Showing posts with label math discourse. Show all posts
Showing posts with label math discourse. Show all posts

Wednesday, August 23, 2017

10 days in...

I'm exhausted.

It's only two weeks in.

Open House was last week and I still haven't recovered.





In addition to ya know, teaching, I've sat in on a planning meeting for our upcoming Rodeo night, an ELL presentation, had a meeting about advanced students, had a grade level meeting, and gotten my room ready for Open House...by Wednesday.

Thursday morning I helped to lead a new teacher training, will teach all day, make a quick run to Sonic, and get ready for two hours of Open House.  

I've got amazing parents who brought me cookies for Open House:

 

Thank goodness Friday was already planned, next week is planned, and I've got a busy weekend ahead of me!

There were some late nights, but I've got this view:

 

In terms of long range plans and grade level plans, I'm already behind.  I was behind on day 2.  I'm not really sorry about it.

By no means have we wasted time in the classroom.  Instead, I'm in an adjustment period where I'm quickly realizing things in third grade take much longer than I'm used to...because they're 7 and 8 years old.  

In math, we've explored number talks, built problems with cubes, learned about arrays, and started making the connection between repeated addition and multiplication.  



I picked a student who was struggling to give me the number of items in each box.  That ownership and helping me make our reference guide was really important to that kiddo.

They've taken their first three "entrance tickets" (10% formative assessments) and are continuing to learn about math discourse.  Two of them went into the grade book.



In reading, we've built up our independent reading stamina, read several picture books,  taken our STAR test for beginning of the year benchmarks, reviewed fiction and nonfiction, completed sorts, and I've begun benchmarking for AIMSweb oral reading fluency.




In writing we've covered nouns (common vs. proper), friendly letters, and brainstormed ideas for our letter to ourselves at the end of the year. 


(The post-its were a spur of the moment decision but I like how the notebooks turned out.  Students wrote their own examples underneath the post-its.  We also got up and labeled different nouns around the classroom.)

I also used the post-its on the anchor chart:

  



Last week we began drafting our three paragraph essays and revised/edited with partners.  Final drafts are due Monday, but it's not for a grade. I'm using their first papers as a benchmark so I can make a list of mini-lessons the class needs.  We've also been doing morning journals (available {here}) and I'm slowly incorporating mini language lessons about restating the question in the answer, capitalizing proper nouns, and using evidence to explain our thinking.

They also built up their writing stamina and enjoyed free choice seating:



They've learned about summaries and practiced whole group (to My Mouth is a Volcano and Alexander and the Terrible, Horrible, No Good, Very Bad Day), in table teams (to Thank You Mr. Falker), and individually with their books.



We've reviewed fiction and nonfiction writing. They also cut up extra book orders to sort into F and NF, which allowed me to go over procedures for gluing, cutting, and using class supplies.




We spent a few hours doing activities on Monday's solar eclipse and have most of our classroom routines down.  



We've already changed seats, know where our privacy folders are kept, and have our graduation count down board ready. 



We've established our sentence frames for talking to one another:




We've done some get to know you activities and brain breaks as well.  We've practiced gallery walks and structured movement in the classroom.  We've taken pictures, celebrated a birthday, practiced routines, and taken pictures in our class photo booth. We've reviewed assembly procedures and learned about our first fundraiser for the school in a popcorn assembly.

I'm not a sit quietly and do worksheets kind of teacher.  So while I may technically be behind 10 days in, I think we've done some quality learning.  That's what makes this worth while. 

Tuesday, November 17, 2015

Where was admin?


I had a beautiful conversation erupt during math time today.

Here was the problem:



They were solving with a partial products array (they're not quite ready for traditional or standard algorithms for multiplication) and a very loud, very passionate conversation erupted.  One student argued that having the "zero tens" row in the second factor (409) wasn't necessary.  Another passionately disagreed.  

Soon, I lost the whole class to this beautiful, loud conversation about if zero is a value or simply a place holder.  

Did it need to be represented? 

Could it be skipped? Always?

