple of math problems. The math problems practiced regrouping, which is a new skill we’ve been working on for the past couple of weeks.

The math concept I have outlined for the week is about rounding off, which we started working with yesterday, but we hardly touched on it in today’s lesson. Just to make sure we had some touch-in review of it, I asked them a couple of rounding off questions later in the day, before diving into skills class.

The main review activity of the day was to review the measurements of the inch and the yard. We did a guided main lesson page with drawings and writing about both of those measurements. This activity was not about any of our core academic skills, but it was a challenging page to complete. There was a lot of instruction about drawing technique and arranging elements on the page.

This page is my own. So far this year I mostly haven’t been completing a book of my own — the students can complete most of it without a model — but for a page like this, that doesn’t follow our usual arrangement, I needed to do it in the morning to think it through before leading the class. Because I did this, I discovered improvements and guided my students to do it the new, better way. In this example, I wished that I had put the king on the right side and the hand on the left side, so my writing about the thumb could be right next to my thumb. (If I was left-handed, I would have traced my right hand and it would have worked out right.)

Completing this page took the rest of our main lesson.

As I think about it, maybe this lesson isn’t the best example, but the point I’m trying to make here is that your main lesson review/practice time is where the skills practice component of the lesson happens. And with a curriculum that approaches all subjects in such varied ways, the kind of practice you do can really vary. Last week, my students wrote independent compositions, engaged in group activities, did math practice pages and guided drawings — all as part of the review portion during a math main lesson block. On those writing-heavy main lesson days, I brought a little more math into skills class.

I’m all about having a lot of clarity about what I am teaching and when I am teaching it, but sometimes things need to be more fluid. It’s times like these that I am so grateful that I don’t have a prescribed curriculum to follow.

Outlining goals is one thing, but finding the way to accomplish them is truly the art of teaching.

Happy challah makers!

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How to Teach Waldorf Math https://oldsite.awaldorfjourney.com/2019/02/how-to-teach-waldorf-math/?utm_source=rss&utm_medium=rss&utm_campaign=how-to-teach-waldorf-math https://oldsite.awaldorfjourney.com/2019/02/how-to-teach-waldorf-math/#respond Tue, 05 Feb 2019 19:50:58 +0000 https://www.awaldorfjourney.com/?p=13258 Seems like lately I’ve been having lots of conversations with my colleagues about math. Could be because (if you ask me) January is a perfect time for a math block. The more inward, reflective quality of this time of year makes it a great time to sit down and crunch numbers. (That’s what we’re doing […]

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Seems like lately I’ve been having lots of conversations with my colleagues about math.

Could be because (if you ask me) January is a perfect time for a math block. The more inward, reflective quality of this time of year makes it a great time to sit down and crunch numbers. (That’s what we’re doing this month!)

But teaching math in a Waldorf way is not so straightforward. Developing an approach to math that aligns with Waldorf ideals, but gives students enough solid skill-building time is a challenge. Here are some of the challenges I have faced when teaching math. These are issues lots of readers have emailed me about and colleagues ask questions about.

  • How do we make math (a subject that can be so abstract) lively and imaginative?
  • How do we make sure our students get enough practice without it becoming “kill and drill”?
  • How do we keep our students feeling confident and capable about math, especially when they struggle?

Here are some ways I’ve managed these challenges.

Keeping Waldorf Math Imaginative

Here’s the thing. Often, when I try to create an imaginative picture around a mathematical concept it feels forced. Our place value block this year is a perfect example. I came up with a story that explained the concept of place value. (You can read more about it in this blog post.)

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While the story I came up with was good, as we moved through the block, I found a couple of challenges. First, those little math stories were not the kinds of stories my students loved and enjoyed together. We were used to rich fairy tales with strong images and cosmic significance. My little stories about a character collecting firewood and putting it into bundles just didn’t compare.

The other challenge with the story is that it can sometimes feel forced. We create characters and situations that bring the mathematical concept we want, regardless of whether it makes an enjoyable or believable story. It’s hard to tell stories like this with confidence and our students often see right through them.

If you ask me, one of the most important things in working with students is that the story feels right. If I try to tell my students a story that doesn’t resonate with me and I’m telling just because it’s what my colleague did, I’m asking for trouble. The lesson inevitably falls flat.

