I'm so confused!!!

Being new to the empty nester world, it's time to work on my bucket list.  One thing I have always wanted to do is learn how to play the guitar.  My lessons started a few weeks ago.

At the end of the first lesson, I left excited and inspired, playing a few notes.  That quickly changed. During the second lesson, my instructor was zooming through the content or so I thought.  I left confused and overwhelmed.  As I tried to practice at home, I struggled.  The practice pages looked like a foreign language.  What happened?

When I got back together with my teacher, the first thing I did was tell her that we needed to slow down.  I asked lots of questions and the guitar teacher had an "ah-ha moment".  You see, I have absolutely no musical background - zippo.  As she answered my questions she realized I could not differentiate between notes and chords.  Heck, I couldn't even keep the notes straight.

This experience really helped me to resonate with my students on a whole new level.  How many of them are confused?  Would a student raise his or her hand and announce, "Excuse me, Mrs. Martensen, but this is going too fast and we need to slow down."  Meanwhile others may be thinking, "I know this already.  Let's do something else."

As I collaborate with teachers, we very purposely plan with the lens of making the learning accessible for all.  We talk though the lessons with our student population in mind - who needs strategy work with concrete models, who is ready for the task to be extended to a deeper level.

To support our work, I have created "menus" of instructional moves to either scaffold or enrich the lesson.  These menus are tools to guide our planning.  We pick and choose the strategy or strategies that we think will support student learning.  Note I said, "we think".  We all know the importance of a back-up plan.  The other strategies that we did not initially choose from the instructional moves menu can be folded into the lesson where needed.

The rewards of our planning are so powerful.  Students' learning is centered on their zones of proximal development.  They are not only learning, but exhibiting confidence and expressing that they are having fun, too.  Yahoo!

Keep in mind that this planning goes hand-in-hand with continuous formative assessment, but I will save that for another blog post.

Please share your strategies for meeting the varied learner needs in your math classroom.  We all learn from each other.

Comparing Fractions - The Fourth Grade Discovery

I have been collaborating with teachers as we plan to make learning accessible to all.  When it comes to fractions, this is a real challenge.  I've really been grappling with why fractions are so challenging for our students and what we can do to support this learning.

The other day a teacher I was working with asked her class, "Are fractions numbers?"  To our complete surprise about a third of the students did not think they were numbers, but that there were numbers in fractions.  So with that misconception in mind, our fraction lessons have centered on concrete visual models and discovery.

In the world of nine and ten year olds, fraction exposure is so limited.  Yes, they hear about a 1/2 price sale or 3/4 of a mile, but their world thus far has been filled with whole numbers.  Their fraction understanding is in its infantile stages.

Hence - concrete models.  The students' tools include fraction bars, compliments of Math Coach's Corner and fraction number lines.

Our plan was to start by introducing the comparison of fractions with the same denominator.  We thought this would be a quick review.  Not!  The students actively used their tools to determine the size of 2/6 as compared to 5/6.  Yes, some quickly grasped the concept, but the majority of the children were relying heavily on their tools.

So we decided to take the approach of coming up with a theory and then testing this theory out.  The students noticed that the denominators were the same.  Then after several trials, they were ready to write a rule:

Next we posed comparisons with the same numerator:  3/4 compared to 3/10.  Again we took the same approach.  We asked the students what they noticed.  They developed a theory, tested it out several times using their tools, and eventually created a rule:

Yes, this took some time, but time so well spent.  The children really persevered and made the discoveries on their own.  As they realized their theories were actually strategies for comparing fractions, an air of confidence filled the room.

At the climax of this two day lesson, a student came up to the teacher and said that she use to not like math, but now she likes it.  Priceless!!!

I am learning so much from the kids - they need visual models, time to explore, discuss, and discover, and lots of repeated practice.  What do you do to foster fraction fundamentals?  Please share your ideas.  We all learn from each other.

Bedtime Math - There's an app for that!

We've all heard countless research on the importance of parents reading to their children.  The question is what about math?  NPR just published a captivating article on just that:  Where the Wild Fractions are: The Power of a Bedtime (Math) Story.

A University of Chicago study suggests that parents doing math with their kids can help to strengthen their kids' math achievement, even if it's as little as once or twice a week.  The article goes on to highlight  the Bedtime Math app, as the place to go for parents to do some math with their children.

