What is Computational Fluency

February 7th, 2010

Hi everyone,

Recently a great conversation regarding computational fluency flew across the internet highways. I thought it was worth sharing with all of you here on this blog  I’d like to start by sharing a quote from the National Math Panel Report that encapsulates the essence of  the growing body of research calling forth discussion around this topic.

“The mathematics curriculum must simultaneously develop conceptual understanding, computational fluency, and problem-solving skills. The development of these concepts and skills is intertwined, each supporting the other and reinforcing learning.

Teachers can help by providing students with sufficient practice distributed over time and including a conceptually rich and varied mix of problems to support their learning. In addition, teachers should encourage and support students in their efforts to master difficult mathematics content. Students who believe that effort, not just inherent talent, counts in learning mathematics can improve their performance.”

For more discussion on this topic, I’d like to point you to another great resource. The very first newsletter on the Teacher to Teacher website (October 2008) was called Developing Computational Fluency. I’d encourage you all to check it out and also read through the question and comments below.

Do you have any other questions or comments that haven’t been explored here?  I’d love to hear your thoughts on this topic. Please post your comments or questions below.

Now, here is the question as it was originally posed:

From: “Hall, Kathryn B (TDO Eng.)” <kathy.b.hall@hp.com

Hi –

I am working with the elementary teachers in Lebanon throughout this year to help them transfer their instruction to the new standards, work on concept retention, and make sure that the focus of their curriculum are the new standards and focal points. They have a question for OMEC that I’ll bet occurs in many other districts.

What does “fluency” mean? How is it measured?  For example, there are targets for reading speed (40 wpm, 100 wpm, etc. that grow as the grade grows). Writing has targeted length of essays, by grade. Math just says “fluent” in multiplication, or addition or whatever, depending on the grade.  It is clear that different teachers have wildly different ideas of what fluent means.

What did the authors of the standard have in mind with this phrase?

Kathy Hall

The rest of this blog is devoted to sharing all the comments that came in regarding this topic from OMEC members and other math professionals from around the state.

Hi Kathy,

I do not have a precise answer.  I don’t like a quantitative measure like 50 facts in 2 min. as that assumes fluency for the fast thinker/writer who in fact may be counting in his head or on his fingers, and assumes non-fluency for the slow methodical kid who can’t do anything quickly, but may be fluent in his thinking and strategies.  To me fluency implies a non-effort comfort.  I can find the answer using my strategies and it isn’t a problem. Non-fluency would imply a struggle, that finding the answer is work. Perhaps our progression is in the skills–addition facts in first (or at least most of them), subtraction in 2nd, multiplication (most) in 3rd, all mult. and div. in 4th, expand this knowledge to decimals in fifth. Just thinking as I write. I personally hate the idea of time as it penalizes the slow thinker, also the ADD or ADHD if the task is more than about a minute as they can’t hold concentrated attention under stress for very long. I’m sure you hear my special ed. bias.

Kathy Reed, Retired Teacher and Math Consultant

Hi,

I totally agree with your thoughts Kathy. For kids, taking out the writing piece is very important. As math TOSA in my district, I have been helping with first grade fluency interviews. If they KNOW it, quickly (verbally) or use a  smart, quick strategy like our  district adopted material Bridges teaches—I think that is fluency.  Just had another thougtht. When I taught 3rd grade, we used a rule of  3 seconds per problem. Somewhere I heard someone important say “they should be able to do the problem in the time it takes to say the problem—like five plus seven is —-12.   Hope that helps.  I will ponder this some more and get back to you if any more thoughts occur to me. :-)

Jane Osborne, Hood River School District Math TOSA

Hi Kathy,

I have been working with teachers and ODE folks to help write items to the 3rd grade standards for 2007. Fluency has been a tricky one to write to because it does mean exactly what you said, that students no longer need calculators to help them to quickly recall their facts, be it addition, subtraction, multiplication or division.

