Friday, November 30, 2012

Subtracting by Counting UP!

I find it amusing that even though we are already into our 64th day of school some of my student don't know what to do with the signs +, -. Well actually they do know what to do with those signs but the indecision on which one to use is complex in some of their minds. I began using the Subtracting by Counting Up strategy. This is an amazingly powerful way to subtract. Van de Walle in his book "Teaching Student Centered Mathematics" explains it as students working on the think addition strategy for their basic facts can also be solving problems with larger numbers. The concept is the same. It is important to use join with change unknown problems or missing-part problems to encourage the counting-up strategy he explained. I have noticed that although we have done many 2.OA.1 word problems that when I use the terminalogy "how many fewer did Jack have than Bob" or when I use a problem like Korryn has 9 dolls and Kate has 3 more dolls than Korryn. How many dolls does Kate have? My students come up with some amazing ways to solve this word problem. Many got it right on target but many were more than a little confused. I have begun to use the subtracting by counting up strategy and I hope on next weeks summative assessment I will see more students "get it". Does anyone else have this sort of problem when adding words or creating a word problem. They can actually add 9 + 3 = 12 but it seems with the CCSS terminology they get confused. I have been adding one to three of these each week and hopefully next week I won't have to omit it. YIKES!

Monday, November 26, 2012

How to Assess in a Problem-Based Classroom

One of the things I have learned as we have begun our journey with CCSS is that assessment can and does happen every day.  It is an integral part of my instruction.  I have gained knowledge through my readings of Van de Walls' book Teaching Student-Centered Mathematics, I realized that in the past I  missed the point.  Now I see how assessment has allowed me to help my students grow and how these assessments have informed and driven my instruction.

Previously,  I used assessment in test form and now I use a task or problem which allows my students to demonstrate what they know. Since my classroom has become more problem-based I no longer focus on assessments that require recall, skill, or closed response items that send a message to my students that getting answers is valued. Now I am focused upon engaging discussions and proudly watch as my students problem solve in teams.  I realize that even lower-ability level students should be encouraged to use the best ideas they have to work on a problem, even if their way is not the same skill or strategy everyone else in the room is using.

Ticket Out the Door has been a useful tool that has allowed me to see what student are thinking and how their errors were made.  I am more capable of assisting them in learning and not controlling their learning.  I love the TOD because it gives me a snapshot of what each child is capable of, the diversity among students or groups has guided my instruction.  I am enjoying the new things I am learning this year in math.  So keep an open mind, be willing to bend in the winds of change, and enjoy your students as they work to solve real world problems.  They are seeing the revelance of math in their universe.  They seem excited and engaged this year.  I can see the change that has taken place within my classroom and I like what I see.

Sunday, November 25, 2012

The Common Core Expectations

What a wonderful resource for teachers! These little books put out by McGraw Hill "The Common Core, Clarifying Expectations for Teachers & Students."  Align, Assess, Achieve, LLC or is the place to go to when purchasing this handy little resource. 

Our principle purchased one of these for each teacher that did the planning in that subject. One of us plans ELA first grade, one ELA second grade, one Math first, and one Math second. I must say that honestly this book is the best resource I have in planning.  They provide the cluster, standard, suggested Mathematical Practices, Enduring Understandings, Essential Questions, Suggested Learning Targets, and vocabulary.  Along the very bottom right of the page is the 2.MD.7 standard listed, on the page it is clarified and described.  These books are a must have in my humble opinion.

Please excuse my blog's appearance.  It is under construction and within a week or so it will be looking spiffy.  Check out these essential books if you are entering CCSS.  I absolutley love mine.

Sunday, September 2, 2012

So much to think about and so much to consider when planning a lesson. This is a very interesting read.  Just sharing thoughts and comments that are not my own.

Thinking Through a Lesson Protocol

By Margaret Schwan Smith, Victoria Bill, & Elizabeth K. Hughes

The main purpose of the Thinking Through a Lesson protocol is to prompt you in thinking deeply about a specific lesson that you will be teaching. The goal here is to move beyond the structural components associated with lesson planning (e.g., listing the materials you will need, describing the way students will be grouped, determining teacher actions during the lesson) to a deeper consideration of how you are going to advance students’ mathematical understanding during the lesson. This is not to say that structural components of a lesson are not important, but rather that a focus on structural components alone is not sufficient to ensure that students learn mathematics.