So, what to do? Do we have to use a story, even if it doesn’t resonate? Well, go back to the reason we use stories in the first place. We do it because we recognize that for the elementary age child, the path to interest is through the feeling life, and imagination is a huge part of the child’s feeling life. But, the truth is, a story is just one way to capture your students’ imaginations.

  • Connect your math work with art. If imagination is king for the elementary school child, art is queen. Those beautiful geometry drawings, paper folding activities and free-rendering activities with all kinds of crafty supplies can allow your students to explore mathematical concepts in a way that comes alive for them.
  • Connect your math work with the senses. You know that 4th grade fractions block where you divide up the pizza and then eat your fraction? That’s a lesson that always sticks. Look for other ways you can involve your students’ senses of smell and taste (the ones that often get neglected.)
  • Explore math socially. Get your students working on a project together, talking it through, explaining to each other. Middle schoolers especially learn really well in a social environment.
waldorf sixth grade geometry

Now, I’m not suggesting that you completely abandon story time. There’s nothing I enjoy more than telling stories and collectively building images with my students. But I’d much rather do that with a rich and meaningful story, rather than something I made up just to get to a particular math concept. I call this “a story for the sake of a story” and I love that it opens up my options and gives us good, rich stories to explore, even during a math block.

Getting Enough Practice

Oh boy, I don’t know a single Waldorf teacher who hasn’t asked herself if her students were getting enough math practice. That old Waldorf idea that a subject needs to “go to sleep” before you bring it back and expand just doesn’t seem to apply to skills like math. If you ask me, students need daily practice with skills like math, reading and writing.

But does a creative, inspired Waldorf approach allow for routine practice. In short, YES!

Giving your students a worksheet (I like to call them “practices pages”) is not anti-Waldorf. If worksheets were the only thing you ever did, then yes, that would not be an inspired Waldorf approach. But try giving your students a worksheet and see how they respond. Very often I find my students inspired by the challenge of a paper full of questions that they get to answer! They like it!

Again, the important part is that you are working to engage your students. If your students are showing signs of being engaged and interested, even with a worksheet, that’s your measure. If they’re bored and overwhelmed by a worksheet, that’s your cue to do something different. Math games (involving the social realm), riddles and puzzles are good ways to get the practice in.

The other mistake I sometimes see teachers make is holding on to the image for too long. At a certain point, that image that you’ve used to introduce a concept becomes cumbersome. The concept itself becomes solidified in your students and going back to the image every time can confuse things. Use the image as a tool to introduce an idea, practice with it and then move on.

By the way, the amount of practice your students need depends somewhat on their age. Here’s how I see it.

Grades 1 & 2 — In these grades we’re working with big ideas — number concepts, the feeling for numbers, place value and how the processes and our number system works. Practice comes in movement, rhythm and circle activities. They do need some practice writing the numbers and solving problems, but not as much as in other grades.

Grades 3-6 — These are the prime skill-building years, and this applies to every subject. Skill-building requires practice. They’re learning and practicing how to use the processes and they need daily practice using them — over and over and over.

Grades 7-8 — In these years we go back to the big concepts. Here they have solid computation skills and they are being presented with lots of different opportunities for using them. They’re figuring out how and when to use those skills. Less practice is required and ideally their skills are solid enough that they can explore the world mathematically.

Building Math Confidence

I have worked with so many students who, despite my best efforts, get the idea that they just don’t get math. And it’s true, there is something magical about thinking mathematically. When I think about my strongest math students, I think that their genius with the subject is something that they were born with. Their brains just work that way.

I’m not usually one to categorize students and there is plenty of overlap here, but bear with me. In my experience there are different kinds of math students. There are the Intuitive Geniuses and the Rule Followers. Both can be wildly successful but I think our traditional Waldorf ways favor the Intuitive Geniuses. I’m here in support of the Rule Followers.

I was one of those students who didn’t have that natural connection with math. For me it wasn’t that I didn’t understand math, it was just that, when given the choice, I always preferred to read or write. When it came time to do math, I was a Rule Follower. Luckily I had some really good teachers along the way who helped me find my way to actually enjoying math.

When I think about my experiences with those really good math teachers, I remember that they laid things out and explained them very clearly — step-by-step.

