Virtual Manipulatives in My Classroom!

As a teacher in a grade 5 Mathematics classroom, I'm always trying to find a way to help my students make connections and understand what they are doing and learning in the math classroom. The particular group of students I'm working with this year, are not a vocal group. They are intimidated by classmates and fearful of being wrong in front of them.


I'd been trying to get them to demonstrate their understanding by using small groups and then making presentations. A few of the "leaders in the class" tended to do all the communicating, leaving me, the teacher, at a point where I was able to get feedback from only a few of the students.


I wanted a way to make my students feel comfortable with me and willing to explain and discuss their Mathematical knowledge. When I heard about Virtual Manipulatives during a SMARTBoard in-service it intrigued me; however, it also intimidated me and my technology skills to create interactive activities.


Over the past little, while I've been searching and researching about Virtual Manipulatives during this inquiry project and started to see what was out there, on the Internet, that was accessable for myself and my students. I know my students enjoy technology, they are active learners and enjoy hands-on activities. What a better way to get them interested in Math, make connections and communicate their learning, then through technology.

When I first introduced the NLVM site on adding and subtracting base ten blocks, to help in their learning of decimals, I was amazed on their focus and determination to figure out the program. A lot of them worked their way through the problems needing little assistance from me. They would ask a neighbour or work it through, on their own. I intervened only to get them to see the connection between the representation of the manipulatives and the number operations that were being displayed at the same time  helping them make the connection. I saw for one of the first times this year, excitement in the students as they solved their problems. They were having fun and doing Math!!!

Getting ready for the lesson did take some time.I had to make sure the activity using the virtual manipulatives matched my outcome. It took me some time to find the activity and site I wanted to use, of course if I created the activity on Notebook (SMARTBoard program) it would have taken me even longer.  I then had to create a sheet to guide the students so that I would not be bombarded with raised hands or to have instructions repeated (THIS WORKED WELL and TO MY ADVANTAGE!!!). There was always the fear that the Internet would not be working, then the entire lesson would have to wait! A common occurrence when it comes to planned technology lessons.

Over all my experience with using virtual manipulatives was a positive one, and is something I plan on using more often in my teaching. In the future I hope to use it not only as an exploration but a teaching tool and assessment tool for my students learning in Mathematics.

Angela

Students Reactions

I was able to meet with a few of my students from my math class and have a little discussion about the activities they did using virtual manipulatives.

Here are some of the comments I received:

Question- What do you think of using manipulatives on the computer?

"At first I found it a little bit hard, but after I found it fun, I liked the game that we played." 
"It was lots of fun"
"It's fun to use and it helps you a lot"
"A mix of game and learning at the same time"

Question- What did you like best about using virtual manipulatives?

"I like it because we didn't have to use all the base 10 blocks and try to carry them to our desk"
"I'd really like to use them again, it's something different"
"You have to put things in a certain place, it told me if I was right or wrong"
"I could add or subtract blocks, it simulated my brain a little"

 I had one boy within about 10 mins of starting with the manipulatives coming up to me and asking "Miss can I have the website for at home, cause I want to try this again at home." When I asked this same boy why he wanted to try this out at home his response was: "I wanted to do it at home to see if would help me cause I have some trouble in math"

My Little Research Results...

The survey that I created regarding Math teachers use of Virtual Manipulatives has been analyzed and the following results were shown:

Suvveys sent to 45-  16 teachers responded

The results can only be based on those that responded.

Q1- What grade level do you teach Math?
            4- Primary
            4- Elementary
            4- Jr. High
            4- Sr. High

Q2- Do you use any manipulatives in your math lessons?
             100% use manipulatives in their math lessons.