Selecting and Setting up a Mathematical Task
  • What are your goals for the lesson? What mathematical content and processes do you hope students will learn from their work on this task?
  • In what ways does the task build on students’ previous knowledge? What definitions, concepts, or ideas do students need to know in order to begin to work on the task?
  • What are all the ways the task can be solved?
    • Which of these methods do you think your students will use?
    • What misconceptions might students have?
    • What errors might students make?
  • How will you ensure that students remain engaged in the task?
    • What will you do if a student does not know how to begin to solve the task?
    • What will you do if a student finishes the task almost immediately and becomes bored or disruptive?
    • What will you do if students focus on non-mathematical aspects of the activity (e.g., spend most of their time making a beautiful poster of their work)?
  • What are your expectations for students as they work on and complete this task?
    • What resources or tools will students have to use in their work?
    • How will the students work -- independently, in small groups, or in pairs -- to explore this task? How long will they work individually or in small groups/pairs? Will students be partnered in a specific way? If so, in what way?
    • How will students record and report their work?
  • How will you introduce students to the activity so as not to reduce the demands of the task? What will you hear that lets you know students understand the task?
Supporting Students’ Exploration of the Task
  • As students are working independently or in small groups:
    • What questions will you ask to focus their thinking?
    • What will you see or hear that lets you know how students are thinking about the mathematical ideas?
    • What questions will you ask to assess students’ understanding of key mathematical ideas, problem-solving strategies, or the representations?
    • What questions will you ask to advance students’ understanding of the mathematical ideas?
    • What questions will you ask to encourage students to share their thinking with others or to assess their understanding of their peer’s ideas?

Sharing and Discussing the Task

  • Which solution paths do you want to have shared during the class discussion in order to accomplish the goals for the lesson?
    • Which will be shared first, second, etc.? Why?
    • In what ways will the order of the solution paths help students make connections between the strategies and mathematical ideas?
  • What will you see or hear that lets you know that students in the class understand the mathematical ideas or problem-solving strategies that are being shared?
  • How will you orchestrate the class discussion so that students:
    • make sense of the mathematical ideas being shared?
    • expand on, debate, and question the solutions being shared?
    • make connections between their solution strategy and the one shared?
    • look for patterns and form generalizations?
  • What extensions to the task will you pose that will help students look for patterns, make connections or form a generalization?

Smith, M.S., Bill, V., & Hughes, E.K. (2008). Thinking through a lesson: Successfully implementing high-level tasks. Mathematics Teaching in the Middle School, 14(3), 132-138.

Wednesday, August 15, 2012

Where Am I Taking My Students? How Will I Get Them There?

Oh my!  We learned so much today about planning our lessons and how useful it is to think about the larger, lasting instructional concepts as Enduring Understanding or the lasting understanding that exceeds the curriculum content.  I realize that Enduring Understanding is the ultimate goal of my instructional planning which my students will develop through meaningful engagement based on the carefully planned Essential Questions I will formulate.  These questions help my students dig deeper and make connections between content and concepts they are learning. I must focus on designing questions that spark inquiry that invokes a deeper connection for students between concepts and connections they are learning on a daily basis. 

I learned that there are four types of learning targets which are based on what I ask my students to do: Knowledge (K), Reasoning (R), Skill (S) and Product (P). These were adapted from Stiggins et al. Classroom Assessment for Student Learning.   I recognized that based on what I ask my students to do I must ask, "What is the goal of instruction?"  Once I have answered that question, I select a learning target or targets that will align with my instructional goal.

Instructional Goal                       Types of Learning Targets                            Key Verbs
Recall basic information            Knowledge (K)                                             Name, identify, describe
and facts

Think and develop an                 Reasoning/Understanding,  (R)                     Explain, compare and
understanding                                                                                                  contrast, predict
Apply knowledge and                Skill (S)                                                         Use, solve, calculate

Synthesize to create                    Product (P)                                                     Create, write, present
original work

So much to learn and so little time to learn it.  I am thankful that there are only four critical areas
in second grade math.  I have a lot more to learn especially when it comes to Quad D Moments.
Well I will save my study on that for another day. 

Saturday, August 11, 2012

Talking Points training your student to talk in Cooperative Learning Groups

Are you having difficulty training young learners to speak appropriately to each other during cooperative learning?  Do you have a source of questions to train them to use during whole group or small group discussions?  Have you looked at the Teacher Evaluation Rubric in your state to see what you will be scored upon? 

Tuesday, August 7, 2012

Classroom just about ready!

Oh wow things are coming together and my classroom is almost ready to welcome my new students.
Here are a few photos of what I have done so far.  Here are my daily folders...I am a frog collector in case you have not guessed that already. My school started my collection, when I became National Board Certified in 2002! They wanted to give me gifts and asked if I collected anything. My response was, "Yes I collect dust!" I had seen some ceramic frogs and loved them.  Someone gave them the information and I  have been hooked ever since.

Flipped signs (Daily Folder) are a gift from Ladybug's Files...thanks so much for that free download.  Here is my favorite frog of all times!  The Yellow Frog!

