Exploring Technology

During this lesson, students were taught how to use VoiceThread.  They each had previously published a poem using Word, so I uploaded the poems to a thread.  First students recorded their poem using headsets.  Then they had the opportunity to listen to each other’s poems and to comment on specific poetic elements or traits that they noticed were strong in their peers’ writing.  Finally, they were able to return to their own poem and hear the feedback given by others.  The lesson plan remained the same as it was when it was initially turned in for feedback.

I taught this lesson to both fifth grade classes in my building, which each have thirty students.  At the end of the lesson we had a ten minute discussion regarding the lesson.  For the most part, students really enjoyed sharing their work using VoiceThread.  Some of the reasons they gave were that it was easier to hear from more people, and also more comfortable than having to give a comment in front of the entire class.  It went pretty smoothly.  The one challenge we discovered was that If you made a comment but weren’t happy with it, you needed to delete it before you re-recorded.  If this process was not followed, then there were several repeats of comments or mistakes recorded on the thread.  As I discovered this with the first class, I began to delete those mistakes so that they wouldn’t interfere with the rest of the process.  It also helped me to be sure to caution the second class before beginning, which led to less “extra” comments.  After the lesson, I sent the thread to the principal, as well as some of the other teachers in the building, so that they could leave comments too.  Next week, the students will return to the computer lab so that they can hear these additional comments.

In this lesson, students learned how to practice listening and speaking skills as they read their own poems aloud and listened to the poetry of others.  They also practiced recognizing poetic elements in their classmates’ poems.  The underlying assumptions about learning were that learning is collaborative and is best served by having an opportunity to engage with the content by being an active participant.  Because this lesson is based on the idea that we learn from each other, it has many elements of social-constructivism.  Students had the opportunity to hear from their peers.  In addition, the students were taught how to use the technology, VoiceThread, in a manner that provided scaffolding and reflected a fading process.  We began by experiencing an example together, moved toward guided practice, and finally they began commenting on each other’s poetry independently.

One of the affordances of using this type of technology is that students are able to experience the content visually and audibly.  The poems were uploaded so that students were able to read each other’s poems, but they also created an audio recording of their own poem for each other to listen to.  In addition, students had the ability to learn from others by hearing their comments on the various poems.  If they were unsure of where to begin, they could start by seeing what other students had chosen to say.

This lesson was an enhancement for our current poetry unit.  It provided a natural means for assessing how students were practicing their listening and speaking skills, and also the chance to evaluate how successfully they were able to recognize and comment on the poetic elements we had discussed such as metaphor, simile, personification, and word choice.

My students really enjoyed using VoiceThread to hear each other’s poems.  Several of my shy students commented that they felt more comfortable sharing their thoughts this way versus in front of the entire class in a different setting.  A few commented that they liked being able to participate in something that felt more advanced.  Most are not allowed to be a part of social networking sites at home yet, or to engage in text-messaging, so this helped them to feel like they had a piece in that part of our world.

One of the role’s the technology plays in this lesson is that it allowed the students to share their work with a larger audience.  Not only are they able to share with me and their classmates, but also other adults in their immediate community.  The technology came second to the content though.  It was a means of sharing.  My students did have to learn how to use VoiceThread, but it was only a small portion of the lesson.  The majority of the focus was on responding to each other’s poetry.  I would definitely try something similar to this again in the future.

My digital story about decimal place value can be viewed here!

Here is my podcast in which I interviewed one of my students about what decides whether something is considered living or nonliving.

Student Understanding Podcast

Research can be found supporting any position. So, what constitutes scientific, reliable research then? There are several criteria to consider when evaluating research.

The first is to learn who conducted or published the research, and similarly who funded it. This can speak to the credibility of the research by revealing the motive behind it. For instance, research from a source outside a product or theory tends to be more reliable then one conducted within an organization because the researchers are more likely to be unbiased.

Another point to consider is how a research study relates to other theories and studies previously conducted. It should build upon other peoples’ work and what has already been learned in the given field. In addition, the work itself should be reviewed and critiqued by academic peers in order to gain validity. The interactions of a research study with other academic works and people are essential.

Finally, the methods of a research study should be evaluated. The methods chosen should allow direct examination of the questions posed. In order to do this effectively, the questions should be able to be measured empirically. Additionally, the methods chosen and the analysis of the data collected from these methods should be able to be explained using logic and simple reasoning. If a researcher is unable to answer questions regarding the reasoning behind the methods chosen or the analysis of the results, it would suggest that there is something unreliable about the study.

When evaluating research it is important to consider who conducted it, how it relates to other studies, and the methods that were selected.

Research Plan

Research Questions

How does the use of technology in learning basic multiplication and division facts affect students?

Sub-Questions:

· How does it affect students’ retention of these facts?

Sample

Since I team teach two fifth grade classes, the students in my sample will come from those two classes. The intervention is needed with students who struggle to retain their basic multiplication and division facts. I will choose between three and five students from each classroom who demonstrate the need for extra support in this area.

