Math Concepts, Math Skills, and Problem Solving Educational Applications

My last blog post focused on educational applications for students that are struggling with visual-spatial or motor control difficulties. I had no idea about all of these wonderful supports and assistive technologies for students struggling in math before reading this chapter in the textbook. Next, in this post I am going to focus on educational applications that can be used to teach math concepts, math skills, and problem solving. In order for students to become effective problem solvers, they need to have conceptual understanding.

Check out these great educational applications to support students struggling with math concepts, math skills, and problem solving in the classroom.

• Virtual Manipulatives
• National Library of Virtual Manipulatives maintained by Utah State University
• http://nlvm.usu.edu/
• Users can navigate the site by category ( number and operations, algebra, geometry, etc.) 
• Illuminations
• Provides visual representations of concepts and interactive activities.
• Computing Technology for Math Excellence
• Provides explanatory information related to using virtual manipulatives. 

• Internet 4 Classrooms
• High-quality free internet resources to use in classroom instruction and to reinforce specific subject matter areas at home.

• Virtual Laboratories in Probability and Statistics
• Great resource for students studying advanced math.
• Provides text to help students understand basic theories.

• Math Playground
• Supports learning math concepts, skills, and problem solving.
• Free, online activities provided in different categories. (math games, word problems, and logic puzzles)

• Conceptua Math
• Focuses on fractions and offers a variety of tools for teachers to use to enhance their whole class instruction.
• Provides visual models that are accompanied by spoken text to facilitate independent use.
• Grades 2-7

• Destination Math
• Targets development of skills in math reasoning, conceptual understanding, and problem solving for students K-12. 
• Use of animation and audio output keeps students engaged. 
• Also has a full Spanish version to support ELL students!

During my student teaching experience last year I had a student in my third grade class that was struggling with math sense. He was fine with math automaticity and fluency. However, he had trouble with math concepts and problem solving. Additionally, he would have trouble recognizing why his answer did not make sense. I worked with him one-on-one throughout the year to help him better understand math concepts, therefore making less errors in his problem solving. I wish I knew about some of these great educational applications because I think he would have really benefitted from them. My favorite educational application that I learned about was destination math because it supports students with step-by-step instructions much like a teacher would. I also loved that there is now a full Spanish version to support ELL students who are becoming more and more popular in todays classrooms. 

Amy G. Dell, Deborah A. Newton, Jerry G. Petroff. Assistive Technology in the Classroom: Enhancing the School Experiences of Students with Disabilities. (Chapter 5) 2012. Second Edition. 

Visual-Spatial / Motor Control Difficulties and Technology Tools

In my last post I discussed educational applications that teachers could use to support students struggling with automaticity and fluency in math. This post will focus on technology tools that can be used to support students with visual-spatial or motor control difficulties. Lets start with what visual-spatial and motor control difficulties are.

Students with disabilities may experience difficulty with writing numbers, aligning digits in computation problems, and creating visual representations usually due to fine motor control or visual spatial issues. Additionally, these students may not be able to understand and interpret their own written work.

So, what can we do to support these struggling students in the classroom. The textbook provides several educational applications that address visual-spatial and motor control difficulties.

• MathPad
• Talking math worksheet program that enables students to perform arithmetic computations with whole numbers on the computer in much the same way they would using pencil and paper. 
• Allows students with fine motor difficulties to demonstrate their skill simply by using the keyboard or clicking the mouse. 
• Provides speech output options for those with visual impairments.
• MathPad Plus
• Extends all of the features or MathPad to arithmetic computations with fractions and decimals.
• Provides several additional features to support student success.

• Virtual Pencil (VP) Arithmetic
• Designed for students who are unable to operate a pencil effectively.
• Allows students to access addition, subtraction, multiplication, and division with whole numbers, fractions, and decimals without using a pencil and paper.
• Offers a speech feedback option for those who cannot see the problem.
• Virtual Pencil (VP) Algebra
• Extends most of the features of VP Arithmetic so students with disabilities can solve algebraic equations.
• Speech feedback option for those who struggle with sight or reading.

• Number Navigator
• Simple math processor to enter and solve basic math problems on the computer.
• Colors, fonts, and font sizes are customizable.
• Free!