This is Ladybug Files' flipped numbers.  I laminated them cut them out and went to our district media center and ran them through the sticker machine.  Just peeled and stuck them on. Her flipped signs are so cute!

I saw this on Pinterest!  Car Riders, Bus Riders, and After Care signs I have clipped on the mini
pins and will write each students' name on a pin.  Great way to keep up with the changes in parental plans that happen throughout the day.  At a glance we know where they are going.

My math center with manipulative items.  Love pastels and I created my own flipped signs because my baskets were small.  So happy I am organized this year!

Finally my classroom "Supply Cake" another treasure from Pinterest.  I will change the ribbon on the top layer after I pick up something tomorrow.  I wasn't quite prepared, but it is still a cutie. I can't wait for my students to see it. 

Finally, my last Pinterest treasure was the dry erase board with lined scrapbook paper (looks like a sheet of notebook paper) inside a picture frame along with a little frog bow on the top right.  I forgot to take a pic of that today.  Well just sharing my classroom so far.  Almost done! Our students arrive on August 20th and we start on August 14th with in services for four days prior to the arrival of students. I hope everyone has a great year!  I am busy making lessons and creating items that implement CCSS.  I am very excited to start this new school year.

Saturday, August 4, 2012

Finally Found Pastels and Polka Dots

Today was my lucky day!  Tax Free day in our state, items on clearance, and an extra 20% off. I am not even a coupon lady.  I have been searching high and low for something like the trays below in plastic and I found them in tin. 

I recently found an item on TPT called Bucket Filler Compliment Starter and love the idea.
I was able to find the polka dot ice bucket below with the scoop and the napkin holder that will hold the little notes students will write on with a monthly starter for each month which scaffolds from
easier to complex.  This will be a great way to get writing in and teach my students how to compliment their fellow classmate at the same time.  I am going to put Flipped Signs on the bucket which I am going to refer to as Filling our Bucket with Friendship Scoops.  Fits perfectly with the
little silver scoop that dangles on the side.  The napkin holder with hold the squares of notes that
students will use to write their friendship scoop and fill our Bucket.  I know this will help my students share positive thoughts on each classmate. Back to school to finish up the classroom Monday and Tuesday because time is running out so quickly.  Have a great rest of the weekend,.

Thursday, August 2, 2012

One full week left! YIKES

Oh my where has all my summer gone?  We have one full week left and then we're off to a new school year.  I actually start back on August 7th with Master Teacher duties.  Therefore, although
the perimeter of my room is done....there is a center that is still very much undone.  I hope I get
it all done in 2 more days.  I am doing like Common Core...LOL...I am digging DEEP!  The hoarder of papers is actually going to throw all the old stuff.  The new assessments differ a lot from what will
be expected from CCSS.  Now to build up all those files of new items in new formats.  I have been
putting up all my flipped signs and Ladybug's numbers to 40 which I love because of the bright colors.  I definitely have a basket full of surprises for my new kiddies!  The 8 students I had last year in first (now in 2nd) will think they are in the wrong room.  Teaching two grades in the same amount of time most teachers have for one grade level is a challenge, but very rewarding.  I hope everyone has a great year!

Tuesday, July 31, 2012

I failed to put all the top beads on the right side when I took the photograph.  I noted it was important to establish the norm that all the beads should be on the right end of the string as the problem begins. The importance of this is that students learn that once the beads move from the right they become "in play" as they slide them from the right to the middle or left.

The suggestion is that the beads are moved in clusters whenever possible to do so.  To promote subitization by modeling sliding the beads in groups instead of counting them as individuals. Kinders would start with only 5 beads so that they can solidify the number relationships from zero to five.

When ten beads are used it is strongly suggested to use only two colors so that the focus is on five and ten.  Advanced students' Rekenrek can be extended to 40 beads which I will be doing with my second grade math class.  The emphasis is thinking in groups of 5 and 10 even as the numbers get larger.

The beginning demonstration should have all beads on the right side as you are facing it. Refer to this as orientaiton or "Start Position" and constantly reinforce that "Start Point" using the top row to demo to younger students.  Inquire what students notice about the Rekenrek and encourage all possible answers whether you hear 2 colors, some red, some white, five colors of each bead, ten beads in a row etc.  Some focus questions could be..."How many red beads are on the top line?" "How many beads are there in all?"  "Do you see more red beads, or white beads?"  It was suggested that after some open ended questions, inform the student to explore or work with the Rekenrek and come up with a discovery about the Rekenrek that they can share with their classmates.

Next, have them put the beads in start position.  Tell them without touching the beads count three beads in their mind. On the count of three slide all three beads at once across the string.  Do this with several numbers to encourage the movement of the beads in one push across the sting.  Okay more later....

