Mastery Learning, Mathematics & Technology

Mastery Learning, Mathematics & Technology

My interest in the mathematics achievement of students has given me the opportunity to read many articles and studies related to theories that aid in the mathematics achievements of students.  This has lead me to mastery learning.  In this paper, the reader will garner a better understanding of mastery learning and how is can be used as a tool to improve student achievement in mathematics.

The mathematics achievement of elementary, middle, and high school students in the United States is an issue of concern for educators and policy makers, alike. The influential book The World Is Flat (Friedman, 2005) claimed that secondary mathematics achievement is a predictor of a nations long-term economic potential.  The National Mathematics Advisory Panel (2008) argued that to continue to progress in mathematics achievement, we must improve the quality of math instruction received by all students.  Although many factors affect a student’s mathematics learning, one factor over which schools have the most immediate control is the choice of mathematics programs to be implemented by teachers, administrators and curriculum developers.

            One possibility is mastery learning.  Mastery learning (Collins & Halverson, 2009) is an approach to learning intended to bring all students to a specific level of mastery on a set of instructional objectives.  This model provides teachers with timely feedback about the improvement and deficiencies of students in specific areas and presents a curriculum that provides for extended time and opportunities for all students to gain mastery.

            One definitive characteristic of mastery learning is the establishment of a standard baseline of achievement that signifies “mastery” of a specific concept or skill.  Mastery learning is measured by frequent assessments of student progress toward the mastery standard with opportunities to do so on later comparable assessment (Slavin, 1987; Guskey & Pigott, 1988).  A baseline for mastery learning is in the range of 80% correct on the assessment instrument.  Corrective instruction may take the form of tutoring, re-teaching, computer assisted instruction, or inverted teaching by the teacher, student tutors or classmates who have achieved mastery of the topic.  Additionally, small groups may be formed in which students review concepts or alternate assessment activities may be created for students to complete independently (Bloom, 1978).

            A second characteristic of mastery learning is frequent and concise formative assessments that guide both learning and teaching (Guskey, 2005).  Theses assessments provide both students and teachers with feedback about whether a particular concept or kill was mastered.  Those students who do not achieve the baseline standard for mastery are given alternate activities, peer tutoring, computer assisted instruction, and then, the student is assessed a second time.  If they are still unsuccessful, additional opportunities to study and re-take the test are given until the student reaches mastery.   Therefore, practically all student achieve mastery before moving on.  Students who achieve mastery on the initial assessment are given enrichment activities or given the opportunity to advance through the curriculum at an accelerated pace (Zimmerman & Dibenedetto, 2008).

            Finally, technology and mastery learning in mathematics are natural companions.  In this time of economic belt tightening, schools may be unable to hire tutors to help those students in need of remediation.  One such solution is the use of corrective math materials online available anytime and anywhere an Internet connection can be established.  Similarly, students that have mastered the concept can proceed by accessing materials online, too.   For example, BrainPOP creates animated, curriculum-based content that engages students, supports educators, and bolsters achievement.  Mastery learning teachers can retrieve free lesson plans, video tutorials, professional development tools, graphic organizers, best practices, groups and forums, to name a few uses of BrainPop. 

            Technology use in the mathematics classroom can aid students in working out solutions to problems that teachers would theoretically spend hours of instructional time teaching.  In this era of technology, mathematically thinking has become more important than ever (Slavin, Lake & Groff, 2009).  Finally, understanding mathematical concepts in the mastery learning environment may have been complicated in our past life of paper and pencil learning.  Conversely, with the use of the Internet, mastery teachers are able to provide dynamic and remedial lesson using online videos, software, simulated games, and so forth that presents materials using multiple representations as well as customized remedial lessons tailored to the individual student’s deficiencies.

References

Bloom, B.S. (1978). New views of the learner: Implications for instruction and

curriculum. Educational Leadership, 35(7), 563-576.

Collins, A. & Halverson, R. (2009). Rethinking education in the age of technology. New

York: Teachers College Press.

Friedman, T. (2005).  The world is flat. New York: Farrar, Straus & Giroux.