If you look at the Number and Operations, Algebra and Data Analysis standard, 3.2, in Oregon, it uses verbs such as: represent, apply models or apply increasingly sophisticated strategies based on the number properties to solve multiplication problems involving basic facts.

In the Test Specifications for grade 3 (page 4) it says:” Central to this Standard is the development of number sense – the ability to decompose numbers naturally, use particular numbers like 100 or 0.5 as referents, use the relationships among arithmetic operations to solve problems, understand the base-ten system, estimate, make sense of numbers, and recognize the relative and absolute magnitude of numbers.

In these Standards, understanding number and operations, developing number sense, and gaining fluency in arithmetic computation form the core of mathematics education for the elementary grades…”

So this is looked at as a holistic approach to arithmetic and mathematics. Check out the Curriculum Focal Points from N.C.T.M. and you will see the same approach, using the terms “developing understandings of multiplication and division and strategies for basic multiplication facts and related division facts.”

Hope this helps!

Ann McMahon, Retired Educator and Math Consultant

From: Nicole Rigelman, PSU Math Education Faculty

Hello All,

Thank you for sharing your thoughts on this and pointing out the importance of solid number sense as a means to support fluency… not to mention, sensemaking.

A colleague of ours, Tanya Ghattas, former math specialist in Salem-Keizer now administrator in Portland Public gave me a number that is helpful – 3 seconds per problem on average. What this allows for is both facts one knows with automaticity and facts that one may use a known fact to get to (i.e., 6 + 7 can be solved by knowing the fact 6 + 6 = 12 and adding 1 or by knowing the fact 7 + 7 = 14 and subtracting 1… along with others like knowing 6 + 4 = 10 and needing to add 3 more since 4 + 3 = 7, additionally knowing 7 + 3 = 10 and add 3 more since 3 + 3 = 6.). I’m sure you can imagine the corollary with subtraction or multiplication/division. You should note that role of strong number sense in accomplishing this work with known facts not to mention the connections to important number properties (associative and commutative).

What I like about this number too is if a teacher gives an occassional 100 problem practice sheet, easily generated from resources on the internet (AKA Mad Minute), he/she would only need to dedicate 300 seconds (or 5 minutes) to this practice and then know which kids have met this level of “fluency” and which kids need further support. If a teacher is also supporting kids by coaching them to go through and do all that they know automatically first and then work on those that are more challenging… then he/she has gathered more formative assessment data and can share with parents what they might like to work on at home with their child… or share with school support individuals number facts to target, etc.

I think that we also need to keep our eye on the standards advocated by the National Governors’ Association and the CCSSO, the Common Core Standards.

Take Care,
:) Nicole

Hi Kathy,

Thanks for asking this question. I was not there when the standards was drafted, so I can’t speak to the conversations that occurred around the concept of fluency when the document was drafted.  But I’d be happy to share my understanding of the concept of fluency within math education research, since it sounds like an open discussion on the topic.

The concept of fluency is more than just a rate, just as fluency in Spanish is more than how fast one can say words.  It is a larger idea that has more to do with the concept of automaticity, that is how automatic, or effortless, it is to access the needed facts to carry out a procedure.  The National Research Council in Adding it Up, defined fluency as:

“Procedural fluency – skill in carrying out procedures flexibly, accurately, efficiently, and appropriately” (National Research Council, Adding it Up, 2001, p. 5)

Thus four aspects of fluency include:

Flexibility – The ability to carry out a procedure using more than one method, or strategy.  I like Bruner’s model of concrete, pictorial, and symbolic representations, and like to think that students should able to calculate answers with each method.  This may include such methods as base-10 blocks and 10 frames (concrete), sets and base-10 grids (pictorial), in addition to symbolic methods including both alternative (e.g. partial sums, partial products) and traditional algorithms.