There will be two main factors in determining which students become a part of the sample. First, two timed tests will be given to all students in both classes on a weekly basis. One test will consist of eighty multiplication problems and the other eighty division problems. Students will be given five minutes to complete as many problems as possible. I’ve given these tests weekly for three years now. From this experience I’ve observed that about one-fifth of the students demonstrate a strong showing on these tests at the beginning of the year, usually achieving a score of sixty-five questions or more correct. These students demonstrate quick memory retrieval of basic facts, and typically only make occasional errors. About three-fifths of the students give an average showing on these tests, scoring between forty and sixty-four questions correct. Not always, but often these students improve their scores naturally over the course of the year. Sometimes these students show a dramatic increase in score after just a month or two, which may be due to not having practiced or used their basic facts over the summer. A final one-fifth of the students score below forty questions correct at the beginning of the year. Every year some of these students routinely score below twenty questions correct. That translates to completing only four questions in a minute, or a question every fifteen seconds. Much of the time these students do not show much improvement in their scores over the course of the year. There are always exceptions, but this is the pattern I have observed in three years of teaching.

It is this final one-fifth of students I hope to target, the ones who score very poorly at the beginning of the year and struggle to show marked improvement throughout the year. I would hypothesize that these students do not understand the relationships between the basic facts and are therefore struggling to retain the memorization of them. Again, there are exceptions, but often these students are also the ones that do not have parents taking initiative to help them practice or understand these basic facts at home.

The second factor that will be considered when trying to choose the students that will make up the research sample is teacher observation. In my classroom, computation is practiced daily in a number of more advanced mathematical concepts, such as listing multiples, multiplying fractions, or performing long division. I circulate around the room and watch students complete problems, helping as needed. For these observations, I will be looking to see what strategies students are using to carry out the basic fact portion of the problems. Specifically, I will be watching to see if fact retrieval is quick from memory, requires a short computation, or involves a counting or listing technique.

Most of the time, students who make lists of multiples or count on their fingers are the ones who don’t have a firm grasp on their basic multiplication and division facts. Some students do choose to use short computation problems, but often they still demonstrate fact knowledge through this process. For instance, in figuring out 6 x 6, a student may choose to recall that 6 x 3 = 18 and 6 x 6 is 6 x 3 doubled. Therefore, to find the answer they may write down 18 + 18 = 36. These students don’t necessarily demonstrate automatic fact retrieval, but there is some fact knowledge utilized. This shows that the fact family understanding is present, and these problems usually don’t require much time to complete. Because of this, I have chosen not to include students who fit in this category as part of the sample.

The students chosen for the sample will reveal a need on the timed tests, as well as in everyday problem completion.

Study Design

The six to ten students chosen for the sample will be divided into two groups. The first group will practice basic multiplication and division facts with partners using flashcards. This is an intervention that has been widely used in the past by schools and families. Students will be instructed to give the correct answer to a problem when their partner gets an answer incorrect. This is to help students to recognize their mistakes and learn the correct answer to a problem. Also, each group will begin with easier multiplication and division facts, and then add new problems as these smaller facts are mastered. Students will need to complete all problems correctly in a fact family (i.e. multiplying by fives) before moving on to a new family.

The second group will utilize the FASTT Math software for ten minutes each day. FASTT Math was chosen because it meets all of the criteria of a strong technology-based intervention that were discovered when researching. First, it provides immediate and corrective feedback. Students know when a problem is done incorrectly and they also know what the error was. Second, it focuses on only non-fluent math facts, instead of those that a student has mastered. Next, it connects non-fluent math facts to those students are already fluent in by showing the relationship between the two. Finally, it allows student data to be remembered and tracked over time using data tables and graphs.

Students will use these two interventions in place of the ten-minute math warm-up that is given to the entire class. There are six computers available, and they are located in the extended learning area (ELA) found between the two fifth grade classrooms. There are several perceived benefits to this arrangement. First, the students will be slightly isolated from their peers when using the FASTT Math program. This will allow them to have a quiet environment to focus in, and will also ensure that their program results are not affected by any other students intervening. Second, it will help other students not to feel slighted for not receiving the computer option. I don’t believe this would be too much of a problem as there are multiple opportunities to use computers in math during the existing independent contract learning time.

For those using the flashcards, they may work in the hall, which will also keep them from standing out from the rest of the class. In addition, this is often a motivating learning location for students, would provide a quiet area for students to focus in, and would also keep other students from intervening during the practice.

These two groups will be followed over the course of a year. This will allow any progress that is made, whether slowly or quickly, to have the opportunity to manifest itself and show continuity throughout the weeks the interventions are used. The gains made by each group will be compared to see how the technology-based intervention, FASTT Math, and the flashcards intervention measure against each other. Both groups will be receiving the same amount of practice time-wise, helping to ensure that one group does not have an edge over the other.

Data Sources

Data will be collected weekly from students. First, data will be collected from each group regarding the intervention used. Those using FASTT Math will print out a report and/or graph of their progress, showing what facts are fluent and which are not. Students using flashcards will keep track of the current fact family being used and will chart their progress on a graph too. This graph will show when each fact family was mastered and what the current family being studied and learned is.