I reeled them back in after about five minutes of debate, much to the horror of the original instigators who hadn't successfully defended their perspectives.

What a beautiful, natural example of the math practices coming to life.



Now, where was admin?! That would have been a lovely example of math discourse in the classroom for my end of year evaluation.


Thursday, August 20, 2015

Math Training, Day 2

Last Friday, I attended {day 1} of a math training.  Monday I attended part two. 

Overall, it was a decent training.  It's frustrating that due to scheduling issues, they condensed two days into one.  When they did this, we lost a lot of the processing, collaboration, and reflection time.

Clicks:

-We were in a smaller break out room. We were encouraged to talk to our neighbors.

-The focus was much more on using manipulatives (place value blocks, centimeter grid paper, etc) to show the math.  i think that my fifth graders don't necessarily get enough practice time and exposure to the concrete math, which leads to conceptual misunderstandings.  The focus was on shifting students from concrete to representational to abstract methods of problem solving.  (Manipulatives to diagrams with manipulatives to just numbers).  By fifth grade, the concrete step is often skipped but when students have conceptual gaps or it's a new concept, they need hands-on time to explore.

Clunks:

-There was no processing time.  It was very high paced and for six straight hours.  There was no reflection time to write down thoughts or think about where to use these strategies in the classroom.

-It was an hour away.  That's frustrating.

However, since 3/5 of my grade level was there, we are bound to use most of what we learned! I'm glad I'm not the only one responsible for remembering this information!

 

Sunday, May 24, 2015

The Metric System

Ahh, the metric system.  Usually students either have an easy time with this or they think it's the most confusing thing, ever.

My students this year, however, did fairly well with the metric conversions.  I think a large part of this success is because we spent so much time in the beginning of the year building number sense and working with powers of ten.

I also modeled exactly what a meter looks like and passed around a meter stick:

                                              

As with every math unit, we did a gallery walk with challenge questions before the test:


We also did some sorting activities and used our "I have, who has" cards in small groups.



I also sent them on a scavenger hunt in their own fridges to find items that were listed in the customary system but that were also labeled with the metric system.

How do you teach the metric system?

Monday, May 11, 2015

mini-math

My students needed a little extra practice with fractions before our test.  I could have assigned them book problems to work on silently, but that wasn't what they needed. They needed to work with each other and learn from each other.  During this time, I pulled the students who really weren't getting it to the back table for some intervention work.

The novelty of having mini-math problems was extremely motivating for them.  I also like to include the "create your own" option.  I can see their levels of comfort with the ideas based on the problems they choose to create and then solve.



Since it's May, many of my fifth graders are plagued with the end of the year-itis.  Any new strategies that keep them engaged are always welcome!

How do you keep your students motivated in May?

Tuesday, March 31, 2015

Math explorations

I am a huge advocate of the use of manipulatives and hands-on exploration.  Right before spring break we dived into volume.

Our first day was focused on exploring cubic volume with cubes.  It was such a great opportunity to watch them struggle through the challenge sheets and learn from one another with no pressure of assessment.  

Their task:






They had a great time exploring with cubes.  I also frequently allow them to work on the floor and move around.  They're ten and need to wiggle sometimes.  I might as well embrace this and provide these opportunities in the classroom.
 



They had a specific task sheet (for accountability).  I gave them ten minutes to explore, then they shared with a partner (Kagan hand up, stand up, pair up, and share).
 

One group was super excited that their blocks were ASU colored!



After a day of exploration, we dived into strategies, formulas, and problem solving.  We spent a few days on regular shapes before diving into the irregular ones.  I posed the problem as a challenge and let them struggle as a team.  Most groups figured out that they could find the volumes separately, then add them together.  

They had so much fun exploring volume.  Instead of just giving them the formula, I felt it was more important for them to have hands-on practice exploring exactly what volume means.

Who says math can't be fun?

Friday, November 21, 2014

But...that was intentional...