We are often taught to allow our students to approach math with a spirit of exploration and we encourage them to make connections and discoveries on their own. And truly, this is a fantastic way for them to learn. My strongest math students LOVE being presented with a real world math situation and then thinking it through to come up with the answers. With math tools at their disposal, they are ready to conquer the world, make connections and find solutions. They’re Intuitive Geniuses when it comes to math.

But this kind of experience is overwhelming for the Rule Followers. Those students need things laid out in a very clear, step-by-step way. Teach them the steps (the Rules to follow) and they will implement them flawlessly, eventually developing an understanding for the concept and how and when to use the rules.

I implore you, in your enthusiasm to keep math lively and interesting, don’t overlook the Rule Followers. If you are an Intuitive Genius yourself, this might be really difficult for you. Slow down, observe your students and think through the topics you are teaching step-by-step.

That ability to observe your students and intuit how to meet them is your number one job as a teacher. Don’t forget.

And if you’re looking for support and resources to help, here are some of my favorites.

Resources

Curriculum Guides

Blog Posts

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Waldorf Grade 2, January Math https://oldsite.awaldorfjourney.com/2019/01/waldorf-grade-2-january-math/?utm_source=rss&utm_medium=rss&utm_campaign=waldorf-grade-2-january-math https://oldsite.awaldorfjourney.com/2019/01/waldorf-grade-2-january-math/#comments Thu, 10 Jan 2019 01:42:44 +0000 https://www.awaldorfjourney.com/?p=12838 It’s been a little bit since I’ve written a little update post. Since coming back from the holiday break (just 3 days ago?!), the 2nd graders and I have been working on math. As always, to map out the block, I sat down with my planning book and figured out our objectives. I began by […]

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It’s been a little bit since I’ve written a little update post.

Since coming back from the holiday break (just 3 days ago?!), the 2nd graders and I have been working on math. As always, to map out the block, I sat down with my planning book and figured out our objectives.

I began by thinking about where we left off with our last math block, thought about the skills my students need more practice with and then compared those thoughts with the objectives I laid out over the summer.

I was surprised to find that we’re remarkably on target and my intuitive sense for what my students need to practice is almost exactly what I had planned for this block months ago.

You can see in this photo that I also thought through the various aspects of our daily lessons and the activities that would allow us to practice the different skills.

  • Blue highlight means main lesson bookwork.
  • Yellow highlight skills will be practiced in mental math/warm-up time.
  • Orange highlight will be during our circle, or rhythmic activities.
  • The last category is for good old fashioned math worksheets — a term that can be somewhat charged, so I call them “practice pages” instead.

When I put it all together, the 3-week block looks like this:

  • Week 1: Review place value and extend to 100,000. Continue with horizontal addition and subtraction.
  • Week 2: Review multiplication and division. Extend to practice with number sentences.
  • Week 3: Continue multiplication and division work. Move away from manipulatives and rhythm and towards working on paper.

(And if you’re looking for resources for planning your own block, here are my favorites.)

I really recognized that my students need more practice with multiplication and division. We have done some work with skip counting, times table songs and rhythm exercises, but moving from those activities to working with number sentences (ex. 3 x 4 = 12) is a leap we haven’t made yet. That will be a big goal for this math block.

January in Portland means that just about every day is a “full rain gear” day.

At the same time, we’ll be working on reviewing the double-digit addition and subtraction skills that we learned in our first block and extending them to working with 1000’s, 10,000 and beyond. To read more about those different strategies, you can read my blog post about our first math block.

I also put together a 2nd grade math curriculum guide which is all about that first math block. You can find that here.

Waldorf Grade 2 Stories

Throughout the block I’m telling the story The King of Ireland’s Son. I’m not using the story to bring the math content — it’s just a “story for the sake of a story.” I confess, even after having three of my own children go through the Waldorf grade school, my daughter playing Fedelma in her 2nd grade play and being a Waldorf teacher for 12 years, I had never read this story. I’ve heard mixed reviews from colleagues, but I am just loving it. After months of simple little fables and one-off saint stories, The King of Ireland’s Son feels deep and rich, with the same flavor as the fairy tales I told in first grade. Just what we all need!

During our practice classes, we’re taking a little break from kid writing to give more attention to form drawing. My plan is to teach cursive after our February Break, and many of the second graders need to review lower case and do some good practice with form drawing to be prepared.