So I checked it out and here's the run down:

1.  It's a FREE app!

2.  The problems are organized into levels:

• "Wee Ones" for preschool kids
• "Little Kids" for Kindergarten through Grade 2
• "Big Kids" for Grades 2 and onward (in my opinion it's mainly Grades 3 -5)
• "Sky's the Limit" for really big kids and grown-ups

3.  Each math problem starts with a little story to set the stage, many with illustrations.

 4.  There are three buttons to choose at the bottom of the screen:  Wee Ones, Little Kids, or Big Ones.  All the problems connect with the story scenario and the questions build off each other.  This is perfect for the parent that is sitting with children of different ages - the kindergartner gets to work on the Wee One questions and the 2nd graders tackles the Little Kids questions, all enjoying math together.

Wee Ones

Little Kids

Big Kids

5.  The answers are given - just click on the star!
6.  Sometimes, when the answer is given animations or a bonus question appears.
7.  On the average, there are three new math problems posted per week.  Plus, parents can opt to receive an email for new daily Bedtime Math Problems (just click on the envelop on the home page).
8.  By clicking on the "sorting" link, problems can be sorted by date or by title.
9.  If you click on the star listed before the title of the math problem, it goes to your favorites.  This makes it easy to go mark the problems you want to revisit another time.
10.  Lastly, you can sort the problems by categories.  Animals, nature, sports are just a few.

Of course, the best part of this "bedtime" math routine is sparking a discussion about the math. Asking an open ended question strengthens the child's reasoning skills.  For example:  What the problem asking?  How did you decide to solve the problem?  Does your answer make sense?  What are some other strategies you might try?

Bottom line - It's so easy to use, it's an incredibly engaging way to do some math with your kiddos, and it's free!  So, parents, add some paper and a pencil with this app to your bedtime routine and watch your children's math muscles grow.

By the way, if apps are not your thing, there is a series of three Bedtime Math books available.  So start a new routine and do the math!

The Size of the Whole Matters

How to deepen students' fraction sense has been a real challenge for me.  Our fourth graders just started a new fraction unit.  Yesterday they focused on brushing out the cob webs by making some simple visual representations of a given fraction.

When students were posed with this question:

                 Kyle read 2/3 of his independent reading book.  Justin also read 2/3 of his

                 independent reading book.  Kyle said he read more pages than Justin did.  

                 Justin said they both read 2/3 of their books so they read the same amount.  

                 Who is correct?  

95% of the students said Justin was right.  The one student that questioned that said she didn't think he was right, but also added, "I really don't know."  

So the teacher and I put our heads together.  We used a LearnZillion Lesson as a spring board for our lesson.  

As we thought about posing this inquiry scenario, our goal was to make this learning accessible to all. It's one thing to see this visual illustration, but we thought we could really reach students by having them simulate the planning of these two gardens.  Manipulates were the answer!

As the students used the hexagons and triangles, the partnerships instantly embarked in engaging conversations about the value of the triangle in each garden.  

 

We, the teachers, really gave the students control of their learning and boy, did they run with it.  Themes included:

The students even went on to share that Meg's garden would need to have 2/12 planted to equal 1/6 of Sam's garden - and we have not even introduced equivalent fractions yet.  

Of course, the true test is when students can explain their reasoning independently.  

So as I reflect on this lesson I know that making these fraction lessons as hands-on as possible will make the learning as accessible as possible for all learners.

Stay tuned as we continue our journey to deepen fraction understanding!

How do we deepen place value understanding when using the standard algorithm for addition?

This week I joined some fourth graders as they tackled missing digit addition problems.  Prior to this lesson, they had spent a great deal of time on both their place value understanding and strengthening their use of the standard algorithm for addition.  The new goal was to apply this place value understanding as they added multi-digit numbers using the standard algorithm.  I was in awe over how they persevered.

To start the class, the teacher asked the students how they felt about the homework that had done the night before, which was an introduction to the missing digit problems that are highlighted below.  Most comments were negative:

• "I struggled with it at first."  
• "It was challenging without the teacher to help me."  
• "It felt tricky...when I had to carry."  
• One student said that he tried and put a mark where he was unsure so he could ask today.

What raw honesty from these mathematicians!  We are three weeks into school and they felt secure enough to share their challenges.  Bravo to the classroom teacher for establishing such a nurturing and warm classroom community.

The teacher then selected several problems for the students to grapple with, starting with a simpler 2-digit by 2-digit addition problem.  The students worked to solve it on white boards.  Yes, white boards are an engaging tool and it's so easy to erase when you change your thinking.
                                                     

    The teacher certainly facilitated the discussion, but all the thinking came from the students.  They verbalized how they needed one more in the ones place to make eight and some had to pause to think about how they could make thirteen tens (or three tens and one hundred).

The next problem upped the ante.

They shared their ideas around place value and the need to "carry" one group of ten , if they had 17 ones.  As students shared their thinking, other students took it all in.  At this point the student who had originally marked where he got stuck on his homework, raised his hand to share.  YES!