It's okay to disagree with a fellow teacher.  It's okay to not want to deliver a lesson the same way as another teacher. It's okay to put your own spin on things.  Some things should be the same (the assessments, the vocabulary, the definitions), but we aren't going to teach the same way.  That's okay. I have a difficult time following instructions or lesson plans verbatim, even when I'm the one who wrote them.  Don't get me wrong, I am always meticulously prepared for my day.  I just also take advantage of teachable moments.

However, I do get a little frustrated when it seems almost every instructional decision I make is questioned.  I've got a lot of background working with special ed kiddos and with the pacing of units.  Things are sequenced intentionally to help students make connections between background knowledge and new content.  The use of manipulatives (hands-on materials) during the first few days of a unit is quite necessary.  Students, even my fifth graders, need the concrete examples to investigate a concept.  They need experience in the concrete before moving to representational and abstract understandings of content.

We are starting division on Monday.  The standards quite explicitly state do not teach the standard long division algorithm. This is not to be introduced until sixth grade because students don't have the number sense nor mathematical understanding to reason through what is occurring.  

Here it is, straight from our professional development department:



I'm not really sure how much more clear this could be, but there were still debates about what it means.  

The first few days in our math unit has a lot of investigation by the students.  I'm giving them a bunch of paper clips to sort into smaller groups.  Some problems will divide evenly, some won't.  

I want them to tackle it. I want them to struggle.  Some kids will count those 48 paper clips into the groups one at a time, driving their partners bonkers in the process.  Some will make the connection to multiples and give away larger groups.  Some will use their multiplication facts to estimate the quotient.  Some will see division as repeated subtraction while others will see it as repeated addition up to the dividend.  

That's okay.

I want my students to understand what they're doing.  I want them to make connections.  I want them to discover how division is related to the other operations and take ownership over their strategies.

My math unit is scaffolded intentionally.  The first day is exploration.  The next introduces vocabulary terms, goes over making sense of the problems (hello math practices), and has student generated strategies.  Direct instruction doesn't begin until day 3 after students have had ample time to investigate sorting and making groups with paper clips and cubes.  From there, we'll move to hundreds grids and talk about regrouping.  We'll make the connection from the physical orange flats, rods, and cubes to the paper versions and drawings, thus moving from concrete to representational. From there, we'll move into number based strategies that build upon other operations, powers of ten, place value, and multiples.  Again, scaffolded from representational drawings and grids to strictly numbers (abstract).  There's a plan.  It took hours to design, but I'm really excited about it. The plan, which spans thirteen instructional days, scaffolds so students will feel successful and anticipates common misconceptions.

However, another teacher entirely disregarded the plan...and told me about it, gleefully.  She had them try one problem with manipulatives and then gave them the algorithm.  I'm so disappointed and feel sad for her students.  I'm sad they lost the opportunity to make their own discoveries. I'm sad they lost the chance to feel ownership over the concept. I'm sad they lost the opportunity to have a meaningful struggle with the tasks.

Her justification? They'll learn it next year and she's doing the sixth grade teachers a favor.  Besides, the standard algorithm is just faster.

I'm aware it's faster.  Faster yet? Whipping out my phone and using its calculator function.  But what's the point in that?  What do they learn when they're just handed the short cut?

I'm standing my ground on this one. My goal is not to teach math.  Yes, you read that correctly.  My goal is not to teach math.

My goal is to have my students understand math.  I want them to know what they're doing, why they're doing it, what happens to their numbers, and why their problem works out mathematically.

I'm making critical thinkers and problem solvers, not robots.  I'm aware it takes more time, but this mindset also encourages stronger students and that's my ultimate end goal.

Sunday, November 2, 2014

Table Solving

We like to switch things up in my classroom.  A majority of my math block is spent with students collaboratively solving problems and discussing them.  I pull a small group a few times a week during their independent work, which is usually for about ten minutes.  I give 5 problems or so and get through 2 with my small group (that's ok).  I think they should be collaborating during math time.

While not everyone agrees on my math practices, I'd rather have my students solving challenging problems together and talking about strategies as opposed to the opposite: always silently working in ancient text books.