Q3- In what approach do you use manipulative in your math classroom?
            100% Teacher Modelling (demonstrations in front of the students)
            100% Student Modelling (individual students use)
            93.8% Student Need (use with students who require additional support)
            68.8% Evaluation (during student-teacher conferences)

Q4- What types of manipulatives have you used in your classroom?
           =  playing cards, spinners, tangrams, square tiles, connector straws, faction pies, meter sticks, shapes, mirrors, fraction pieces, interlocking cubes miras integer tiles, Unifix cubes,  mini clocks, counters, dice, pattern blocks, Fraction tiles, Smart board, Algebra Tiles, Link Blocks, protractors, rulers, calculators, place value mats, geoboards, links, pattern blocks,  graphing mat, ten frames, Cuisinaire Rods, plastic chain links, coloured squares, number balance,  measuring cups, base ten blocks, tangrams, popsicle sticks, individual white boards, coins, metre sticks, newspapers, cardboard tubes, spinners, geometric solids, counters, geometric solids, attribute blocks,  fraction bars

Q5- Have you ever used Virtual Manipulatives in your classroom? (Virtual manipulatives are interactive web based representations of concrete manipulatives that students can manipulate and move in a similar manor)
          81.3% YES
          18.8% NO

Q6 - How did the students respond to the use of Virtual Manipulatives?

  (13 responded) - Sample Answers          

"some enjoyed some played", "

"They like it but it is not something they can take back to their seat.

                        (Unless in the computer room)" 

"They loved them! students love to come to the smart board and move objects!"

Q7- What were some of the benefits, as a teacher, to using Virtual Manipulatives?

    (13 responded) - Sample Answers

"There is enough for everyone. They take up no space, they can be projected easier, the

     kids can use them at home, they have only one function"             

"Observing students using them as a way of evaluation and understanding if the concepts

     of a certain topic is met."

"Students were engaged for longer periods of time, especially those with needs."

"Able to appeal to all kinds of learners and shows a different perspective"

"Instant engagement...may or may not be lasting...novel, as of yet"

Q8- Manipulatives in your lessons?

     (12 responded)
Generally any issues were with computer issues of Internet or computer malfunctions

Q9- What are some of the sites you have used to access Virtual Manipulatives?

  (11 responded)
2 most popular were the NLVM and NCTM illuminations     

This survey was a nice way to see teachers of different grade levels use of manipulatives. (I am unable to identify those that didn't respond to specific questions- therefore I am unable to determine grade level suitability for manipulatives and if there was one grade level that did not respond to the various questions)

The survey revealed a few things to me:

1- Teachers are using manipulatives in the classroom k-12

     (level of use undetermined)

2- Teachers (some) have used virtual manipulatives

3- Teachers see the advantages of virtual manipulatives, and were

    similar to the research that I shared in earlier postings.

4- Limitations are technology based- often out of everyday

    teachers control (Internet, computer malfunctions)

Angela

Survey results analized through http://www.surveymonkey.com/

NL Curriculum and Use of Manipulatives

The  Newfoundland and Labrador Department of Education has developed a set of mathematical processes for the students and teachers of our province.

The Mathematical Processes are:

•  Communication [C]
•  Connections [CN]
•  Mental Mathematics and Estimation [ME]
•  Problem Solving [PS]
•  Reasoning [R]
• Technology [T]
• Visualization [V]

- these critical components that students must encounter in a mathematics program in order to achieve the goals of mathematics education and embrace lifelong learning in mathematics. (NL Dept of ED, Grade 5 Curriculum Guide, pg 5; retrieved Nov 2011)

When using virtual manipulatives teachers are helping students experience many of the mathematical processes listed above. Students are able to visualise and manipulate various tools through technology to help them in connections, problem solving, reasoning, estimation and then help to improve their communication. When students are exposed to a variety of manipulatives and ways to represent a concept they have a larger knowledge bast to help them communicate and reason their understandings.   

The Curriculum Guides makes a note to teachers to consider the following when planning for instruction:

• There is to be a balance among mental mathematics and estimation, paper and pencil exercises, and the use of technology, including calculators and computers. Concepts should be introduced using manipulatives and be developed concretely, pictorially and symbolically.(NL Dept of ED, Grade 5 Math Curriculum guide, pg. 14; retrieved Nov 2011)

When the Curriculum guides are sent to the provinces schools they are also supplied with a sample of concrete manipulatives for the grade level. However, the amount of supplies is just a sample. Often classes of 20+ are left to borrow manipulatives, from other classes or grade, when they are working with a particular unit. Of course if you have a large storage area in your classroom this is great! Also, trouble arises when grade levels are working on similar topic units at the same time!