• Microsoft Word/ Microsoft Equation Editor
• Enables students who have difficulty with handwriting but have good mouse control to create simple or advanced equations in correct mathematical notation.
• Numerous symbols are provided and are entered via a mouse click.

• Scientific Notebook
• High-end application that is designed to solve equations. 
• Provides students who have disabilities the opportunity to participate in advanced math classes. 
• I think this is so great to have support for students with disabilities in advanced math classes. Just because someone has a disability does not mean that they cannot be successful in advanced classes with appropriate supports. 

• Meanders' Annotation
• Provides a solution to handwriting problems in geometry.
• This is an add-on tool that works in Microsoft Office. 
• Enables students to draw on diagrams, record legible markings, and plot lines. 

Check out this video below on MathPad.

Amy G. Dell, Deborah A. Newton, Jerry G. Petroff. Assistive Technology in the Classroom: Enhancing the School Experiences of Students with Disabilities. (Chapter 5) 2012. Second Edition. 

Automaticity & Math Fluency Educational Applications

In my last post I discussed three key questions for teachers to consider when selecting educational applications to meet students' goals and objectives. This post I want to focus more specifically on what kinds of educational applications can be used to address automaticity and math fluency. Before getting started, I wanted to address the question what does automaticity and math fluency entail?

Automaticity refers to the fast, accurate, and effortless processing of content information. Automaticity is also referred to as math fact fluency. 

Students with disabilities often have difficulty reaching benchmarks in automaticity and math fluency because they need more instruction, practice, and reinforcement than their peers. Additionally they have difficulty remembering as many facts as their peers, fail to transfer the facts to long-term memory, and have difficulty retrieving those math facts quickly. So, how can we help? There are educational applications specifically designed to support automaticity and math fluency

• FASTT Math (Fluency and Automaticity through Systematic Teaching with Technology)

• Assesses students' command of basic facts by measuring response time and then generates customized activities based on the results.
• Students progress through the customized series of activities to strengthen memorization of facts and eliminate the need to rely on counting strategies to solve problems. 

• Timez Attack
  
• Solely focuses on multiplication facts, teaching the 2 to 12 times tables.
• Engages students in a high-tech video game environment featuring high-quality graphics. 

• ArithmAttack
  
• Practice addition, subtraction, multiplication, division facts.
• Customized problem sets are easily generated by setting the highest and lowest numbers to use so students' practice can be targeted to their particular areas of need. 

• Arcademic Skill Builder

• Math games are designed to help develop automaticity in addition, subtraction, multiplication, division, integers, fractions, and ratios.
• Various speeds of the game- slow, normal, fast. 

My favorite part about these educational applications was that only a limited number of keys are required to control the games so they could easily become accessible to students who are unable to use the standard keyboard or mouse!

Amy G. Dell, Deborah A. Newton, Jerry G. Petroff. Assistive Technology in the Classroom: Enhancing the School Experiences of Students with Disabilities. (Chapter 5) 2012. Second Edition. 

Key Questions When Selecting Educational Applications...

As I mentioned in my last post, my next posts will shift focuses from students with reading and writing disabilities. Rather, I will be discussing students with math disabilities. I am going to discuss the different assistive technology devices that are available for students struggling in math areas. Before we get started with that, the point of this post is to help teachers know what key questions to ask when they are selecting educational applications for their students to meet their goals and objectives. As a new teacher, this is something definitely something that I will want to keep in mind for the future. Teachers should employ a user-centered approach when selecting educational applications, matching them to the students' IEP goals to keep students on target with the curriculum. Teachers should also consider the following key questions...

• What is the intended outcome of the use of the educational application?
• For example, is it meant to strengthen math skills in problem solving or is it meant to build speed and accuracy with basic math facts?
• Is the educational applications likely to fulfill its stated purpose?
• For example, if the stated purpose of the activity is to build problem-solving skills, does it provide explanatory feedback needed to do so or simply assess whether or not problems are solved correctly?
• Can the educational applications be used as an alternative to traditional classroom activities to enhance students' participation?
• For example, will students learn as effectively using online manipulatives as they would using traditional manipulatives?

"Students interests must be considered. If the educational application matches students' interests, they will be more apt to dedicate their attention to it. When students find learning activities meaningful and interesting, including those that are computer-based, they spend more time on task and are more likely to meet learning objectives." 

- I think this is something essential to keep in mind whether teaching in regular education or special education. 

Amy G. Dell, Deborah A. Newton, Jerry G. Petroff. Assistive Technology in the Classroom: Enhancing the School Experiences of Students with Disabilities. (Chapter 5) 2012. Second Edition. 

Assistive Technology & Math

After watching the webinar a few days ago on assistive technology and math I became more curious on the topic and I hope you did as well. If you have not read that post or visited the website, I suggest you do so! Math has always been one of my favorite subjects growing up and I absolutely love teaching it! However, I do sometimes run out of ideas on how to support struggling students. I also have no experience teaching math in special education. Therefore, my next few posts will focus specifically on assistive technology and math. Most of the research that I will be discussing will be taken from my textbook, another great resource. (Assistive Technology in the Classroom, Enhancing the School Experience of Students with Disabilities). 

What experience do you have teaching math in special education? 

Did you have any assistive technology incorporated? 

Websites- Inspiration & Kidblog

This post will wrap up my module 3 assignment. My last few posts have really allowed me to piece together all the information that I have been learning in grad school about special education and assistive technology. As educators we are always on a journey, improving to become better and trying out new techniques and strategies with our students. There are so many great ways to support these students in the classroom and I cannot wait to try them. I wanted to provide you with additional resources in this post therefore I am taking some websites from my textbook chapter regarding assistive technology supporting writing.

• Graphic Organizers
• Inspiration/ Kidspiration
• This software supports visual thinking. Visual thinking allows the learner to better understand and retain information because ideas, words, and concepts are associated with images. Visual learning helps students organize and analyze information, integrate new knowledge and think critically. Graphic organizers, diagrams and outlines are just some strategies. 
• Graphic organizers are especially useful for the prewriting and brainstorming stage. They allow for students to organize their information and ideas for a writing assignment. 

http://www.inspiration.com/

• Blogs in Education
• Kidblog
• Kidblog is built by teachers, for teachers, so students can get the most out of the writing process. This allows teachers to benefit from the digital revolution of technology in education. 
• Blogging is something that is new to me this semester and I already love it. I can just imagine how excited older elementary students would be to use kidblog for their writing. This would definitely support those writers who struggle with fine motor and use portable word processors as assistive technology. 

http://kidblog.org/home/

Standards-based math instruction for students with intellectual disabilities

Last post I discussed assistive technology in regards to a reading webinar that I watched. The purpose of this post is to share with you some more information about assistive technology that I learned from an assignment. This post focuses on another webinar that I watched from the same website as last time. I will post the link for you again because it is such a valuable resource to pull information from.

http://www.gatfl.gatech.edu/tflwiki/index.php?title=Webinar_Archives

During my undergraduate courses at Cabrini, I had a course specifically about how to teach math in elementary school. Throughout the course I learned different ways to get students engaged, involved, and using manipulatives to be successful in math. Additionally, math was always one of my favorite subjects growing up so I really enjoyed teaching. However, I was never taught what to do with struggling students, especially those with disabilities. Having a class with 24 students, makes it difficult to meet with those struggling students for one on one support. This webinar provided me with great techniques and strategies for those with disabilities in regards to math instruction. I really enjoyed learning about how assistive technology can go hand in hand in supporting math instruction.

Key points...

• IEP goals do not equal curriculum!
• Goals: what to measure. 
• Curriculum: guide for progression of learning

• Practice is not instruction!

• Concept knowledge is as essential to math as comprehension is to literacy. 

• Educators rising expectations allows for students to have better opportunities to learn math.

• Good instruction includes...
• Scope and sequence of skills aligned to standards
• Comprehensive and systematic progression of learning
• Multiple hands-on math tools, methods, and materials
• Differentiated tools, materials, and instructions
• Break skills down, slow the pace down

• Assistive technology can help those with disabilities access math...
• Talk and write about math
• Understand math
• Perform a math task
• Engage in math
• Learn in the best way