We are in the midst of a long weekend (thank you Nevada Day followed by 2 staff development days), so I gave a math test on the Thursday before the weekend.  On Wednesday, we played jeopardy.

In the past, I noticed that some students were being passive participants, merely smiling and letting their tables do the work.  Not coincidentally, these students weren't doing so great on their tests.  So I let my students pick their own groups and limited the number of students to 4 rather than 6.   This helped with engagement and participation.  True, there were a few students who still didn't want to work but instead of me harping on them, their teams did.  Nothing like some positive peer pressure!

Instead of having them solve on white boards, I got large sheets of butcher paper for each group.  We also used markers because that always seems to make math more exciting!  

They had a great time working together to solve multiplication problems!



On a post-grading note, I had higher scores on this test than previous ones!

Saturday, October 4, 2014

October

I'm a firm believer that school, especially elementary school, should be a fun and welcoming learning environment.  Since moving over to my new school, this mindset has grown because it's supported building-wide.

I checked with my students and since all celebrate Halloween, I put up a banner on the board.  I gave them new class jobs and the assignment sheet is orange.  The librarian is buying each classroom a pumpkin for us to decorate as a class with a book character.  Since we're reading The Lightning Thief as our class read aloud (and loving it), I'm hoping to steer them toward a Camp Half-Blood pumpkin. 

Our lounge was decorated with the most adorable Halloween signs and there was a feast of treats Friday morning.  I keep forgetting that the first Friday of every month is a brunch, so it's a pleasant surprise to find an assortment of homemade goodies awaiting me in the morning.  Our grade level is responsible for March's surprise, so we've got some time to think of a theme.  Although I'm seeing lots of shamrocks and green things on our table!

We are about half way through our math unit on decimals (NBT 3, 4) where we are focusing on rounding, reading, and ordering decimal place values to the thousandths.  I decided to take a day to do math games while I pulled small groups for reteaching.  I set the timer for 15 minutes for each game, went over the materials and expectations for each center, and allowed the table teams to pick.  For our first time, they did an awesome job treating my centers with respect and cleaning up after themselves.  I was very pleased with their respectful attitudes and how excited they were to talk about math.

For privacy concerns, I won't share the pictures because my students' faces are in them.  However, they had an amazing time playing.  I walked around and listened to their math conversations and they did such a great job coaching one another.  Many groups, without prompting, were explaining their thinking to each other.  Sometimes they can explain concepts in a way that makes sense to each other and as long as my kiddos understand the math, I don't care who they learned it from.  Plus, when they can explain their thinking, it shows me that they've truly mastered the content.

Some of the activities I made, but some I found on TpT.  The next two freebies were awesome and these hard working educators deserve a virtual high five! Thanks for making great activities to help students learn.

Here were some of the centers we played:

Spooky Sort, made by Jennifer Findley.



They sorted by the underlined place value, then put the cards in order from greatest to least.  If they had time left over (we used a timer), they played war with the cards.

Decimals to the Thousandths, made by Allison Harig.



They had some awesome discussions about math.  I love that one table had two students really struggling with comparing, so they chose to do this activity twice during the rotation time to make sure their classmates understood the concept.  

What's even more exciting is I found more cute standards-based games for the next math topic!  My fifth graders, while they might not admit it, are loving these festive fun learning activities.  Who says kinder should have all the fun?

Monday, September 1, 2014

Day 5

I made it to Friday!  



I did start my morning with duty...I'm not a fan of the gate.  I picked up my kiddos, took them off to Art, then planned math with another teacher in my grade level.  We had a grade level meeting yesterday and split up who is planning what subject.  This is an adjustment for me. Instead of planning everything, I'm planning one subject, writing up super explicit lesson plans, and making the copies for the grade level.  So far, I'm liking it!  I still read over their lesson plans and put my own flair on them, but it's nice that collaboration and team work is the norm for my grade level.

After I picked my kiddos up from specials, we jumped right into math.  For our number talk, it's "fact Fridays" where I gave them their first timed multiplication test.  