The use of Virtual Manipulatives is a way for teachers to have access to manipulatives for all! It allows all students to be involved and make connections.

Angela

Department of Education (2009). Grade 5 Mathematics Curriculum Guide-Interm Edition. Retrieved from http://www.ed.gov.nl.ca/edu/k12/curriculum/guides/mathematics/gr5_math_guide.pdf 

Finding Good Sites!!!

Throughout this project, I've been constantly looking for good sites, that are user friendly (for students and teachers), easy to access and hopefully free. I have been posting links, to the right, of some sites that I have found, which is not extremely long.

What should you look for what trying to find good virtual manipulatives?

According to Judy Donovan and The Center for Implementing Technology in Education you should consider

• Can the level of difficulty be adjusted for different students?
• What type of feedback so they provide?
• Will teachers need to provide feedback or support?
• How clear are the instruction for use?

For me when I was searching, I found a lot of the sites confusing to use, and I felt that students might get a little lost in what to do and end up just "playing" and not seeing the connection to the math concept. So testing out the site and trying to complete some of the problems is a sure way to see if it the virtual manipulative you are looking for!

There are a lot of math sites, however they lean towards games and drill activities. Actual manipulation of math manipulatives was harder to find, and most often they linked back to NLVM activities, or notebook activities for the SMARTBoard.

Angela

Donovan, Judy (2008): Teaching Mathematics with Virtual Manipulatives: Educators eZone. Retrieved November 5, 201. From Tech & Learning website: http://www.techlearning.com/article/teaching-mathematics-with-virtual-manipulatives/45397 

SMARTBoard & Virtual Manipulatives

The first time I was introduced to virtual manipulatives I was at an in-service on using an interactive whiteboard- which I piloted in my Math class for the Department of Education.

The program Notebook, which comes with a SMARTBoard Interactive Whiteboard, allows users to create worksheets and activities that are interactive and manipulative. There is an option when creating Notebook lessons that the manipulatives are infinite, that meaning you can have an endless supply to move and manipulate. An option that when using concrete or physical manipulatives is impossible.

The only limitation is that it requires a lot of work, by the teacher, to create these lessons. However, There is a wonderful sharing site http://exchange.smarttech.com/ where teachers can select their country, province, grade level and subject and there are numerous lessons done for you. Of course you would need to have an Interactive SMARTBoard and the notebook program on your computer.

Angela

Video of Interest on NLVM site

This video shows how the National Library of Virtual Manipulatives is useful for grade K-12 then it shows how to navigate the site!

Virtual Manipulatives Used by K-8 Teachers for Mathematics Instruction

This following post will discuss the study done by Patricia S. Moyer-Packenham, Gwenanne Salkind, and Johnna J. Bolyard.

The article is titled Virtual Manipulatives Use by K-8 Teachers for Mathematics Instruction: Considering Mathematical, Cognitive, and Pedagogical Fidelity. In this study the researchers examined teachers' use of virtual manipulative across the K-8 Grade range. They analyzed lesson summaries described by 116 teachers on their use of various virtual manipulatives for Mathematics instruction.

From this study Moyer-Packenham, Salkind and Bolyard found that majority of the virtual manipulatives use came from the area of Number Operations- most frequently using Virtual Geoboards, Pattern Blocks, Tangrams, and Base 10 Blocks. (Which was noted to be very similar to the types of physical manipulatives that are used most often)

How were these virtual manipulatives used by teachers? The study revealed that majority of the lessons used virtual manipulatives focused on investigation and skill solidification- this was linked to the way in which the teachers were instructed on how to use manipulatives during summer institutes. Virtual manipulatives can also be used to introduce lessons, games, and to aid, model, or extend ideas, yet, these were not prevalent in the lessons the teachers used in this study.

During the lessons, researchers also looked at how other tools were used along with the virtual manipulatives. They discovered that teachers used virtual manipulatives along with physical (concrete) manipulatives. Reference was made to a study by Terry in 1995 on a study of grade 2 and 3 students found that ".. when students used a combination of both physical and virtual manipulatives, they showed significant gain between the pretest and post test when compared to students using only physical manipulatives or only virtual manipulatives" (Moyer - Packenham et al. pg 213).