Accuracy – There is no fixed number here, but I’d image the goal would be to have students as close to 100% accurate as possible.  Thus the accuracy of a “mad minute” is part of fluency as much as the speed.

Efficiency – This is a reference to how well a student can go straight to the correct answer.  Researchers tend to stay away from defining a specific rate (such as problems per minute), since the rate can certainly vary.  It is fine to calculate and track how many problems were correctly done in a fixed time, recognizing there is a range of rates that would be acceptable and should change with age and experience.  With the goal of automaticity in mind, a better question would be “how laborious is finding an answer for the student?”, rather than simply how fast they can calculate. I would encourage more conceptual, perhaps less efficient, approaches at first, with the goal to refine methods to more efficient ones over time.

Appropriately – The final aspect of fluency refers to a student’s ability to select the appropriate method for the task.  That is, they can pick an appropriate math “tool(s)” to find a solution. BTW, using a calculator is another algorithm (a very efficient one at that!), and teachers cannot simply ignore or “outlaw” the method.  I think teachers within a district need to decide how, and when, will using a calculator would be appropriate.  I image that students should be able to use calculators more as they get older and demonstrate fluency within arithmetic.   It is also a practical method when needing to carry out repetitive tasks such as calculating the mean of large data sets.

This is as close to a working definition of “fluency” that I’ve been able to come up with, and is what I used when I taught my methods courses.  I’d be happy to know if it is helpful, or if the definition needs clarification.

Mark R. Freed

Mathematics Education Specialist

Oregon Department of Education

255 Capitol St. NE, Salem, OR 97310

Office 503.947.5610 | Fax 503.378.5156

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Oregon CORE and Process Standards Resource

January 4th, 2010

Happy New Year Everyone,

Over the winter break, I was able to spend some time putting together  a web page that is intended to provide links to supplemental resources that are aligned to Oregon’s CORE Standards. As you may know, every grade level starts with this statement:

It is essential that these standards be addressed in contexts that promote problem solving, reasoning, communication, making connections, and designing and analyzing representations.

I’ve found some great internet resources aligned to the process standards (especially mathematical problem solving) and the grade level CORE standards, too. I wanted to share them with all of you. This site is only a beginning, hence there is a note at the top of the page informing readers that it is currently under construction. I’d  love to hear from you if you’ve found some internet resources that you believe align well with one of Oregon’s Process Standards or a particular grade level CORE standard. Together we can create a resource that is truly useful to teachers everywhere since Oregon’s CORE standards are founded on the NCTM Curriculum Focal Points.

For more great resources, click on the Teacher to Teacher link in the Blog Roll at the right to go to the Teacher to Teacher website.

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Problem Solving Contests

December 6th, 2009

This last week I had the privilege of being a facilitator for several different groups of teachers who  were interested in increasing their mathematics content knowledge and exploring effective mathematics instructional practices. One of these opportunities was as a facilitator for the Building Mathematics Leadership (BML) Across Oregon training workshops.  These workshops were held in Ashland, Salem and a third one is scheduled for the Pendleton area next week. This series of workshops is co-sponsored by Oregon Department of Education and Oregon Council of Teachers of Mathematics’ Professional Development Cadre.  There will be two more of the  BML  series of workshops in February and March. The BML link above includes registration information. Saturday found me in the Education Building at Portland State University teaching the final face-to-face session for a PrISM Oregon course called Deepening Algebraic Reasoning in the Elementary Classroom.