Guskey, T.R. (2005). Formative classroom assessment and Benjamin S. Bloom: Theory,

research and implications. Paper presented at the nnual Meeting of the American Educational Research Association. Montreal, Canada.

Guskey, T.R. & Pigott, T.D. (1988). Research on group-based mastery learning

programs: A meta-analysis. The Journal of Educational Research, 81(4), 197-216.

Slavin, R.E., Lake, C. & Groff, C. (2009). Effective programs in middle and high school

mathematics: A best-evidence synthesis. Review of Educational Research, 79(2), 839-911.

Zimmerman, B.J. & Dibenedetto, M. (2008). Mastery learning and assessment:

Implications for students and teachers in an era of high-stakes testing. Psychology in the Schools, 45(3), 206-216.

7 Stories From Educators About Teaching In The Flipped Classroom

7 Stories From Educators About Teaching In The Flipped Classroom

Steve Hargadon: Web 2.0 Is the Future of Education

Steve Hargadon: Web 2.0 Is the Future of Education: (Cross-posted from TechLearning ) A moment of extreme clarity became an obsession for me last week. A session that I had prepared for the ...

Experential Learning Theory

Experiential Learning Theory Carl Rogers distinguished two types of learning: cognitive (meaningless) and experiential (significant). The first has to do with academic knowledge, such as learning vocabulary or multiplication tables and the second is about applied knowledge such as learning about technology integration into the curriculum. What makes experiential learning distinctive? It addresses the needs and wants of the learner. Rogers identifies four qualities in relation to this; a) experiential learning; b) personal involvement; c) self-initiated, evaluated by learner, and d) pervasive effects on the learner. Experiential learning can primarily be thought of as an affective learning style. For example, for affective learning to take place, students in a class that their beliefs or values are supported are much more likely to "let down their guard" and accept the learning points. Rogers stresses that the learner needs to be emotionally safe for the learning to take place and have a genuine interest in learning the material in order for transfer of knowledge. According to Rogers, learning is facilitated when: (1) the student participates completely in the learning process and has control over its nature and direction, (2) it is primarily based upon direct confrontation with practical, social, personal or research problems, and (3) self-evaluation is the principal method of assessing progress or success. Rogers also emphasizes the importance of learning to learn and an openness to change. This theory approaches learning from the individuals’ needs and capacities for understanding of the presented topic. The learner is affected though self-exploration and self development of ideas though direct exposure and instructional direction. This approach to learning is similar to the group projects completed in Dr. Lambert’s class this semester. Not only did the group project force me to become a self-starter, I believe all of the assignments were arranged so that all students had an opportunity, albeit unknowingly, to experience experiential learning theory. Both the learner and instructor control learning. The instructor is there to set a positive climate, clarify the purposes of the learner, organization and provision of the learning materials, balance intellectual and emotional components of learning, and share thoughts and feeling with the learner without dominating the learning environment. The role of the learner is to become personally involved, self- initiated, self-evaluating, and acknowledge the pervasive effects that the learner experiences through the learning process. This theory is best applied to learning situations in which the learner participates out of internal motivations. The basis upon which this theory has been developed states that learning is based upon the needs and wants of the individual learner. This theory can be seen in practice in internship programs, psychological self-help programs, and self-help learning environments. Furthermore, one could conclude that Rogers developed a theory that is applicable to many different and varied teaching topics and environments. In conclusion, eexperiential learning theory helps teachers to understand learning and flexibility at a deeper and yet more comprehensive level. It also provides guidance for applications for helping students improve their learning and designing better processes in education and technology development. As it relates to technology and education, it further provides a theory and assessment method for the inclusion of the study of individual differences while addressing learning at many levels in education and society. This theory is very useful in the fact that every student is at a different level cognitively and academically; therefore, it would, in my opinion, increase student participation, engagement and ownership of their learning. Reference Deanery, L. (n.d.). Experiential learning theory. Carl Rogers. Retrieved on March 12, 2012, from http://simulation.londondeanery.ac.uk/educational-resources/salift-underpinning-learning-theories-experiential Smith, M. K. (1997, 2004) 'Carl Rogers and informal education', the encyclopaedia of informal education. Retrieved on March 13, 2012, from www.infed.org/thinkers/et-rogers.htm. Sternberg, R.J. & Zhang, L.F. (2000). Perspectives on cognitive, learning, and thinking styles. NJ: Lawrence Erlbaum.