To conclude the research, Moyer-Packenham et al made the statement "the transformative nature of many virtual tools simply allows students to explore ideas flexibly, modelling the fluidity of the brain's activity and human thinking is way that cannot be done in a physical space" (pg 215).  This statement summarises the need for virtual manipulatives and making the connection with symbols, physical manipulatives and real math understanding.

Angela

Moyer-Packenham, P.S., Salkind, G., & Bolyard, J.J (2008). Virtual Manipulatie used by K-8 teachers for mathematics instruction: Considering mathematical, cognitive, and pedagogical fidelity. Contemporary Issues in Technology and Teacher Education, 8(3), 202-218

A little Research by me!

I have decided to do a little research among the Math teachers in my school, near by schools,  ED 6630 students, and a group of teachers piloting a technology curriculum for Dept of ED. Of course the responses to the survey I have created will be dependant on them volunteering to complete the survey, and some teachers are more technology focused than others!

I created a short 9 question survey on www.surveymonkey.com  that I have sent out to the teachers. When I receive the responses I will share the general trends of the survey responses.

The questions were as follows:

1. What grade level do you teach math?

               a) Primary (K-3)

               b) Elementary (4-6)

               c) Jr High (7-9)

               d) Sr High (10-12)

2. Do you use any type of manipulatives in your math lessons?

               a) Yes

               b) No

3. In what way do you use the manipulatives?

               a) Teacher modelling (demonstrations in front of the class)

                b) Student modelling (individual student work)

                c) Student Need (individuals who needs additional support to understand concept)

                d) Evaluation (during teacher-student conferences)

4. What types of manipulatives have you used in your teaching?

            OPEN RESPONSE

 5.
Have you ever used Virtual manipulatives in your math lessons? (Virtual manipulatives are interactive web based representations of concrete manipulatives that can be moved in a similar manor)

               a) Yes

               b) No

6. How did the students respond to the use of virtual manipulatives?

            OPEN RESPONSE

7. What were some of the benefits, as a teacher, of using Virtual manipulates in the classroom?

            OPEN RESPONSE

8. What were some of the problems you faced, as a teacher,  when using virtual manipulatives in the classroom.

           OPEN RESPONSE

9. What are some sites that you have used to access Virtual Manipulatives?

          OPEN RESPONSE

Virtual Manipulatives Research 'Part 2'...

Well it has been evident in my searching that there is not a whole lot of research out there for easy access concerning the use of Virtual manipulatives in the classroom. I guess with being a somewhat recent topic (approx since 2000) and the slow increase of technology in the classroom this was to be expected.

I did; however, find a few articles that dealt with research regarding the use of Virtual Manipulatives.

(1) Manipulatives in middle Grade Mathematics- Research Summary- by National Middle School Association (NMSA), Westerville, Ohio

(2) Virtual Manipuatives on the Interactive Whiteboard A preliminary investigation - by Paula Mildenhall, Paul Swan, Maria Northcote and Linda Marshall- Edith Cowan University. WA

Both these articles dealt with research concerning the use of Virtual Manipulatives and their advantages in the classroom
      - ability to record, replay, change and view actions made by students- encourage real math exploration(NMSA)
        - direct immediate link between object and symbolic representation (NMSA)
        - they are freely available on the Web (Mildenhall et al.)
        - parents and students can use them at home on their own computers (Mildenhall et al.)
        - can help overcome classroom management issues with concrete manipulatives (Mildenhall et al.)
        - make manipulatives accessible to diverse groups (such as special needs students) (Mildenhall et al.)
        - appeal to older students, seen as more sophisticated than concrete manipulatives (Mildenhall et al.)

With all these advantages why are they not used more often in the classroom???