Additionally, these students will participate in the weekly timed tests given to all students in both fifth grade classrooms. As described above, these timed tests each have eighty multiplication or division problems, ranging from 0-12. Finally, I will continue to observe students as they complete daily problems in class and in small groups, and will write down these observations in a notebook. As I work with these students, I will watch to see what strategies they are utilizing. Are they still counting on their fingers or making lists? Or are they beginning to demonstrate fact retrieval from memory? In conducting these observations, I will also note the time it takes for these students to retrieve a basic math fact. I will be looking to see if the intervals of time are getting shorter for fact retrieval.

Procedure

During the first three weeks of school, all students will be given the multiplication and division timed tests. The first three weeks of data will help to establish a baseline of where each student is performing as they enter fifth grade. I will look for trends that show who is performing in the lower one-fifth of the class, specifically searching for scores of forty or less in the data. In addition, as we review basic computation before jumping into the fifth grade curriculum, I will observe and take notes about what strategies students use for basic fact retrieval.

At the end of three weeks, I will review both the timed test results and my notes to choose the six to ten students that will form the research sample. These students will then be divided into two groups. One group will receive the flashcard intervention and the other the FASTT Math intervention for ten minutes a day, at the beginning of each math period. Each week, I will have students in the sample chart their progress and keep track of it in a student folder. Those who are in the FASTT Math group will print a report of their math fact chart, which shows which facts are fluent and which are not. They will highlight the facts for each week that are now fluent that weren’t the previous week. The group using the flashcard intervention will also chart their progress using a similar data table. They too will highlight the facts that were mastered throughout the course of the week.

I believe it is important for students to play a part in collecting this data. If they can see they are making progress, they are more likely to invest in the intervention. Secondly, by having students track their progress and then bring it to me to put in their folder, it will provide an opportunity to have conversations with these students about the intervention, their feelings regarding it, and the gains they achieve.

Also, these students will continue to participate in the weekly multiplication and division timed tests given to all students. These tests will be given weekly to supply regular data points in which to measure student progress over time. This data will be recorded on a spreadsheet and will become a part of each student’s folder. The timed test data will also provide another piece of information for students to examine and recognize achievement in.

Finally, I will continue to take notes about these students as I work with them in whole-group instruction and during small group work. These notes will still focus on the strategies that these students employ to figure out basic fact computations, as well as the time it takes to complete these problems. By observing students in the regular classroom setting, I can see if the facts being learned in the intervention are carrying over into daily work.

Data Analysis

The data in the folder will be examined each week with students, and will also be looked at monthly by me for trends and patterns. I will be looking to see how much progress is being made by the students in each group, specifically how many non-fluent facts are becoming fluent facts over the course of each month. This information will be tracked in a spreadsheet, just as the timed test information is which will allow easy comparisons between the two intervention groups.

When looking at the data each month, both the weekly reports and timed tests scores, I will be watching for any differences in the two groups. For example, if students in one group were mastering ten new fluent facts a month, and students in another group were mastering only two new fluent facts a month, this would lead me to believe that one intervention is more effective than the other. If both interventions were showing about the same amount of fluent facts gained, I would assume that both interventions were equally effective. The number of fluent facts mastered by each student and group will be evaluated each month, as stated above, but then as time goes on, the data will be examined for trends that span several months.

The notes I will take will also be examined monthly to look for patterns. It can be difficult to remember what happens each day in class accurately, so the notes will afford me the opportunity to review what I noticed on different given days. If I start noticing that a student who used to commonly make lists for harder basic facts, such as 6 x 8, begins to be able to retrieve some of these facts from memory, I will begin to believe the intervention they are using is working. I do not expect this to happen immediately. This research will happen over the course of a year to give students time to become more fluent in basic facts and to show what they have learned. The notes will allow me to see if a student is able to retrieve a more difficult fact from memory just one time, or if it is happening multiple times throughout a month.

The notes, timed tests and intervention reports will allow me to draw conclusions about both the FASTT Math intervention and the flashcard intervention. They will allow me to see if one or both of the interventions is effective in helping students learn to master basic multiplication and division facts. In addition, these pieces of information will allow me to compare how effective the two interventions are if both are shown to help students progress in this area.

            According to Hasselbring, Lott & Zydney (2006), “To better understand how to enhance mathematical thinking and learning in today’s students, especially students with math difficulty, we must first understand the nature of mathematical knowledge.”  They divide mathematical knowledge into three basic types:  declarative, procedural, and conceptual.  Declarative knowledge is considered factual knowledge about mathematics, such as knowing that 3 x 5 = 15 or knowing that a square has four right angles.   Procedural knowledge is then defined as the rules, algorithms and procedures used to solve problems.  Finally, conceptual knowledge reflects an understanding of mathematical principles, beyond the ability to merely complete a problem.

            Declarative knowledge serves as the building blocks for procedural knowledge.  One of the most frequent types of declarative knowledge used is the ability to recall from memorization basic mathematical facts in the areas of addition, subtraction, multiplication and division.  This is known as the area of computational fluency.  When researching, Hasselbring, Lott & Zydney (2006) learned of studies from cognitive psychologists that demonstrated humans have a fixed capacity of attention and memory that is useful for problem solving.  In order to overcome that, some tasks must become rote and routine so that they can be done fluently and automatically. 