In both the BML and PSU PrISM sessions a question came up about how to better promote mathematical problem solving in schools.  During the BML session in Salem a teacher shared how she was using some of the tasks we’d shared at previous sessions with all the teachers at  her grade level. These grade level teachers jointly created a bulletin board they were using to display student responses. They were pleased with the amount of interest and discussion this board was generating with their students.  I also shared an idea. In the late 90’s a couple of  my sisters and I were all teaching at the same elementary school in Gresham. We decided to create a Math Problem Solving Contest schoolwide. Each month we would post a new problem. The principal would include the tasks   in the weekly newsletter that was sent home to parents. Students submitted their solutions to any one of us. Students who had solutions that worked were given small prizes (free popcorn at lunch, a coupon to the student store for a pencil, a special bookmark, etc.) At the end of the year, all students who participated in the contest got to participate in a Math Celebration. (It was similar to a field day  except all events had  a math component.) Washington State Mathematics Council’s Everything in Its Proper Place “Apples:  Part 1 and Part 2“,  Noyce Foundation’s “Problems of the Month, and PDC’s Penny’s Ancestors Math Lesson Design are examples of  tasks students solved in these contests. Any of the  Teacher to Teacher Problem Solving Tasks would also work well. What do you do to promote problem solving in your school? We’d love to hear from you.

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Why Scaffold Sharing of Solutions?

November 13th, 2009

Last year when I was teaching second grade, I believe I taught what would be considered a “typical” elementary classroom. I had 23 second grade students. Three of my students were identified with 504 plans for ADHD. One had an IEP for special education and three for speech and language services. Eight of my students were English Language Learners, one had an IQ in the low 80’s and 6 were reading beyond 3rd Grade level. Recently I came across the following quote in the book What Successful Math Teachers Do, Grades Pre-K- 5: Research Based Strategies for Standards-Based Classrooms by Edward S. Wall and Alfred Posamennier.

“Although a teacher may be tempted to have all children begin with the most efficient computational strategy, all children do not come into the classroom with the same skills and prior understanding. Children need opportunities to build on their own understandings and to publicly compare and contrast their strategies and those of their peers.”

The author was talking about this in regards to the teacher simply showing students strategies to solve problems rather then creating opportunities for students to construct their own strategies as they work towards solutions to problem solving tasks and then present their thinking to the class. I’ve used the idea expressed in this quote as the foundation for deciding which students I’d ask to share their thinking and in what order. When studenst are engaged in working through a task, I circulate around the room looking at student work and asking students to justify and explain what they are thinking. As I walk around, I hand out stickies to students with a number written on them letting them know the order I am going to ask them to present. Sequentially, I look for students who have elements that are on the right track and represent the thinking of those students who are still on a concrete level of understanding. Then I progress through the continuum. The final student presenting will represent those who are working at a more complex or abstract level of thought.

But their are other organizational strategies that can be considered. Recently, I attended a session by Jo Boaler at the NCTM Regional Conference in Boston, MA. During this sesson I watched a video clip of students engaged in solving a task. After working privately for a very short time, the teacher stopped the group and asked a student to present his thinking so far and then raise any questions he still had. There was not time for any students to work through to the solution. What ensued was a very lively discussion by the group with other students coming up to respond to the first student and demonstrate their own thoughts and strategies as the whole group worked together to come up with a communal solutiion.

Part of the craft of teaching is to make these kinds of instructional decisions such as how to structure the sharing out afterwards. The following is a list of a few possible ways to organize how the discourse around solutions will occur:

• Pair student work that contains common misconceptions with work containing correct solutions to bring out in discussion the similarities, differences, and contradictions.
• Present work with communication gaps to get student questions and feedback that will help clarify and fill in the gaps.
• If a problem lends itself to using a variety of math manipulatives, drawings, math tools, etc., the presentations could be focused on showing the variety of representations.
• Select students who represent the most common way the class chose to solve a task and then proceed through the continuum to the least common.
• Havie a student present a divergent way of thinking about a problem to broaden the group’s thinking.
• Have the whole class display their work on a table, in the hallway, or hung on the classroom walls and have the class do a gallery walk in random order to view all the work. Students record their questions and comments on sticky notes.