Then they moved onto three digit numbers.  In this situation, three different answers surfaced among the students.  The white boards offered instant feedback on who was challenged with carrying a group of ten.

We can all learn from misconceptions.

Students shared how they knew 6 + 4 = 10, but were still not sure how to show that because they were not considering that they may also need to continue to carry to the hundreds place.  The idea of adding your own box to carry resurfaced.  Another idea that came up was checking your work with subtraction.  The students were justifying their thinking and learning from each other.

When the students went off to work independently, the task involved adding four and five digit numbers with missing digits.  No student wavered.  They were deeply thinking about place value and some continued to try out their thinking on the white board before putting the pencil to paper.

As I observed students working, I notice two students had made different errors on the same problem.  This was a perfect opportunity for them to continue to learn together.  The two students talked about the place value of each digit and both "discovered" their errors as they explained their thinking. They were really taking ownership of their learning.

As the teacher gathered students back together to share their new learning, the energy and tone of the class had completely changed.  Many felt empowered by working through this struggle.  In turn, they had deepened their understanding of place value.

In the end the teacher reminded them, that when they learn something new, it can be hard, but to stop and think, "I may not understand it yet."  I loved the word, "YET" - this is the growth mindset of this classroom.

What are some ways you offer your students a productive struggle as they deepen their understanding of place value.  Share your ideas.  We learn from each other.

                                               

Fostering the "Can do!" Attitude

The other day I brought my daughter to college.  This leaves my husband and I labeled as "empty nesters".  Several years back when her brother went off to college, I ended up on blood pressure medicine.  So I was expecting this move to be rough to say the least.

I am thrilled to report that this time around it was an amazing experience!  I embraced the day, savoring the countless opportunities I saw unfold before us.  To my complete surprise, for the last couple days, rather than looking in her room with sadness, I have been filled with such a feeling of joy for her.

Those of you that know me are thinking, "Is this Lori talking?"  I have always been the person that does not welcome change.  This new found thinking really caused me to pause and reflect about how it came to be.

I can honestly say that the change in my mindset has evolved over time - a real process.  What influenced me?  I am surrounded by some dear friends and colleagues that have showed me how to welcome these new experiences.  I guess you could say that they've really rubbed off on me.

This brought me to thinking about kids who say or think, "I'm not good at math."  We all have them.  Heck, we have adults around us singing the same tune.  So how do we influence our students' mindset?

In my blog post, Tackling the Summer Slide, I discuss encouraging young mathematicians by using the language, "I'm still learning to..."  As I have worked with students who have tried out this phrase, I could actually hear a lighter tone in their voices as they say it.  They feel empowered to have permission to express that they are working on their learning, rather than having a feeling a defeat.  But what else can we do as educators to foster this growth mindset?

Making sense of problems and persevere in solving them is the overarching habit of mind in the Common Core Math Practices.   Last year I witnessed students in both primary and secondary grades who could not persevere.  They believed that they could not do the math without teacher help.

The teachers and I worked together over several months to influence their mindsets.  Our strategy was three-pronged:

1. Use read-alouds and class discussions about these stories to help children start to build awareness that we can all learn and that making mistakes is a big part of learning.
2. Use ongoing think-alouds when modeling math to help students see what it looks like to be stuck.  Show them how to pause and think about what you know or what tool you could use to help you.
3. Create an anchor chart with the students, highlighting the tools and moves they can use to help themselves when they feel stuck.  

In the primary grades, students quickly connect with these stories about the importance of determination:

Try and Stick with It by Cheri J. Meiners, M. Ed.

It's hard to try something new.  When things get tough, the characters take us on a journey filled with flexibility, perseverance, and the importance of sticking with it.

I Can Do It!:  A First Look at Not Giving Up by Pat Thomas

The message in this book is about trying your best when you attempt something new and not being afraid to make mistakes.

If Only I Could! by David and Mutiya Vision

The child in this story gets frustrated when things don't go her way. Surprisingly, her baby sister teaches her the importance of perseverance.





In the secondary grades, these titles foster powerful discussions around perseverance:

The Most Magnificent Thing by Ashley Spires

A girl sets out to make something magnificent.  When things do not go as she hopes, she becomes discouraged and quits.  Her dog and faithful friend helps her to realize the importance of perseverance.

The Girl Who Never Made Mistakes by Mark Pett

Beatrice Bottomwell never makes mistakes.  When she ends up making a mistake for all to see, she learns that it's not a big deal to mess up.

Butterflies for Kiri by Cathryn Falwell

Kiri get frustrated that she cannot make origami butterflies.  She perseveres and through her creativity and determination, she learns more than just how to make butterflies.