This is funny!

Social Media

 This week we looked at the benefits and risks of social media.  Below you will find my responses to the questions that were posted:

1.  I joined several groups:  build your own curriculum, e-Mentoring for Student Success, Close Math Gaps Now, Visual Thinking Evolution.  I chose these groups primarily due to my primary interests in mathematics, curriculum, student achievement, & software.  I signed up for diigo about two weeks ago and each morning I receive links related to these interests and it's been very helpful and exciting.
2.  Young people are more likely to play games, communicate to their friends, and "bully" other students.   Older adults are more likely to use it for keeping in touch with family and friends.
3.  Pros - teachers are able to increase students' engagement in their education, increase technological proficiency, contribute to a greater sense of collaboration in the classroom, and build better communication skills.  Cons - increased cyberbullying, online predators, and less face-to-face with family and peers.
4.  Most of the time I am on Facebook because it allows me the chance to stay in touch with my relatives who live out of state.  I also monitor some of the things that are posted by students that might impact the school climate and culture.
5.  Benefits - increased connection to others, increased self-esteem, promotes participation, meet technology expectations of students, more awareness of social issues, and networking with others and professionals.
Cons - increased depression, especially among teens, potential to trigger eating disorders in adolescent females and causes deterioration and conflict in marriages, and poor vocabulary, spelling, and increase in acronyms

Thus far, this has been a very enlightening and worthwhile experience.  The assignment this week as given me a greater understand of the importance of the use of social media in teaching and learning. Finally, I really enjoy being able to share my new knowledge with the teachers in my building.

Gaming

Benefits of gaming, virtual realities, and simulations

The benefits in the classroom are endless.  Gaming allow students to enter worlds that would otherwise be impossible to visit.  Gaming, simulations, and virtual realities allow students to go back in history, understand the complexities of running a major city or corporation, and so forth.  Other benefits I see are increased student engagement, exploration, ongoing and responsive feedback, individualized instruction/learning, and motivation to explore beyond the limits of their abilities.  Gaming, VR's, and simulations also stimulate conversation and discussion, allow for the exchange/share ideas and provides supportive and engaging learning environments.

In an article I read by Engelbrecht and Harding (2005), it stated that, educational literature reflects a paradigm shift linked to education and the web due to the, “anytime, anywhere promise.”  They site authors who argue that, the paradigm shift should occur in the interaction between pedagogy.  Teacher's play a very important role in the implementation of gaming in the classroom.  Most importantly in order for gaming/VR's/simulations to be effective in the classroom, the teacher should consider the following:

• Be clear about the learning objectives that learners are intending to achieve over the course of the work.
• Use games appropriately.  They do not have to be used in their entirety in order to achieve educational goals and stimulate motivation. Certain game aspects can be extracted or isolated from the game as a whole.
• Allow for sufficient time for both you and your students to become familiar with the game.

As a self-proclaimed "techy," it is my belief that student achievement can become a reality if we, educators, utilize the tools we have at hand.  I also believe students would be more stimulated, engaged, and energized when teacher's realize that today's student are less likely to verbally communicate and more likely to communicate through technology.  As an educator, I believe, scores, graduation rates, and participation would rise when we eliminate paper and pencil and use the technological tools available at home and school.

Three sites I visited

Gamequarium - an interactive site that has activities related to the core subjects.  It is my belief that students up to 9th grade would benefit from this site, even though the site is geared towards K-6 grades.  The math game I played was interesting; the concept was similar to "Who Wants to be a Millionaire" except you didn't get "lifelines" only three chances to get the right answer before the game was over. 

Darfus is Dying - a narrative based simulation that from the players perspective must fight or negotiate against the enemy in order to protect the refugee camp.  It appears the idea came from the war in Iraq and other foreign wars, like Pakistan and the Sudan.  Although I'm no history buff, the simulation appears to be very interesting and helps make a difficult concept simple.