To keep up our language arts practice, we’re doing independent “read to self” time with our book boxes in the afternoons and practicing five sight words per week. As always, the 2nd graders are astounding me with their progress.

Sight word flash cards!

What are you teaching these days?

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A New Curriculum Guide — Waldorf Grade Two Math #1 https://oldsite.awaldorfjourney.com/2018/10/a-new-curriculum-guide-waldorf-grade-two-math-1/?utm_source=rss&utm_medium=rss&utm_campaign=a-new-curriculum-guide-waldorf-grade-two-math-1 https://oldsite.awaldorfjourney.com/2018/10/a-new-curriculum-guide-waldorf-grade-two-math-1/#respond Fri, 12 Oct 2018 18:10:14 +0000 https://www.awaldorfjourney.com/?p=12212 This year I’ve made a commitment to myself (and my readers) to make every effort to share my curriculum materials as soon as possible. Waldorf Math You see, my curriculum guides come straight from my lesson planner. When I sit down to put them all together in a final polished document for all of you, […]

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This year I’ve made a commitment to myself (and my readers) to make every effort to share my curriculum materials as soon as possible.

Waldorf Math

You see, my curriculum guides come straight from my lesson planner. When I sit down to put them all together in a final polished document for all of you, I flip through my lesson books and reflect on how my students absorbed the material and what I learned in teaching it.

I’ve found that if I sit down and go through this process right away, everything is fresh in my mind and the insights and inspirations flow easily.

Well, that ease certainly happened when I put together this Waldorf Grade Two Math curriculum guide.

My approach in this block was somewhat unconventional. Typically, Waldorf teachers are taught to tell the students a story that will bring the concept of place value in a practical and imaginative way. With this story firmly in the imaginations of your students, you can move into manipulating double and triple digit addition and subtraction problems by setting them up vertically.

A Developmental Approach

This summer I read a lot of information put out by developmental math specialists (you can check out my favorite go-to resource here) and it became quite clear to me that when children set up problems vertically, they lose sight of the value of the numbers they are working with.

I discovered that to help children truly think mathematically it is best to keep the problems horizontal and encourage them to find other strategies for solving the problems.

In our lessons we talked about a few of different strategies.

  • Using a 100 Chart. This was the first strategy we used and my 2nd graders got really good at using this tool. Eventually they could use the 100 Chart that was “in their heads.”
  • “Jumping 10s.” We discovered that you can count by tens starting at any number. Just as we can say “10, 20, 30, 40, . . . ” we can also say “33, 43, 53, . . . ” We found this strategy to be really helpful for adding problems like 33 + 20.
  • “Pretending” a number is another number. We talked about how in a problem like 19 + 32, it sure would be easier if that 19 was 20. So we practiced “pretending” it was 20, doing the math and then adjusting.

My resources supported encouraging children to find strategies, but not necessarily outright teaching them. Of course, I love when my students discover their own strategies, but I wanted to give a leg up to those students who needed it, so these strategies made it in to my daily lesson plans and we practiced using them together.

Some students said that they already knew to do math in this way and it was great to see that the work we were doing aligned so well with their intuitive sense.

Want to read more about this math block? Check out this blog post. I wrote another one here, as well.

At the very end of the block I presented the students with a problem set up vertically, mainly because I wanted to arrange the information in a chart. As we worked through the content, I made sure we were all clear that we were counting sticks, bundles and sacks of firewood (which represented 1s, 10s and 100s.)

All of this information, and the progression that I followed as I taught the material, is in this curriculum guide. Along the way, I told stories about knights and dragons, which was a nice way to move away from the fairy tales of first grade and into some more dramatic stories.

Here’s what you’ll find in this guide.

  • Day-to-day lesson plans, including stories, new material and suggestions for review activities
  • An overview of the curriculum and how it takes shape in a daily lesson
  • The stories that I told throughout the block (including links and suggested resources for the stories themselves) that created the “knights and dragons” theme
  • Photographs of student main lesson pages
  • A guide to creating enlivening circle activities, with instructions for crafting your own circle exercises
  • The specific content of the circle activities I used this block — including specific songs and poems

I’m really proud of the work that has gone into this guide, and the progress that my students made in this first block of the year. I think you’ll find it really useful.

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