According to NMSA teaching using concrete manipulatives often is directly linked to the teacher.
- Teacher use is related to teacher past experience with manipulatives
- Childrens' comprehension of manipulatives depends on instruction, and appropriate correlation of the concept with the manipulative
- Manipulatives alone cannot improve mathematics education
- Often teachers use of manipulative were for the purpose of 'fun' or a 'change of pace' yet teachers did not see how they can be used to teach the curriculum objectives effectively

More to come....
Angela

References:

Mildenhall,  P., Swan, P., Northcote,M.,  and Marshall, L. (n.d) Virtual Manipuatives on the Interactive Whiteboard A preliminary investigation  retrieved from ERIC on October 25, 2001 from http://www.eric.ed.gov/PDFS/EJ793992.pdf

National Middle School Association. (n.d). Manipulatives in Middle Grades Mathematics retrieved on October 26, 2011 from  http://www.amle.org/portals/0/pdf/research/Research_Summaries/Math.pdf

What are Virtual Manipulatives?

After doing some reading on the topic of Virtual Manipulatives I realized that what I thought were virtual manipulatives were really not. I made the assumption that virtual manipulative were any form of math manipulative that was used on-line or on a computer program. For example Base 10 Blocks, Fraction Bars, or Pattern Blocks.

According to Patricia S. Moyer, Johnna J Bolyard, and Mark A Spikell the definition of a virtual manipulative is a little more specific.  "A virtual manipulative is best defined as an interactive, Web-based visual representation of a dynamic object that presents opportunities for constructing mathematical knowledge" (Moyer, Bolyard and Spikell, 2002 pg, 373).

There are many sites that use manipulatives that represent the concrete manipulatives that are used in the math classroom like the fraction bars, geoboards, or patten block, However; what makes a manipulative truly virtual according to Moyer et al, is that they "allow the used to engage and control the physical action of theses objects..."

When I searched Wikipedia I found this definition of Virtual Manipulatives:
"Virtual manipulatives are a relatively new technology and are modelled after existing manipulatives such as base ten blocks, coins, blocks, tangrams, spinners, rulers, fraction bars, algebra tiles, geoboards, geometric plane, and solids figures. They are usually in the form of Java or Flash applets. Virtual manipulatives allow teachers to allow for efficient use of multiple representations and to provide concrete models of abstract mathematical concepts for learners of mathematics." (retrieved Nov 13/11 at http://en.wikipedia.org/wiki/Virtual_manipulatives_for_mathematics )

Angela

References:
Moyer, Patricia S., Bolyard, Johnna J., and Spikell, Mark A.  What are Virtual Manipulatives? Teaching Children Mathematics Feb 2002, pg 372- 377)

Why did I choose this topic for my inquiry project?

This topic has a personal interest in my own teaching, as it is an area that I will be focusing on this year in my Professional Growth and Development Plan. I have also accepted to take part in a pilot project with the Department of Education using technology in my Math classroom. I hope that this inquiry project will guide my teaching and keep me focused on incorporating virtual manipulatives to my lesson planning in Mathematics. This topic was brought to my attention in my math class over two weeks ago. I was teaching a lesson on decimals using Base 10 materials students were to write the decimal that was represented by the overhead projector Base 10 materials that I showed on the board. Students presented their results using dry-erase markers and personal mini white boards. They were so interested in the lesson, that we actually went over the time and used the next full period as well. They just wanted more and more challenges with the decimals. When I saw how excited my students were over the mini whiteboards I knew the area of virtual manipulatives would be a great motivator for this year’s classroom and a great time for me, as a teacher, to become more familiar and comfortable with using technology in my math classroom.

My goals of this personal inquiry are, through the use of a Blog, to report my classroom experiences I will share with classmates in my course the experiences that I have experienced and researched, in regards to using technology in the math classroom, specifically the use of virtual manipulatives. I also hope to motivate my students to enjoy math through the use of virtual manipulatives in activities and lessons that I will incorporate in my teaching. I will look at student success (academic), positive interaction with groups, personal attitudes towards using virtual manipulatives and Math in general. I will also keep a personal account of my attitude and experience in teaching math using more technology and virtual manipulatives.

Research of Virtual Manipuatives (Part I)

Over the past few weeks I have been doing research in the area of Virtual Manipulatives use in Mathematics. I have found some articles however, I was surprised that there was as little as there was.

I did however, find that Patricia s. Moyer of Utah State University has done a fair bit of research and article writing on the topic of Virtual Manipulatives.

I have also done several searches on virtual manipulative sites and I have discovered that there are thousands of sites, now my job will be to see which one's are suitable and useful to myself and my students.

Angela