There - a virtual reality site that allows the user to use their imagination to the fullest.  Since I'm not very imaginative, this site was a little boring and overwhelming for me.  I think the site would be a great vehicle for at-risk students.  Oftentimes these students have "wild" imaginations and no one taps into it, which makes it easy for them to join gangs and be a part of the wrong crowd. 


This weeks assignment allowed me the opportunity to broaden and deepen my knowledge of gaming, simulations, and virtual realities.  It also gave me some ideas for my dissertation and I will be able to share these sites with teachers in my building.  

Internet, Ethics & Open Content

Copyrights & eBooks
"Copyright is a form of protection provided by the laws of the United States to the authors of original works of authorship (US Copyright Office, 2008)." In other words, copyrights are automatically secured once the information has been written or recorded.  As a result, anything written in ebook form automatically becomes copyrighted.  However, ownership of an ebook does not give the possessor the ebook copyright.  For example if you download an ebook, you do not have the ebook copyright.  Only the author of that book or someone who has been given rights by the author has that ebook copyright.

Internet & Ethics
Now doesn't this title sound like an oxymoron?

The Internet is not only a text-based medium made up of communities, newsgroups and email lists.  It is also a medium of publication, and significantly one where users can take control of the means of production, create their own cultural artifacts and intervene in the production of existing ones.  The Internet can thus be perceived as a form of cultural production, in a similar framework to that of the print media, broadcast television and radio.  The difference is that the Internet isn't as censored as other media outlets, although sites like YouTube, have content censorship statements that state the content is monitored 24/7, 365.

It is my opinion, that in recent years, people have no shame about the despicable content they post on the Web.  Respect and courtesy are quaint, outdated notions to these Internet citizens.  The people charged with protecting us from such abhorrent behavior not only fail to prevent it, they tacitly or explicitly encourage these breaches in morality because it means more page views, more customers, and more money.

Open Content & K-12 
A growing movement of K-12 educators is latching on to educational resources that are “open,” or free for others to use, change, and republish on Web sites that promote sharing.  The open-content movement is fueled partly by digital creation tools that make it easy to create “mash-ups,” or digital medleys of content of various types. From a financial standpoint, it saves schools money by spreading the time and expense of developing curricular resources over many contributors.

It also passes on the value that teachers add, when they adapt works originated by others, so other educators can benefit from it.  Many adaptions give schools more ways of differentiating instruction, by adding language translations, shifting grade level, and adjusting for reading ability, a special geographic or cultural focus, and other strategies to promote a standard curriculum.   In addition, open educational resources such as, The Math Open Reference, makes interactive math problems available for extra practice which may not be available to the classroom teacher, especially in these economic times.

The process of content creation and sharing is also a way to build professional relationships between teachers.  Consequently, the more that teachers get their hands into content creation, the better they can teach that material.   Textbooks, however, remain a constant in nearly all schools, and publishers of traditional textbooks do not appear too worried about the open-content movement. However, the 2011 Horizon Report suggests that publishers have at last begun to uncouple print and electronic sales of textbooks, making it easier to choose one or the other as desired.  

In conclusion, the availability of open content materials is growing which means educators will need to set aside time to research these sites, if they are going to make them available to their students.  I think the concept of open content is great and it is important, in my opinion, that school district leaders should take an extensive look in making these sites available which would drastically reduce the amount spent on textbooks and wasteful supplemental materials.  As an administrator, I see firsthand the wasteful spending that happens because textbook publishers entice textbook committees and curriculum directors to purchase "extra" educational stuff, that could be found on open content sites for free.  Furthermore, I believe citizens would be more willing to fund schools and pass levies, as long as districts are able to show taxpayers that they have "tightened" their spending and are utilizing their dollars for things that directly impact instruction and student achievement.   Heck, who knows the salaries of teachers may increase. Lol

In the Clouds

Build Your Own Curriculum - this site is beneficial for students, parents, administrators and teachers. For students, this site helps them view the standards they’re expected to learn and master, see class activities, and access the resources they'll need to complete their work. For parents, they can view curriculum, assignments, and standards from home, work, or your community library. For administrators, they can have access to the information they need to help shape curriculum, to fulfill their role as instructional leader. For teachers, it makes resources readily accessible and it makes it easy for teachers to update and customize their lesson plans in alignment with your district's standards and expectations.