When modeling in a second grade class, I let the students witness my struggle with adding coins.  Several students were quick to give me suggestions on what could help me - the coin chart, the one hundred chart, or the coin manipulatives.  At this point it was easier for them to offer someone else help because they did not personally "feel" the struggle.

Yet this discussion naturally led to charting the tools that can help us.

With the anchor chart in place, the students interacted with the chart to help them start to build their perseverance muscles.  They took ownership of their learning, and the confidence building was so evident.  Some students did continue to quickly come to the teacher and the teacher simply pointed to the anchor chart, redirecting the student.  

Yes, it is a process and each child moves through this process at his or her own rate, just as it's taken me a long time to start to embrace change.  The important thing to remember is that we are all growing.

Please share strategies you have found to foster positive thinking and perseverance with your students.  We all need to keep adding to our tool box.

The Secret Power of Pre-Assessments

In the first few days of school in my district, two teachers have already approached me about how they can meet the varied math needs of their students.

I have always found pre-assessments to really inform my instructional decisions.  It gives me a good gauge on what the students already know and where to focus my teaching.  However, last fall I was fortunate enough to attend a conference given by Rick Wormeli, and he helped me to realize that I wasn't using this valuable tool to its fullest potential.  He spoke about how to involve the students - to give the pre-assessment BACK to the students.  Wormeli said that it "puts important content on students' radar to prime the brain for learning".  I had really never thought of that!

When co-teaching with classroom teachers, we have adopted this practice and I am thrilled to report that the impact has been astonishing.

In each class, differentiation decisions were based on student evidence from the pre-assessment.  This student data drove our planning decisions around how to vary learning for students to meet their individual needs.  This was a continuation of our traditional practice.  What was new was how the students used their original mistakes to strengthen their learning.  In a fifth grade class, the students were given back their pre-assessments throughout the unit.  Each time a new concept was taught and practiced, students independently corrected errors relating to that concept on their pre-assessment.  They could instantly reflect on their growth.  In a third grade class, the students were given the pre-assessment back at the end of the unit as a review.  Again, they made corrections with confidence, giggling at the mistakes they had previously made.

What a powerful way to use this tool!  It informs my instruction, enabling me to see who needs additional support and who needs enrichment.  Equally as important, it truly fosters students taking responsibility for their own learning in a reflective manner.

I wish I had discovered this strategy years ago.  Thank you, Rick Wormeli!

What tools do you use to promote reflective learning with your students?  I'd love to hear your ideas. We learn from each other.

Tackling the Summer Slide

Hello and welcome to my blog!

Colleagues, friends, and especially my daughter have inspired me to join the blogging world, sharing my experiences as an elementary math coach.  I am starting my third year as a math coach, working with teachers from five schools in my district.  I love being able to join a variety of grade levels, working collaboratively with classroom teachers and students.  We learn together.  I especially learn from the kids.  It's so rewarding!

In this role, I am constantly learning - different grade levels, adopting curricular changes, keeping up with the latest research.  This blog is another way for me to learn and grow.

As I drove my daughter and her friend to the beach yesterday, I heard a saddening comment from the back seat; "I feel so stupid when I go back to school and have math.  I don't remember how to do things."  In those first few days of school we've all seen the "summer slide" quickly become evident.  The saying, "If you don't use it, you lose it," is ever so true, especially when it comes to math.

So how do we brush out those cob webs and encourage a positive mindset with our new mathematicians?  For me it's all about being positive about math and making the math fun, hands-on, and engaging!  Confidence is built with opportunities for success.

The teacher's positive attitude about math sets the stage.  As students start out, I often hear, "I don't know that" or "I don't remember that."  I quickly respond with "I am still learning to ..."  Once the children start to hear this language, they quickly adopt it.  They want to be successful, and having a growth mind set starts to become the norm.

In the first few days of school, it's helpful to choose tasks and games that are both engaging and cooperative.  It can be as simple as partner math bingo.  I have done this activity using money, time, or a variety of equations. Partners work together using manipulatives and scrap paper.  We all learn from each other, bringing different strengths to the table.  Plus this gives students the opportunity to get to know or to get reacquainted with their peers.

Regardless of the day's math content, I emphasize starting the school year with reflection.  It's a time to build classroom routines.  What better routine than to self-reflect at the end a lesson.  I ask students to finish this sentence:  "Today in math, I learned, discovered, noticed..."  Some times I call on a few students to share; other times they turn and share with their partner.

As you plan for your students-to-be, I'd love to hear about how you promote math success to kick off the school year.

Happy Almost First Day of School!