Last year my grade level split up multiplication and division facts into "easy", "medium", and "hard" facts.  We made 3 different versions of each test and would give them a chance every other week.  Today they had 3 minutes to do the easy multiplication ones.

Easy facts: 1, 2, 5, 10
Medium: 3, 4, 9, 11
Hard: 6, 7, 8, 12

Of those, about 6 of my students passed their easy facts on the first round.  I'll be making a tracker to glue in their notebooks and a brag wall similar to this:



For them to sign off when they pass each level.  Granted, this is a third grade standard, but many of my students don't have these facts mastered (yet!).  We'll alternate testing and practice weeks.

From there, I had them compare notes on what a good mathematician is before adding their thoughts (on post-its) to our chart:

 
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We also went over the first math practice (make sense of problems and persevere in solving them).  I had them record it in their math notebooks with sticky labels and added the chart to the wall.  I didn't want to put up all 8 without going over them because then students have no connection to what's on the wall.



I also raided another teacher's classroom and found the rods I was looking for!  I modeled that the rods and units represent tens and ones in this case, but made it clear this won't always be the situation.


I had the table teams model 43-29 for me using the manipulatives and they did a pretty good job.  I think most of our math this year will be hands-on because there are some major gaps to fill.  However, after talking with my grade level, I'm not the only one who feels this way so that's nice we're all wanting to give them meaningful practice to help make sense of numbers.


In science, they finished exploring the mystery bags and we had a conversation about all the skills they practiced.  They did a really good job with their team building task.

In writing, they finished their final drafts (which I accidentally left at school...Wednesday problem).  In reading, they took their STAR test to place them for AR and worked on building their stamina in silent reading until everyone was done with writing.

From there, I modeled the importance of previewing a text, again using The Lightning Thief as my mentor text.  I jumped right in and read, without modeling metacognition or stopping to think aloud parts.  A few pages in, they were confused (as they're supposed to be).

We talked about strategies that good readers use, one of them being to preview the text.  What this means is they need to look at the front and back covers, as well as the table of contents, to formulate an idea of what the text is about.  

I then had them practice with a book of their choosing, modeling on a post-it.

We reviewed phrasing and went over rate, adding to our charts in our notebooks.  We'll go over expression and accuracy next week.  We'll also go over buddy coaching and have some fluency practice before we take our beginning of the year Aimsweb benchmarks.

With the bell approaching, they did their classroom jobs and I sent them on their way with this:


They o-fish-ally survived their first week! It's Labor Day weekend and we have a staff development day Tuesday, so I won't see them again until Wednesday.  

One week down!

(On a side note, I did have to write my first citations and lock myself out of my room on Friday. I also forgot to send home last year's CRT scores, so I stapled apology notes to parents and those scores will go home Wednesday.  There were definitely moments of frustration on Friday, mainly due to me forgetting things...so a nice relaxing birthday dinner with B at Red Robin was so deserved!)


Happy birthday to me! (day 4)

Day 4

I really didn't get much done before school because people kept popping into my room to wish me happy birthday, which I thought was very sweet.  My new grade level brought me balloons and cupcakes, along with decorating my room.  Wasn't expecting that from a team I've worked with for basically a week, but it's great to feel so welcomed.

In math, we talked more about persevering through problems, did our number talk, then I introduced them to one of my favorite math games 20 wins.  Basically they are placing digits (0-9) into boxes and trying to make a square equal 20 with any operations.  For the first day, I modeled with me against them before letting them try with a partner.

 

We came back together and talked about strategies that were used:



While they played, I walked around making observations.  For the most part, my class seemed very comfortable with addition strategies.  A few groups tried multiplication to make 20.  They'll play again tomorrow and their weekend homework will be to play with a family member.  I don't think I'll have much trouble getting them to want to play math games.

What they don't realize is how much math they're doing.  Yes, they're adding for the most part. But they're also thinking strategically and looking for patterns with numbers.  They're having to predict what their partners might do and prevent that from happening.  They're using multiple operations, practicing order of operations, and often times trying several different strategies until they can make 20.  I love tricking them into learning!