The key here is to use the student presentations to deepen the collective understanding of the core mathematics presented in the lesson. Gail Gerdeman of OSU’s Scientists and Teachers in Education Partnerships (STEPs) Program has designed a handout called a “Student Response Planning Tool” that talks about this subject in more depth. She
has also created a Sharing Template sheet that helps teachers record their plan for student presentations. I’d love to hear your thoughts on this topic or any other suggestions you may have regarding how to organize student presentations.

Click on the Teacher to Teacher link in the Blog Roll at the right to go to the Teacher to Teacher website. Currently there’s a great newsletter posted that shares more about Jo Boaler’s research.

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Update on New Job

September 22nd, 2009

It has been a blur getting up to speed with my new position as the Title I Technology Teacher at my new school. I find that being a specialist has a whole new set of challenges. Learning the names of all the students in the school is on that list, along with finding time to go to the restroom and trying to stay up on creating lessons for each grade level when I have no set curriculum to use. As I create new technology lessons, I plan to share them on the Highland Computer Lab website .  I thought I’d share one of these resources with all of you here. It’s  a .pdf version (a SmartBoard interactive version of this lesson will be available on the computer lab site, too) of  a lesson I created for my 4th and 5th grade math groups to introduce them to some of the Teacher to Teacher problem solving lessons we’ll be doing this trimester related to their curriculum maps. I got the idea for this slideshow  from the Teacher to Teacher newsletter of March 2009. Teacher Giny Christensen introduced a problem solving analysis guide that helps her students think through the important elements of a new problem they are being introduced to. BTW, the slide show is also linked to a set of problem solving strategy posters. Since this .pdf version is not animated, you can link to the posters on my website. Have you come up with any great ideas to help student become better mathematical problem solvers? I’d love to hear your ideas.

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Welcome Back

September 8th, 2009

It’s the start of a new school year. I hope you all have had as successful and fun a start to your year as I have. This school year finds me at a new school and in a new teaching assignment. I am now working as the Title I Technology Teacher at Highland Elementary School in the Gresham Barlow School District. My job description this year will be to support the math and literacy goals of the school using the tools of technology. My schedule includes weekly rotations of all 1st through 5th grade classes through the lab in 30 minute blocks. In addition, I have two half hour blocks devoted to a 5th Grade Tag Literacy Group and a 4th Grade Math Intervention Group. If you are interested in finding out more about what types of projects I am doing in the lab, visit my web page and follow the new link I’ve added to the Computer Lab page. My plan for this blog is to continue to share any issues around mathematical problem solving that may surface during the year. Hopefully I’d also like to share with you any useful technology enhanced math activities that I come across.Here’s to the start of a great year.

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Math Interview Assessments

April 4th, 2009

Recently I had the pleasure of being asked to present at the 34th ANNUAL CONFERENCE sponsored by ORBIDA (Oregon Branch of the Dyslexia Association of America). My audience was made up primarily of special educators from local area schools. I was asked a great question. I thought I would share it here with the readers of my Blog and also tell you what my response was. The questions was whether I had identified any key concepts children needed to have in place in order to be successful in math. If I thought that there were these concepts, the question then became whether I used any of them as assessments to identify students who might need targeted interventions.

My answer was affirmative that I believe there were key concepts and that that they could be used to identify students who were likely candidates for intervention. I then went on to describe examples for my second grade students. This is the list I shared with that group:

1) The first concept is number sequence and seriation. I assess this concept by asking my students to count for me as high as they can go. Any of my students who cannot count to 100 raise a level of concern. If they can count to at least 100, I then ask the student to tell me what comes before or after targeted 2 digit numbers. Difficulty with this task also raises concern. Either students are having language difficulties or haven’t picked up the patterns present in our number system. Handing students a set of counters and asking them to count them backwards helps me check to see if it is a language issue or difficulty with the patterns of counting. This one also gives me some information about the child’s innate problem solving abilities. Sometimes the child will stare and me and not know how to proceed, other students will start with any number that comes to mind and count backwards from there.