            Kleiman (1983) supports this when he says, “Practice is a necessary to become proficient at any skill, whether it is a musical skills such as playing the piano, a physical skill such as riding a bicycle, or the more cognitive skills of reading, writing and arithmetic.  In each case, the beginner must concentrate their effort and attention on basic components of the skills.”  For mathematics, this is basic facts.  They are the building blocks for more advanced mathematical skills.  Hasselbring, Lott & Zydney (2006) found that students who struggle in the area of mathematics in general usually demonstrate difficulty in the retrieval of these elementary facts.

            In order to help students master these facts, Smith (2006) believes they must be connected to other things that are known.  Without these connections to previous knowledge, learning can be both difficult and inefficient.  He continues by saying, “…efforts to memorize can be completely counterproductive when we have little understanding of what we are doing.  That is one reason why mathematics can suddenly become frustrating and opaque, not matter how highly motivated we are. If we strive to memorize something we don’t understand, if we’re on the wrong side of the glass wall, we’ll have great difficulty trying to remember it.  But we’ll have no difficulty remembering our failure and frustration.”  Calvert (1999) seconds this when she explains that students need to do more than just learn mathematical facts in isolation.  Instead, students need to understand and focus on the relationships of the unknown facts to facts they do know, and should also work to create a mental image of each fact.  If these relationships are ignored, it is much harder to make progress in the area of computational fluency. 

            In addition, items should only be selected that are not already mastered and that are at an appropriate level for the student.  Items that are already mastered do not need to be practiced, and any items that are too difficult will often lead to frustration (Kleiman, 1983).  Furthermore, non-fluent facts should only be presented a few at a time in order to emphasize the crucial relationships between facts and to not overwhelm students.  Also, it can be helpful to have a time limit on practicing these facts after the relationship has been presented.  This ensures that students are relying only on fact retrieval, rather than counting strategies (Scholastic, 2005). 

            One final important element of any type of drill and practice is immediate feedback.  Immediate feedback allows students to recognize errors and see how to correct them while still active in the drill.  If the feedback is not given immediately, it diminishes the effectiveness of the feedback and does not help much in reversing the error committed.  Additionally, feedback should help students explain and understand the errors made, rather than just tell if a problem is correct or incorrect (Kleiman, 1983).

            There are many ways to engage students in drill and practice for the purposes of learning basic mathematical facts.  More traditional methods use paper and pencil or flashcards.  As technology advances though, there are more opportunities for students to begin to commit facts to memory through the use of technological software and games.  Lemire, Mitchell & Seckinger (1989) provide several reasons to use games or simulations with students.  The main reason is that students have a high interest in these types of activities, and are therefore highly motivated to learn what is being taught.  With a higher level of motivation, students’ attitudes and opinions about learning can become more positive, and this will often lead to increased learning.  Cruey (2007) adds to this by saying that when students enjoy a game, they are likely to spend more time practicing, and more practice frequently leads to a stronger grasp on the concept being learned.

            The difficulty often comes in finding technologically based drill and practice programs that meet the criteria mentioned above, which included immediate corrective feedback, and emphasis on number patterns and relationships, and a focus on only non-fluent facts.  There are many free, Internet-based drill and practice programs available for practicing basic mathematical facts, but most do not meet the above criteria.

            One example is Math Baseball, offered through Fun Brain, which is a popular site used in schools.  This game allows students to choose an operation to practice and a difficulty level too.  The setting of baseball would be intriguing to students, but there isn’t a way to target fluent versus non-fluent facts.  It does offer feedback, but it is very small and can be easily overlooked or ignored.  A second example is Number Invaders, which is part of the Math Playground website.  This game does let you choose the fact family you would like to practice, but only offers feedback in the form of sounds.  If you get an answer correct you hear an explosion sound, and if you are incorrect you hear a beeping sound.  Number Invaders has the feel of an arcade game, which students would most likely enjoy.  However, in order to be successful, you must know the multiplication fact and be able to manipulate the keyboard to hit the correct answer.  Finally, another downfall of this game is that multiplication and division relationships are not stressed at all.  It offers only straight drill and practice without any explanations or feedback.

            Another option is to download or purchase software that is centered on practicing basic mathematical facts.  Timez Attack offers multiplication practice in a video-game style manner.  It focuses on one fact-family at a time, and pictures accompany the problems that help students visualize the answer.  However, it does not allow mastered facts to be removed from the game, nor does it offer correction when a wrong answer is given.  It merely lets the player know they made a mistake.  There is a free version, which can be downloaded onto any computer, but there is also a premium version that costs $39.99. 