I made one!

Well I tried making the Rekenrek and it will work.  The cost was $ 1.00 for the 6 x 9 whiteboard at Dollar Tree, red and white pony beads $ 1.97 for a pack of each color with 500 beads in them, and 1/4 inch elastic which is a great size because the beads are secure on the elastic which cost $ .97 for 4 yards.  I cut the elastic 15 1/2 inches long and tied it in the back.  It can be sewed too but didn't want to pull out the sewing machine after a long day working in my classroom.  Therefore the most expensive thing was the dry erase boards.  It could be slipped on and off like a rubber band when not in use and serve a dual purpose.  Here it is!

What I like about it is.....the students have the small whiteboard that they can write the
equation below the beads.  The little white board has the dry erase marker and eraser...I bought 5
boards just to see if it would work.  More time.


Monday, July 30, 2012

Arithmetic Rack or Rekenrek as noted by Math Coach!

I explored the Rekenrek or arithmetic rack when I read about it on Math Coach's Blog. I was impressed with the research I did on it this weekend.  After all, with Common Core we will dig
deeper allowing students to develop powerful understandings of numbers, the meaning of those
numbers, their relationship to one another, and of course how to operate with them. I noted from
my readings that counters, number lines, base-10 blocks and other manipulative items are limited, as a means of cultivating number sense, or to fostering a student's understanding of both addition and subtraction.

It was stated that the Rekenrek or arithmetic rack has emerged as perhaps the most powerful of all
models for young learners. This tool combines the features of the number line, counters, and base-10 models, and I think we can make them easily.  Math Coach had a model on her blog.  I thought about
the dry erase boards from Dollar Tree which are not really that big. I considered using those putting the beads on elastic that could slide on and off easily. Like killing two birds with one stone.  I haven't tried it yet, but I will check it out. I did find the racks online and some were as cheap as $ 5.00 and perhaps, when I get my school allocations I might purchase enough for my small group teaching.

I created the one above in my Smart Notebook and my students will be capable of manipulating it since I teach them how to group objects. They suggested one move to create a number instead of single sliding of  beads. It was suggested that the model could be adapted to accommodate varied levels of students.  Kinders will only need one string to 5. It was stated that the Rekenrek combines features of the number line, counters and base-10 models which makes it highly effective.

The strategy focuses on the highlighting of groups of 5 which offers a visual for early learners as they enter the beginning stages of understanding that one number may be a combination of two or more other numbers. As I created the model above, the student will visually see the number 8 as two distinct parts or one group of 5 and three more.  On the other hand a student that is more advanced may see the number 15 as a group of 10 and 5 more.

It was noted that using the Rekenrek which focuses on 5 and 10 is instrumental in helping children visualize numbers, seeing them as collections of objects in groups.  "This strategy of seeing numbers "inside" other numbers - particularly 5 and 10 - is a precursor to the development of informal strategies for addition and subtraction that students will naturally acquire through repeated use of the Rekenrek." Basically it helps students see numbers as groups of 5 or 10, "doubles" and so on instead of counting every object in a set.

For example, think of subitizing as the ability of the student to instantly recognizance quantities up to 10 without depending on the routine counting.  Using this in an example with the model above, 8 is subitized, and seen as two groups-one group of 5, and one group of 3.  I will share more as I read on and explore more complex decomposition of numbers. This information was taken from my reading of Rekenrek by Dr. Jeffrey Frykholm.  I find this read exciting and plan on using it with my 2nd grade math students. Well off to relax after a long day in my classroom with a few more to come before I am ready to roll!

Saturday, July 28, 2012

Here is what one would look like from another site. She may have posted that also. I am going to post the link so you can see what it would look like. It looks pretty simple to make and would be a great strategy for kindergarten teachers as well as first and second grade students.

I read an exciting post tonight from Math Coach's Corner regarding the Rekenrek strategy. She also showed how to make one on her blog.  You can click on my sidebar and go to her blog to see how she did it.  We talked about making ten bracelets in the math workshop but this is pretty much the same except it uses two rows of tens instead of one. Very interesting concept. I purchased the e book so I will let you know more about it.  Math Coach also posted a link to free lessons check it out. Click on the picture below and if I did it properly you will get free lessons.

Baskets, baskets, baskets are getting me organized

I have been to my classroom twice recently once to place my math items into these cute little baskets. I searched and searched to find the larger baskets to put my home to school folders into, but no luck so far. I hope to print Ladybugs flipped labels soon and can't wait to put them on the baskets. I love, love, love the pastels. If anyone knows where I can get the larger baskets like Ladybug showed today on her blog hit me with the information. I am very new to blogging....BRAND NEW!