2) Next, I check to see if students are able to subitize. For those of you for whom subitize might be a new word, the following definition comes from Wikipedia. “Subitizing, coined in 1949 by E.L. Kaufman et al. refers to the rapid, accurate, and confident judgments of number performed for small numbers of items. The term is derived from the Latin adjective subitus (meaning sudden) and captures a feeling of immediately knowing how many items lie within the visual scene, when the number of items present falls within the subitizing range.”

To assess this concept, I show students random pictures of sets of objects representing the numbers from 1 to 20. My object is to see if they are able to instantly recognize and identify the totals for these sets. The items represented in the sets have been arranged in ways that make it easy for students to group subsets and quickly calculate the total. For example, they may be grouped in chunks of fives or tens plus some extras. Any students having trouble instantly recognizing the total amounts in these sets would raise a red flag.

3) Next on the list is a check to see whether students have the ability to conserve numbers. For this check, I hand students a handful of around 12 two-colored markers. Students shake them up and drop them. I ask them to tell me how many of each color there are and how many markers there are in total. I then repeat this exercise. What I’m looking for here are those students who have to count the total each time even though nothing has been added or taken away from the original set of counters.

4) My next check centers on place value understandings. First, I find out whether students have 1 to 1 correspondence. I hand them a set of about 35 objects and ask them to count them for me. I observe whether they have some kind of organizing strategy like touching or grouping items to help them keep track of what has already been counted. If they count the set accurately, I ask students to write the numeral that represents the total items in the set. So if a student accurately records a total such as 35, I would point to the 3 in the tens digit and ask the student where he or she could find that 3 in the set of objects that has just been counted. For this assessment I am looking for those students who pull out 3 items from the set or say “thirty” but don’t express an understanding that the 3 represents 3 sets of ten.

There are more interview questions I use related to geometry, measurement, time, and money but I won’t list those here to keep the length of this blog to a manageable level. What are your thoughts? Have you found any others you would include? Would this change depending on the grade level?

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Math Station Activities

March 15th, 2009

Recently a visitor to this blog wrote, “I have not used manipulatives with instruction for quite some time. However, I am trying to build up my use of them once again. We really run our math class as centers and I want one to be an exploration of concepts via manipulatives. The only problem is I don’t have enough activity resources to support this. Any thoughts.”  I thought this was another issue related to manipulatives that would be useful to explore. See my response below.

I am unsure what grade level you teach or how many children might be accessing these centers at any one time. However, I will take a stab at your question and describe how I’ve done this while working in a variety of K-5 teaching assignments. Math stations are a part of my math block about 2- 3 times a week. Their purpose is to reinforce and practice math concepts I have introduced in whole group lessons. The whole class participates in stations during this time, so I need enough activities to give some choice to a class of 24 students on average. I have found 10 stations to be a good number. Students organize their completion of the different station activities using math station contracts. They consist of games or activities students participate in that utilize manipulatives in many of them.   Go to: http://www.octm.org/jcooke/GBSD%20Align/CORE.htm to see examples of math station contracts I’ve used in the past. These station contracts are aligned to our state core standards for each grade level (K-5). 4th and 5th grade and literature lists aligned to these standards are found on this site as well. The page is not complete yet but I hope to have it done sometime this summer.

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Time Spent on Problem Solving

March 6th, 2009

Very often when I work with a group of teachers, I hear the question, “How much time do you spend doing Problem Solving?” I have two different answers for this question. I will share both answers below.

For the first response, I remind teachers that problem solving is one of the process standards clearly discussed in the Principles and Standards of School Mathematics (PSSM), NCTM 2000. As is stated in the National Council of Teachers of Mathematics’ Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence (NCTM, 2006),

“Organizing a curriculum around these described focal points, with a clear emphasis on the processes that Principles and Standards addresses in the Process Standards—communication, reasoning, representation, connections, and, particularly, problem solving—can provide students with a connected, coherent, ever expanding body of mathematical knowledge and ways of thinking. Such a comprehensive mathematics experience can prepare students for whatever career or professional path they may choose as well as equip them to solve many problems that they will face in the future.”