            Tom Snyder Productions offers a piece of software called FASTT Math.  This product customizes the program given to each student by giving a pre-assessment before beginning any practice.  This pre-assessment identifies which facts a student is fluent and non-fluent in.  In addition, it only introduces two new non-fluent facts at a time.  The introduction of these non-fluent facts is based on what a student already knows and is fluent in.  Also, it offers time-controlled response time.  If a student takes too longer to answer a question, feedback is given again by showing the problem/answer relationship.  The one negative aspect of this program is that it costs $300 for a one-computer license, or $3000 for a sixty computer school license.

            Computational fluency is important if students are to be successful in the area of mathematics.  In order to complete more advanced mathematical problems, students need to be fluent in knowing their addition, subtraction, multiplication and division facts.  There are many ways to practice these facts in order to help them become memorized, and therefore automatic.  Using technology can be appealing because students are often more motivated when learning involves computers or other technological tools.  However, in order to be effective, these tools must show relationships between basic facts, offer immediate and corrective feedback, and be able to distinguish between fluent and non-fluent facts for each student.

Berliner, D. C. (2002). Educational Research:  The Hardest Science of All. Educational Researcher, 31(8), 18-20.

David Berliner discusses the differences between hard sciences and soft sciences in this article.  He believes that the soft sciences, including educational research, are often more difficult to conduct and understand.  This is largely due to the fact that many factors influence every situation encountered in an educational setting simultaneously.  These factors include aspects of the student, teacher and classroom environment.  He also points out that the local context of each situation differs from those that surround it both near and far.  His final position is that education is constantly changing; therefore it is hard to hold something as “truth” for very long, if at all.

Brennan, J. (2006, March 15). Math Facts. Retrieved May 29, 2009, from http://www.livingmath.net/Articles/MemorizingMathFacts/tabid/306/language/en-US/Default.aspx

The author seeks to argue two major points about memorizing math facts.  The first is that the memorization of basic facts, such as multiplication and division, must be connected to an understanding of number sense, meaning that the concept must be understood before memorization can occur.  Without this connection, Julie Brennan believes rote learning is inefficient and difficult.  The second is that some children will commit facts to memory when they reach this understanding, and others will need additional practice.  Essentially, the author contends that students developmentally reach the ability to commit facts to memory at different ages, and with varying levels of exposure.  In an interesting comparison, Brennan states that, “Games are to math, what books are to language.”  She believes they provide real, relevant, and fun ways to gain the exposure to math concepts that is needed.

Calvert, L. M. (1999). A Dependence on Technology and Algorithms or a Lack of Number Sense?. Teaching Children Mathematics, 6(1), 6-7.

Lynn M. Gordon Calvert seeks to convince readers that peoples’ dependence on mathematical “answers” is not due to technology.  She tries to counter the argument that calculators and other pieces of technology cause dependence by suggesting that the root of the problem lies much deeper.   Her belief is that dependence on mathematical algorithms, executed on paper or by calculator, is caused by a lack of understanding and a development of number sense, not in the use of tools themselves.  In an example, Calvert says that memorization of multiplication facts should not be taught in isolation, but instead by creating mental images of these facts in order to think about their relationship to other facts.  For instance, 6 x 4 can be thought of as 5 x 4 + 4 or as 3 x 4 doubled.  She concludes by saying that focus should remain on promoting mental facility with number concepts and operations, and the ability to invent or apply computation methods will follow.

Cruey, G.  (2007, December 3).  Why Play Math Games? Retried May 29, 2007 from http://curriculalessons.suite101.com/article.cfm/why_play_math_games

Greg Cruey seeks to prove that math games should be used for two major reasons.  The first is that it makes learning more fun, and that because of this more will be accomplished than with traditional drill and practice methods.  He believes that the enjoyment of learning is something that should be nurtured and similarly that if students enjoy what they are learning, they will also remember more.  The second is that is if a child enjoys a game they will spend more time practicing, and the more practicing that is involved, the more likely skills will be acquired.

Department of Education and Early Childhood Development. (2006, July 21). Mathematics Continuum – Number – Fluent recall of multiplication facts -   Learning and Teaching Resources – Prep to Year 10 -   Student Learning -   Department of Education and Early Childhood Development. Retrieved May 27, 2009, from http://www.education.vic.gov.au/studentlearning/teachingresources/maths/mathscontinuum/number/N30006P.htm

This article, published by the United States Department of Education and Early Childhood Development, provides teaching strategies that will help students memorize basic mathematical facts.  It states that some drill-and-practice is needed for this to occur, but that it should be on the basis of a strong understanding of mathematical principles, and that it need not be mundane and boring.  The first strategy discussed is setting realistic goals for students to learn basic facts in stages.  For instance, when working on memorizing multiplication facts begin with 2x, 5x, and 10x.  Then, move on to harder fact families.  Second, it says to stress number patterns and properties.  When learning 9x, students can recognize that the ten’s digit increases by one each time and the one’s digit decreases by one simultaneously.  A third strategy mentioned is to enlist the help of parents and families.  By learning at school and then reinforcing the concepts at home, students are more likely to hold onto that fact knowledge.  Finally, the article suggests using games with an element of chance, so that all students have the opportunity to succeed.  This would include card games and commercial computer games.  The focus should be on each student reaching a personal best.

Hasselbring, T. S., Lott, A. C., & Zydney, J. M. (2006). Technology-Supported Math Instruction for Students with Disabilities:  Two Decades of Research and Development. Retrieved May 27, 2009, from http://www.ldonline.org/article/Technology-Supported_Math_Instruction_for_Students_with_Disabilities:_Two_Decades_of_Research_and_Development

Ted S. Hasselbring, Alan C. Lott, and Janet M. Zydney identify six purposes of technology use for supporting student mathematical learning.  The six purposes are building computational fluency, converting symbols, notations and text, building conceptual understanding, making connections and creating mathematical representations, organizing ideas, and building problem solving and reasoning.  The first purpose, building computational fluency, is based on the idea that the ability to easily recall basic math facts is a necessary condition for helping to learn higher-order math skills.  The authors cite psychologists that have discovered humans have fixed limits on the amount of attention and memory that can be used to solve problems.  One way to overcome this is to have some tasks become so used that they are routine and automatic.  They contend that this should be the case for basic math facts.  Most students who struggle with mathematics as a subject are shown to have difficulty retrieving elementary number facts.  These authors’ research shows that it is not a conceptual deficit that causes this condition, but rather a difference in the amount of instruction that is needed for individual children to become fluent in retrieving these answers.

Ivers, K.S. (2003).  Using Technology in the Classroom. California:  Libraries Unlimited.

Karen Ivers discusses the differences between several types of software, including drill and practice activities, problem-solving exercises and tutorials.  In addition, criteria are provided for evaluating software and resources.  Ivers recommends software should be evaluated to see how it compares to state and district content standards.  She also believes an assessment component should be included as part of the package.  Other items to be considered are whether or not the program provides immediate feedback, is easy to use, allows students to save their work, and is at an appropriate age level for the group it is intended.

Kleiman, G. M. (1983). Learning with Computers. Compute!, 1(34), 135.

Glenn Kleiman explores the debate about using computers for conceptual learning versus for drill and practice programs.  He largely agrees that computers should be primarily used for instructional use centered in higher levels of thinking, but does not believe that drill and practice is always bad.  The case is made that some drill and practice is necessary, and computers make that process more enjoyable.  One of the benefits of using a computer for drill and practice is that is provides immediate feedback.  In addition to being immediate, feedback should also provide information about errors.  Kleiman also says that the selection of practice items is important.  Students do not need to practice already mastered items, and items that are too difficult will lead to frustration.  He closes by saying software for drill-and-practice purposes should be carefully evaluated before purchasing.

Lemire, D., Mitchell, R., & Seckinger, D. (1989). The Use of Educational Simulation and Gaming to Improve Mathematics Teaching.

The authors in this piece discuss the importance of educational simulations and games in learning mathematics.  They believe that one of the major benefits of using these tools is that students have a higher interest in playing games than in other classroom activities, and therefore they are more motivated to learn in this manner.  In addition, they argue that play is an important part of developing socially and intellectually.  Simulations provide an opportunity to “play” in structured, yet open ways.  Finally, these authors believe that when drill and practice can be altered through games or simulation, both motivation and learning will be affected.  Without this boost, they believe the acquisition of skills is severely impaired.

Research and Results. (2006). Research Foundation & Evidence of Effectiveness for FASTT Math. Retrieved May 27, 2009, from www.scholastic.com/administrator/math/pdf/FM_White_Paper.pdf

This article is a review of one piece of specific mathematical software intended to help students learn basic math facts.  The software is known as FASTT Math and was created by Tom Snyder.  It is designed to target students who have more difficulty memorizing basic math facts.  It begins with a computer-based assessment that presents all the basic facts in an operation.  The time used to answer each question correctly is recorded.  By measuring the time each problem requires, the software determines which facts are recalled from memory, and which are utilizing a computational strategy.  A grid is then created showing the fluent and non-fluent facts.  The program builds upon the student’s knowledge of fluent facts to learn the non-fluent facts.  It teaches the connections that exist in fact families.

Research Question

How does the use of technology in learning basic multiplication and division facts affect students?

Sub-Questions:

• How does it affect students’ retention of these facts?
• How does it affect students’ attitudes and practice habits regarding these facts?

Background

I teach fifth grade at Gateway North Elementary in Saint Johns, Michigan.  Currently, I work in a team-teaching situation, in which I teach mathematics and science and my partner teacher teaches social studies and language arts.

Saint Johns is a rural community of about 7,500 people, located twenty miles north of Lansing.  Ninety-four percent of adults have received a high-school diploma and twenty-six percent of adults have earned at least a bachelor’s degree beyond high school.   A significant portion of adults work in factories located in and around Saint Johns, although retaining work in these industries is becoming a challenge for many families, as many of these businesses are down-sizing or closing.  The average income for a family is $41,713.  Saint Johns is also slowly growing, mostly on the southern end of town, and becoming a commuter town for people who work in and around the Lansing area.

Gateway North Elementary is found on the northern end of town and enrolls around three hundred students each school year.  We have two classrooms for each grade, with class sizes ranging from 24 students to 31 students.  Our student population is very transient.  Most of the temporary housing in our school district (apartments, mobile homes) is found within the Gateway North Elementary school zone.  Last year, it was found that only 42% of our graduating fifth graders had attended Gateway North Elementary for all of their elementary school years, kindergarten through fifth grade.  It varies by year, but approximately 40% to 60% of my students live in single-parent homes or homes that include adults other than the child’s parents (step-parents, significant others etc.).

Demographically, 88.6% of our students are of white/Caucasian descent.  Hispanic students make up 3.7% of our population and black students represent 0.3% of all of our students.  Students of Asian/Pacific Islander descent represent 0% of our school and American Indian/Alaska Natives make-up the final 0.7% of our student population.  As you can see, there is not a lot of racial or cultural diversity in our school; however it is slightly more than the district average.  The following table below compares the racial and cultural demographics of Gateway North Elementary to the St. Johns Public School District as a whole:

(http://www.schoolmatters.com)

Although it has been calculated that only 21% of families within the district are considered economically disadvantaged, our school contains almost double that rate, with 38% of our families meeting those criteria.

(www.schoolmatters.com)

As you can see, students and families that are members of our school community tend to be almost twice as likely as the average family in our district to receive some sort of assistance financially.

Significant portions of the students that attend my school also bring behavior and attitude challenges with them each day.  It is my belief that many of the factors stated above, such as financial challenges, household make-up, past family history and transience, are all contributing reasons as to why our students often deal with these additional issues.  Many of our students have worries beyond doing well in school and these difficulties also must be dealt with if students are to succeed.  Although my students may bring more challenges with them than other schools in the district, it makes me all the more determined to want them to succeed and feel good about themselves academically, intellectually, and socially.

Introduction

By the time students reach fifth grade, they are supposed to be able to recall basic multiplication and division facts with ease.  This is largely because these facts are utilized in a variety of more advanced mathematical concepts.  In his book The Glass Wall: Why Mathematics Can Seem Difficult, Frank Smith says, “Although mathematics might seem to be a constant process of ‘working things out,’ the foundation of any kind of mathematical enterprise involves committing mathematical facts and procedures to memory.” (2002). The following Fifth Grade Level Content Expectations are examples of some of the advanced concepts that require a memory base of mathematical facts:

• N.FL.05.04 Multiply a multi-digit number by a two-digit number; recognize and be able to explain common computational errors such as not accounting for place value.
• N.FL.05.06 Divide fluently up to a four-digit number by a two-digit number.
• N.FL.05.14 Add and subtract fractions with unlike denominators through 12 and/or 100, using the common denominator that is the product of the denominators of the 2 fractions.
• N.ME.05.11 Given two fractions express them as fractions with a common denominator, but not necessarily a least common denominator.

In order to complete long division or multi-digit multiplication problems, students must be able to recall the basic multiplication and division facts for numbers zero through nine.  Each year I have students that understand the process for completing these problems, but are unable to do successfully due to computational errors.  When learning long division, students invent acronyms for the process represented here:

DMSB = Divide, Multiply, Subtract, Bring Down

It is not uncommon for students to remember these acronyms and the steps for long division, but then err when finding the answer to a basic fact component, such as 42 divided by 7.

A similar situation arises in the fractions unit.  In order to find equivalent fractions or to express fractions with common denominators, students must be able to utilize basic multiplication and division facts.  For example, when trying to find a common denominator to add two fractions, such as 3/8 + 2/6, students must be able to either know that 6 x 8 = 48, or be able to find another multiple of both 6 and 8.

Because some of my students are not able to recall these facts, they resort to strategies that are not always reliable for arriving at a correct answer.  One strategy commonly utilized is making tally marks.  If dividing, these tally marks are placed into groups, or if multiplying, tally sets are created.  Another strategy used is counting by a number and then making a list of the multiples.   For example, when trying to figure out 6 x 4, students will write down 6 and then count six more and write down 12.  This process continues until 24 is reached.

Although these methods are better than not having any strategies at all, there are several challenges that arise.  First, these are time consuming techniques.  Often by the time a student figures out the basic fact answer, other students are finished with the entire problem.  Second, it does not always yield an accurate answer.  Students often make mistakes when creating these lists or counting tallies.  It then becomes an even more time consuming process.  Finally, the focus is not on the actual mathematical skill or concept that the lesson is about, but instead is centered on basic multiplication and division facts.

It can be very frustrating to watch as a teacher because I see that these facts get in the way of students being able to demonstrate more advanced mathematical understanding.  Similarly, it can be extremely difficult for students too because if the right answer is not achieved they can become discouraged.  When they reach the point of frustration, it often leads to wanting to give up or to no longer wanting to put forth their best effort anymore.

David Berliner raises the idea that education can be difficult to study and understand because there are always a number of different contextual factors in play.  These factors can be related to the student, such as family background and motivation to learn, and they can also be about the teacher, such as the teacher’s beliefs about learning and his/her attitude (2002).  It is my belief that all students can become proficient in recalling multiplication and division facts.

There are tricks that can help, but I also believe a student’s motivation to learn these facts is important too.  I am hoping to see whether technology will increase a student’s motivation to learn these basic facts, thus resulting in better retention of the facts.  Many of my students are immersed in a digital world filled with video games.  Greg Cruey mentions that students like having fun much more than they like working.  He contends that when learning is a motivational issue, playing games accomplishes much more than traditional drill and practice activities, such as filling in charts (2007).  Adding to that, Dave Lemire, Rick Mitchell, and Don Seckinger make the point that without motivation, either intrinsic or extrinsic, learning skills through drill and practice is severely impaired.  They continue to say that when drill and practice can be altered, possibly through a simulation or game, internal motivation rises and increased learning follows (2000).

Perhaps presenting math practice in this format will lead to students who are more proficient in knowing the basic multiplication and division facts, and will also positively affect students’ attitudes and willingness to practice these facts as necessary.

A Reflection on the Researchers from the Movie Nell

At first, Jerry Lovell and Paula Olson seem like very different individuals with a common goal. Their goal is to study and learn about Nell, and to make the decision about what is best for her. Should she remain at her home or should she be taken to a psychiatric institution to be taken care of? Jerry and Paula start with very different viewpoints in regards to this goal, but end up seeing eye-to-eye further into the movie.

In the beginning, Paula begins researching by looking for evidence that will explain Nell’s condition. She is a trained researcher whose job is to study people and explain their patterns of behavior. Paula works and thrives in a city that is very active, and sees many people each day. It appears that she views the people she observes as subjects often, rather than people, although not necessarily in a cold manner. To learn about Nell she sets up video cameras and begins to take notes about Nell’s vocabulary. It seems that she is motivated by curiosity and wanting to know why Nell is the way she is. She gives the impression that she wants to know about Nell in order to add to the knowledge of the scientific community. Paula tries to explain Nell’s behavior with labels and scientific words that have been used to describe conditions in other people. She also keeps her distance initially, observing Nell only on the video cameras or from the boat.

In contrast, Jerry is a family physician in a small, rural town near Nell’s home. His job is to care for people and to make them well. He seems primarily considered with understanding Nell and protecting her, so that she is able to live alone after the death of her mother. When observing Nell he relies on instinct, rather than proven methods of research. At one time he begins trying to speak to her in her own language in order to try and understand her. In another instance, Jerry tries to help Nell get over her fears of being outside during the day by luring her outside with popcorn. Jerry is also protective of Nell. He knows that she is easily frightened. Because of this, he watches her and makes sure that others do not scare her. When the journalist arrived at Nell’s home and tried to take a picture of her and when Nell encountered the man at the bar in town, Jerry was there to step in.

However, at the end, Paula comes to interact with Nell like Jerry does. At some point in the movie, she begins to see Nell as a person, and not just a subject to study. She works just as hard to protect Nell and to try and do what is best for her. At one point, her colleague at the hospital tells her that she is too attached to the patient and cannot decide what is best for her. This is the feeling she fought initially, but is one that also changed her views on Nell. When Jerry takes Nell away from the hospital, she does not stop him, but instead meets up with them later. As Nell is appearing in court, she sits on her side, supporting Nell, and also crying through the process. Both Jerry and Paula witnessed Nell thriving in her own environment in the woods, and also not being able to survive in the hospital. In the end, they unite and fight for the same purpose; to return Nell to her home.

What are some things that you have learned about effective teaching strategies when integrating technology?

• I’ve learned that most of the effective technology integrations involve higher level thinking skills, such as evaluation, analysis, and synthesis.  Problem-solving and simulation activities often promote these levels of thinking.
• I’ve learned that technology is not a teacher on its own.  Although students are often technologically savvy, they still need a guide and someone to help them make connections throughout the learning process.  Teachers can also be helpful with creating time lines, and managing the learning atmosphere.

How did integrating web-based technologies help you think about and evaluate uses of technology?

• When I’m forced to try something myself, I often automatically think about its application to my classroom.  For instance, as I typed the blog entries for my TechQuest, I naturally wonder how it would work with my students, and I sort through the benefits and challenges.  Actually trying to use a technology provides a more realistic application of what it would feel like to try something with students than just reading about one would.

How have you met your own personal goals for learning about technology integration?

• I’ve tried new things with staff members in my building and with my students.  This is often the first step in discovering a great lesson or teaching tool–just giving it a try!  Because of the opportunities I’ve had in this class, I’ve been able to try some new ideas and begin the process of refining them to be more successful in the future.

Do you have any new goals? What are your plans for reaching your new goals and your long-term goals after this course is over?

• My main goal is just to continue to learn about new technologies, and meaningful ways to implement them in my classroom.  I’d also like to try some of the things I’ve created in my certificate courses, including the copyright lesson plan from CEP 812.  I think this will be a great lesson to start with at the beginning of next year.
• I’m planning on continuing in the educational technology program, which will definitely help me reach my goal of continual learning.  In addition, I’m going to continue my TechQuest, using online professional development, in hopes of creating and nurturing a larger technology community in my school.  Finally, I’m planning to continue attending conferences and workshops, such as MACUL, to learn new things.