Wise Mapping - this site allows students to build concept maps in every subject that can be used as study aids and it helps the teacher be able to provide a visual for students which is especially helpful for difficult content.

Targeted Learning Assessments - this web based resource identifies gaps and then guides students through award-winning differentiated instruction, interactive activities and practice in order to fill in these skill gaps and bring students back to grade level.


Word/Tag Clouds
Using word or tag clouds allow students to analyze their own writing. By using a word or tag cloud, a student can easily see if the main points displayed in the cloud match the main points they hoped to cover or convey in their writing. Word or tag clouds are really helpful as a tool that gets students to break their work down and see aspects that they could change. It’s also visually more interesting, which really helps make it a useful exercise for perceiving new things about what you’ve written. Putting a draft into a tag cloud means that you can see if the actual composition of your text matches what you want it to say. Word or tag clouds can be used to help all learning styles gain a better understanding of text by emphasizing the main points in an easy to understand graphic.

Social Bookmarking
Social bookmarking has opened the door to new ways of organizing information and categorizing resources. Tagging information resources with keywords has the potential to change how information is stored and found. It is my belief that remembering how to retrieve information using a framework created by and shared with peers and colleagues will become the wave of the future. Social bookmarking makes the process of distributing reference lists, papers and other resources to students, peers and colleagues more simplified.

Personality assessment in team building - Emotional Intelligence 4 Change

Personality assessment in team building - Emotional Intelligence 4 Change

Blogging & Tweeting

I have learned that a blog is a personal diary. A daily pulpit. A collaborative space. A political soapbox. A breaking-news outlet. A collection of links. My own private thoughts. Memos to the world. And, a means of communicating to students in a way that meets there educational needs.

While watching the video "In Plain English," I have come to realize twittering is a great way to find out the latest news/gossip and it is a microblogging service that allows you to communicate in a quick and easy manner (140 characters or less). My personal beliefs about tweeting is that it is a great venue for "noisy" and "bored" individuals to find out what others are doing. I must admit I was sucked into the twitter craze about two years ago, but it is quite time consuming.

We live in the 21st century where our students "do" social networking. Social networking is a part of who they are as digital brats. To most of us, getting on Facebook, Twitter, or Skype is a huge deal and to our students it is their way of life. Honestly, I think if they didn't have these media outlets, they would think life would be over! Understanding their connection with these sites will increase our connection to our students. With this connection we will be able to talk their language and may even provide an opportunity to breakthrough to an at-risk student.

Many educators have students who seem unreachable. Sometimes educators do not feel comfortable reaching out to their immediate colleagues, so they reach out to people they follow or to the people who follow them on Twitter. Many times their Twitter colleagues can provide really valuable resources that can help them meet the needs of the at-risk student.

Currently, I follow several networks on Twitter. They are "20Obama12," "Oprah," "nytimespolitics, "BarackObama," and "13ABC." Honestly, it has been months since the last time I was on Twitter, but being in this class has caused me to check my account more often.

Martin Luther King - I Have A Dream Speech - August 28, 1963

It seems as if he's still alive. He was a source of inspiration and challenge, he gives me more courage related to racial issues, very impressed by his passivism and how he can make such an impact without showing anger or disdain towards others. I believe every race needs a "drum major" for the ills that are perpetrated on their people. He was very knowledgeable about the issues related to all races, not just African Americans. In addition, he made me very proud to be Black and the statue in Washington, D.C. is replica of the ills and trials he went through to increase our awareness and knowledge. Finally, his christian faith made it possible for him to forgive his enemies and it showed me the importance of loving those who don't or won't love you because of your skin color.

President Obama Sings Al Green Let's Stay Together

Who knew that the 44th President of the United States of America could have been a contestant on American Idol, America's Got Talent, or Sunday's Best?

I definitely didn't, but he is full of surprises!!!! Take a look: