2.7+Tech-knowledgy

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This reflection is a one page summary of "Tech-Knowledgy and Diverse Learners". Paste your reflection followed by your name. This is due Thurs, March 15, before 4 am.

In the document Tech Knowledgy, it talks about how technology can help improve math understanding for students. It also talks about how teachers must have knowledge to best use the technology in the classroom. (1-3)

One thing the article focuses on is how technology helps different kinds of people, like English Language Learners (ELLs) or Special needs students (1-5,6) With ELLs, one of the skills in need of development are developing and sustaining "mathematical talk", which I feel is something that would be a challenge to get across to students who might not understand what you are trying to tell them. Special education students on the other hand usually have a problem with the problem solving aspect of math. Most of the time teachers just teach these kids direct ways of doing the math when research shows that they can develop understanding beyond simple algorithms and procedures (2-2).

I think technology can be used to help ELLs and lower ability learners understand math better, which research supports. I really like the table on page 4, it is an amazing resource and I think it can help me in the future. I feel like a lot of teachers do not give an opportunity for special needs kids to try things on their own.

I thought the examples they showed in the document were really cool. I really like the virtual balance. The use of different visual aids allowed students to think and reason about different math ideas (7-1) I hope to be able to use technology in my future classroom and I hope I will remember this article, especially the table with the different resources so I can use it when I get into the classroom setting. **(Nicole Parry)**

Tech-Knowledgy & Diverse Learners, by Jennifer Suh, poses the answers to two very crucial questions mathematics teachers must ask: how do I successfully use technology in my classroom as well as how do I help my struggling learners understand mathematics. Jennifer Suh has the answer-- use technology in the classroom that will help struggling students.

Our students have a variety of backgrounds in mathematics, and those who are English Language Learners (ELL) are faced with an even greater challenge in learning mathematics, especially with "mathematical talk" (441-5). Students with special needs typically struggle with "identifying and selecting appropriate strategies, organizing information, monitoring problem-solving strategies, and generalizing new situations (Sliva 2004) (442-1). Technology can help assist these students overcome these setbacks-- and thus teachers need the background knowledge on how to incorporate technology in the classroom (442-4).

Technology has many benefits that I had never thought of until reading this article, including allowing students to see representations of the numbers, immediate feedback, representation in nontraditional ways (442-5). I also feel that Suh's table "Tech-Knowledge: Planning with Technology to Meet Diverse Learning Needs" gives real resources for how to bring technology into the classroom for struggling student is especially helpful because it includes several websites teachers can use. These resources are especially important for algebra because the author argues this fundamental class requires a sound understanding for students to go further in mathematics (443-1).

Suh's examples of lessons which use technology in the classroom are surprised me-- even though these lessons are designed for special needs students, I myself feel my conceptual understand would be improved had I been given these lessons when learning algebra. The first example, Healthy Tree, uses technology from brainingcamp.com that compares growth rates a trees with giving students experience working with "rate of change, graphs, functions, problem solving, and connections" (444-1). Suh also stated that the website had "tiered levels of difficulty and language", which makes the lesson adaptable to all levels of understanding (444-4).

Although we have been discussing in class how technology can be a useful teaching tool, looking at Suh's lesson plans and resources has given me more hope that I can incorporate technology in the classroom in a way which enriches knowledge. Because I have not had much experience working with technology in the classroom in this way, I have not really though of the options available. Because Suh offers websites that teachers can use for FREE, I will keep track of this article. --- Katie Pingle

We need to use cognitive technology tools, because these can be used to help students think learn and problem solve beyond their own boundaries (1-1). The key to these tools is that the teacher must know how to use them, along with how to make them usable by students. This "tech-knowledgy" allows teacher to help a diverse group of students learn about the math using these tools (1-4). There are many struggles when working with a diverse group of students, especially when one of those groups is English Language Learners (ELL). One of these struggles is getting the mathematical language to come out in the classroom (1-5), but it is important because without that language, it is hard to teach them. Students with special needs can rise to the critical-thinking level of mathematics, they just need to be pushed past the rote memorization and algorithmic mindset (2-2). These tools can cause less confusion than manipulatives, because manipulatives require the brain to track multiple cognitive events and that is hard to do for many students, especially those with special needs (2-3). Using technology is a good way to work towards critical thinking and understanding concepts, because it allows for students to focus on the concepts and ideas rather than all the calculations. Table 1 on page 3 shows that there are many ways that technology allows many affordances, such as tiered lessons and feedback. These allow students to see right away if they make a mistake, along with letting students at different skill levels work at different paces. They also allow students to create their own problems and find the solutions to that, which gives them a little more interest in the questions.

Much of the technology we have now can also be used in interactive ways. There are many websites that can be used to help teach students mathematics, but the difference is that these websites are much more engaging that a lecture or discussion in the classroom. When problems are put into words and are relatable to the students, they have a much easier time working on the problem, because it gets them much more interested. This is apparent with the downloads problem on pages 5 and 6. The students had special needs, but they were able to get into it and understand it, because it is something they can relate to.

I have spent much of this class criticizing technology in mathematics classrooms because I feel that it gets used as a crutch more often than for critical thinking. If all teachers would use technology like this article talks about, then technology is not such a bad thing, because it allows teachers to use the time for helping students to understand concepts rather than having to spend all their time watching students do calculations. This allows students to take the time they need to understand everything, and it also allows those students that understand something to move ahead.

Technology allows us to give ELL students and students with special needs the time and direction they need. It gives them a way to learn that is different, and probably easier to understand (7-1). It allows ELL students have a visual, which helps them understand the mathematical language, so they do not have as much issue understanding everything in the class (7-2). -**Josh Kaylor**

The article, Tech-Knowledgy & Diverse Learners, discusses how teachers can leverage the power of technology to teach mathematics and engage diverse learners in critical thinking and problem solving.

What are diverse learners? This author focuses on those students who have difficulties with the English language (ELL) and other special needs students. Most of these students have received direct instruction in mathematics, thus having limited opportunity to develop their mathematical understanding (2-2). The traditional model of teaching algorithms and rote repetition to this group of students has resulted in a group of students who have not had the opportunity to construct conceptual understandings of mathematical processes (3-2). What features should the technology possess which grows this population, yet doesn’t overwhelm them?

The author notes various needs which can be met from mathematical technology (Table 1). She proceeds to show three different examples of programs which help students learn mathematical vocabulary, experience tiered levels of difficulty, make conjectures, generate representations allowing for analysis, offload routine tasks, and receive immediate feedback.

I have utilized the online homework programs MathXL and Enhanced Web Assign in teaching courses at WMU and KVCC. These homework programs do offer the opportunity for students to receive immediate problem feedback, view video help, view pictorial images, and link to other resources. They don’t appear robust in meeting the needs of the ELL or special needs student. I have found some innovative applets on the Internet.

As a future instructor in a middle school or high school classroom, it would be very helpful to have access to robust mathematical technology tools that assist the ELL and special needs students. The integration of special needs students with the general student population is common place in today’s schools. This scenario mandates that the instructor utilize as many tools as possible to help all students learn mathematics. One tool which needs to be in the instructor’s toolbox is technology. Instructors must possess “tech-knowledgy” in order to align educational mandates with software resources available (6-5). ** (Susan Copeland) **

When looking back to about 20 years ago, the only mathematical tools used for learning were pen and paper and a basic calculator. However, as new technologies and advances in mathematics are discovered, it is being realized that these things can help greatly in learning mathematics.

When you walk into a middle school mathematics classroom, there is almost a guarantee that the class will be made up of different students with varied abilities. Having the new technologies available can help the teacher reach out to multiple students in their classroom and help them develop conceptual understandings based on which way they learn best. For example, one student may see trends in a linear equation easier using the numbers on the table, while another student might prefer to look at the graph. These things can be achieved on a graphing calculator, which are becoming more and more common each year.

Another thing that is becoming more common would be accommodations made for students with special learning needs. Before, teachers didn’t really know how to tend to each and every student in their classroom, so they only had one method of teaching and had all students do the same things. Now, however, it is realized that there are certain kids who need different instructional methods in order to learn. In this article, “Tech-knowledgy & Diverse Learners” by Jennifer Suh, she states that special needs learners often don’t get the chance to use different technologies to construct conceptual understandings of processes in mathematics (443-2).

Suh then goes on to give three different examples of how technologies can be leveraged. In the first example, it shows a problem on a computer program about tracking the heights of trees after certain periods of time. Since the students are given real pictures, graphs, and situations that complete a scenario in their head, it makes it more engaging and gives them a better understanding of the mathematical concepts, even if they don’t realize it (444-3).

In another example, the students were able to use spreadsheets to graph out the problem given to them. This way, they didn’t have to draw out the graph and plot all of the points, which can become time consuming and tedious and it takes away from the overall lesson (445-2). This creates a more efficient classroom learning center, and it also cuts down on time needed to go through a lesson. Since there isn’t any time wasted on things such as drawing a graph from scratch and plotting out the points (445-5), there is more time allowed for the material that is jam packed into the curriculum.

There is so much material that is required for students to learn, that new technology can help eliminate unnecessary tasks and make classwork more efficient. It helps teachers be able to reach out to their students with special learning disabilities, also and allows them to conceptualize difficult mathematical ideas. **-(Shanna Thorn)**

Jennifer Suh’s “Tech-knowledgy” talks about how to use technology in the classroom and to use it to reach out to students of all needs and of all backgrounds. “Tech-knowledgy” is defined as knowing how to use the technology effectively to aid students in constructing their mathematical understanding and to create learning opportunities with the technology to amplify mathematics and mathematical understanding (441-3). Technology can be focused to help those students with special needs and other types of learners, such as English language learners, ELLs.

The ELLs have a tough time connecting to the classroom that speaks a language they are still learning, and combining that with an academic language and mathematical language, ELLs may have a tough time understanding (441-5). Specials needs students are restricted already physically and/or cognitively and certain technology can be used to help these students more than traditional, lecturing classrooms. When you combine the feeling of poor academics a student may feel with negative experiences with mathematics, this can lead to a feeling of helplessness (442-1).

A real guru can bring the technology to the students without hindering the understanding of abstract concepts or mathematical ideas. Students can use the technology to:

- Make connections and visualize relations between numeric and visual aids

- Receive prompt feedback to avoid any delusions of false progress

- Meet the needs and use it with their mathematical background, no mater the background (442-7)

On page 443 of the article, Jennifer Suh gives examples of technology that can be used to amplify the effectiveness of a lesson in a teacher’s classroom. A graphing calculator seems to be the most easily accessible and a quick, yet one of the best, options for students to use technology at their fingertips. The graphing calculator can visually show students graphs, functions, and other symbolic representations right in their hands (443-2).

Jennifer Suh gave three examples of how technology can be used to enhance instruction, and they briefly are: analyzing rates of change, building rules for specific functions, and using technology to balance equations (444-2?), (444-12), and (445-6).

Teachers commented on how technology made their lives easier. They enjoyed having the technology in the classroom that allowed the students to access the understanding (446-1). Students were also able to make connections and relationship among the visual aids (446-3). When a teacher is a technology guru, then they are capable of using technology to help students, no matter the students’ disadvantage(s) (446-5). ** (Ryan Sherman) **

The article talks about how we as math teachers can use technology in the classroom to teach and engage students in mathematics, especially when we are dealing with diverse learners such as English language learners and special education students. The article is broken into three parts…

1. Needs of Diverse Learners

2. Developing Tech-Knowledgy for Diverse Learners

3. Examples of Cognitive Tech Tools in Use.

The needs of diverse learners are various, with English language learners there are two language challenges to deal with, conversational and academic languages (2-5). Special education students have different sorts of needs to be faced, such as difficulties with the metacognitive aspect of problem solving paired with a poor academic self-concept (3-1). Research has often shown that through physical manipulatives students are able to grasp a deeper understanding of mathematical concepts; but there is an inherent problem with physical manipulatives when dealing with ELL students and special education students. Both sets of students may have difficulty understanding how to use the physical manipulatives, through either difficulties with a language barrier or an overload of cognitive processes. Both of these issues can be solved through the use of technology, with virtual manipulatives the issues can be lessened due to the limitations that are present to ensure proper usage of the tool (3-4).

According to Suh, Johnston, and Doud the use of technology in mathematics can help provide connections between numeric and visual representations, prevent misconceptions by providing immediate feedback, take mathematics from a noun to a verb through interactions with dynamic objects, and give opportunities are to learn and visualize mathematical ideas in nontraditional ways (3-7). There were several examples given of these types of virtual manipulatives, my favorite being the Balancing of Equations Using the Virtual Balance Scale (6-5). - **Hutch**

Opportunities are possible to teach and represent mathematical ideas in nontraditional ways