Therefore, the answer to the question would be, “I would ‘do’ problem solving as often as I possibly can.” For example, whenever I introduce a new concept, I create a problem solving task as part of the introductory Warm Up. Asking students to reflect on their understandings, communicate their thinking, utilize a variety of strategies and so on are the foundations of a problem-based curriculum and are all part of my instructional standard operating procedures.

However, I believe what the questioner really intended to ask was, ” How do you structure your daily and weekly math times? Then, the answer would be the following. My main block of math time runs about 50 minutes. As mentioned above, if the lesson focus is on developing a new concept, the structure will definitely be problem-based. If we are at a point where I want students to practice and reinforce skills, that block will likely consist of small group station activities. Often these games and activities have a problem solving strategy component built into them, as well. At other times of the day, I have a calendar time for about 20 minutes I use to develop math vocabulary and reinforce and practice skills previously taught and a math journaling time that usually runs for another 15 minutes or so, where students reflect and self-evaluate around the concepts they have been learning. Therefore, 90 minutes a day are usually devoted to math in my usual daily routine.

My answer would be a little different if on the other hand, the question being asked is really, “How often do you use the Making Sense of Problem Solving (MSPS) materials?” In that case, the answer would be that approximately once a week I use the MSPS materials. Because there are 15 units, one week I focus on introductory Warm Up activities followed the next week with Problem Solving and Enrichment tasks assigned to the appropriate level students. I may carry over to a second day, student presentations of their solutions. How about you, my readers? How much time do you spend doing math and how is it structured?

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Organizing Math Manipulatives

February 11th, 2009

In my last blog entry, I talked about a common problem teachers are faced with when using math manipulatives — the issue of stealing.  This time I want to talk a little more about another common issue that confronts teachers when trying to incorporate a variety of math manipulatives as part of their instruction.  I often am asked a variation on the following question:

“How  can I better organize all these math manipulatives? I’m tired of finding plastic coins all over the floor at the end of a lesson on money.”

Ultimately, you will have to find the best answer that works for you, but I thought I’d share a couple ideas on this topic. Teachers I know utilize three different strategies for how to disburse manipulatives to use in classroom lessons. Some teachers pass out kits where they give each student a gallon bag containing a variety of the most often used math manipulatives. Other teachers organize table group buckets or baskets and have table group representatives come up and get the supplies for their group at the start of a lesson. The third strategy is to keep each type of manipulative in its own container. I’ve seen containers like plastic dishpans, baskets, or boxes as examples of storage containers.  Again, the teacher asks students to come up a few at a time to help themselves to the number of manipulatives needed per person or for partner  or small group work.

Teachers have shared lots of different strategies for helping to return manipulatives that have fallen on the floor to the place they belong. If the manipulatives are sorted and handed out by shape or color it is that much easier to return a lost manipulative to its proper home. Teachers use “sharpies” to number or letter manipulatives or place small stickers on them as a way to help in the sorting process. When a particular kind of manipulative has a large variety of small pieces, I like to sort them into the kinds of drawer systems found at hardward stores. (You know, the kind used for housing nails, screws, nuts, bolts, etc.) Every year I have a few students who love to help with sorting these math materials. They are often even willing to give up a recess to fill “student orders” for manipulatives.

Here’s a fun variation of this idea used for money manipulatives. Turn one of these drawer sets into the class bank. Identify a few students to be the bankers. They can even wear green eyeshades (cut out from old baseball caps) as they assume their Banker role.

Teacher to Teacher’s Making Sense of Problem Solving Books A and B include information about managing manipulatives, too. Click on the following file: A_Note_About_the_Use_of_Manipulatives to read the excerpt from these books.

What strategies have you come up with to help organize all those math manipulatives? We’d love to hear your comments.

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