After that math fun, we went over phrasing with fluency.  I had them do a sort with their table teams to pre-assess them and for the most part, they know what fluency is so I'm not starting instruction from the beginning.  Of the four components of fluency (rate, expression, accuracy, and phrasing) I decided to model one.  If I modeled all 4 in one day, they'd be bored and probably confuse the components.  I'd rather go a little slower to make sure they've all got it.

I modeled several different times (incorrectly) and had them give me feedback.  They did a really good job with picking out the errors.  We made a chart together in our notebooks before moving to the carpet for today's skill lesson.

I modeled metacognition, which is thinking while reading, using The Lightning Thief.  The first time I read, I modeled great fluency.  Afterward, I asked them how I did to which they responded great!  Then I let them in on a secret: it's not enough to just read the words.  You've got to think about what you're reading.

I modeled again, this time tapping to the book whenever I was "in the text" and tapping to my head, modeling a think-aloud, whenever I was practicing metacognition.  I had two students keep score:



We talked about how we have to think while reading.  Some of them got it, some didn't.  That's okay, it's day 4.  We've got time. 




We also went over what it means to be a good reader, which was part of their homework:



I'm trying to color code my anchor charts (reading being teal) to help my students.  We'll see how long I can keep up this goal!  I had them brainstorm independently, talk as a table team, then add their thoughts on post-its.

In writing, they're continuing to work on their letters to self.  In science, they're having a great time with the mystery bags.  I also had them draw pictures of what a scientist is:



Then we had the conversation that women can be scientists too, since many drew men.  I talked about how I am a scientist whenever I step into the kitchen.  I am a chemist, hoping my ingredients combine the way they're supposed to.  I have to be accurate in my measurements and ensure my oven is preheated to the proper temperatures.  I test my experiments by eating them :)  I also shared that of the real chemists I know, the highest ranking ones are women.  This was very surprising for them but part of my job is to destroy their gender stereotypes about scientists.

All in all, it was a great day.  My biggest concern so far is I've had to move one student's desk twice already, but I think that's just an adjustment back to school and realizing my expectations of listening to instructions the first time they're given.  

Four days down!



Friday, August 29, 2014

Day 3

Day 3.

Also known as the day I pissed off most of my students, on purpose.

I didn't plan to irritate them.

We did our number talk and it involved a subtraction problem with lots of regrouping.  After walking around and seeing my students' answers, I noticed about half of them got the answer right. Others were having calculation issues or subtracting from left to right and getting all confused.

So I started the problem and asked what my next step was (it was regrouping).  The answer I got was to add a "1" to the one's place.  I asked if I was adding one or ten. I was told one.  I asked where this one came from. No one could tell me.

Face palm.  This does not bode well for math this year.

So we stopped solving the problem.

I gave them a two digit subtraction problem instead: 51-37.  Almost all of them got it right with the algorithm.  I saw one student try with a number line (yay!).   Then I modeled the problem with manipulatives (rods and cubes).



I explained that when we are regrouping, I'm not adding numbers out of no where.  I'm taking a set of ten from the next place value and redistributing them.  I wish I had these to use to show them actually breaking apart a set of ten:



But alas, I don't.

I gave them another problem to solve, both numerically and with a picture.  Most of them got it right using both ways.

Next week we'll go back to larger place values.  We'll also use manipulatives because they don't have enough hands on experience with making groups.  I've got some large gaps to fill!

After math, I asked them how they felt using this system:



Most of what I got in response was this:



They aren't there yet.  They told me they need more practice.  I told them good.  

I got a lot of confused faces.

I told them that in math, they aren't going get the concept on the first day. I told them I'm going to require multiple ways of thinking about the problem.  I told them they're going to have to prove they understand what is happening with the math, not just show me the right answer.

Many of my higher students are not happy with this challenge.  

To them, I say good. They'll be better off in the long run.  I had some grumpy math faces today!