Technology Blog

Technology is becoming better and better is what seems to be exponential time. As a future teacher, it is important to look at how technology can positively and negatively affect a classroom.

Our generation today has so much experience with technology. Growing up with a computer, and learning how to play around on programs has been beneficial. When I look at the older generation, I can generally say that many adults feel less comfortable with technology than my generation. Most adults are less likely to spend time experimenting with learning new programs; although this is not always the case. This proves to be beneficial for the younger generation teachers who are entering school districts and know how to learn programs on their own. During my Novice teaching experience, my teacher had me spend an entire day teaching her how to use different technology programs. Knowing how to learn, adapt, and change with the times is important as a teacher. With technology expanding so quickly, it is important that we learn how to figure things out on our own or collaboratively.

With technology expanding so rapidly, it is hard to keep up with all of the new and fancy programs. Students in today's society are used to spending time on computers and using different programs. They are learning how to work the technologies we are using just as quickly. However, I believe that technology can prove to be a negative factor in education if used in the wrong way. Although technology is seen as the new 'fast pace way to life,' technology can actually waste a lot of valuable time for learning as well. When technologies fail, or computer programs do not sync, technology can prove to be a hinderance. Programs are changing and becoming better every day, which means formatting for each program is now different. From computer to computer, technology can prove to be a challenge. Also, when the internet fails, the computer freezes, or any other technical difficulty is faced, technology can waste a lot of time. It is important if we, as teachers, use technology in our classrooms, that we do so in ways that value the learning opportunities of our students. Two examples of valuable educational technologies would be the smart board and the geometer's sketchpad program.

The smart board is an incredible presenting tool that students typically get excited to use. There are many opportunities that the smart board provides that can enhance certain educational topics. My very favorite math technology is Geometer's Sketchpad. For inquiry learning, I believe this is the most valuable math technology program available. Students can explore different math concepts from beginning learning experiences to very advanced learning experiences. I have personally worked on basic geometry concepts in this program as well as advanced calculus ideas. I had a teacher at Bradley who provided guided learning worksheets that went step-by-step through directions on how to create a specific geometry idea or concept. Once we had used the direction to complete the activity, we had to experiment with the shape/design/measurements to figure out what the diagram represented and meant. I learned how to complete many geometry proofs using this program. This is very beneficial, because sometimes students focus more on the formulas rather than the concept. When students get to figure out the concept on their own while visually seeing representations of something they created, they take more value in their learning process. Overall, this is my favorite program. I think this provides many valuable learning opportunities for students and demonstrates one great way that a teacher can apply technology in the classroom.

Calculators are another technology that can be used in the classroom. They can also be great for students to use and check their work. Calculators now can visually show representations of ideas. Students can even explore concepts on calculators to prove how a certain formula or concept works.

I do not believe that technology can 'create the learning experience,' nor do I believe it can solve all the problems for education. I think that when used in the right opportunities, technology can prove to be very beneficial. Math applets provided by Illuminations and NCTM can help students work through inquiry learning to deepen their understanding of concepts. When teachers use technologies that are appropriate, educational experiences can be enhanced. Teachers really need to learn when and when not is appropriate to use technology, find a balance for how much technology should be incorporated, and relate to both the positive and negative aspects of technology in the classroom.

April Journal Article MTMS

Obara, S. (2010). Constructing spatial understanding. Mathematics Teaching in the Middle School (15)8, 472-478.

Students need spatial sense and understanding when using two-dimentional shapes and three-dimentional diagrams. Sometimes, students experience difficulties with spatial understanding becaues it is not intuitive. Students need practice visualizing two-dimentional nets and their transformations to three-dimentional figures. In order to help students understand how shapes are creating through folding, curling, etc. to a net, teachers often use geometry technology software. One teacher used a triangular pyramid and a cube and asked the students to create the nets to these figures. Using Geometer's Sketchpad, the teacher showed the students how to construct a net and modeled construction as well as use of the Sketchpad. Students were then able to explore and create their own net to try to figure out the net for the solids she presented earlier. Another approach the teacher took to developing spatial understanding was to pass out congruent three-dimentional pieces of a shape and had her students try to develop the net for a specific figure. Students often started solving this problem by using a square out of the pieces given to them in order to start building their net. Students were able to see that by creating two identical pieces from equilateral triangles into the form of a trapezoid, that they could construct a tetrahedron from these two 3-D figures.

Working with students to help them develop spatial understanding between 2-D and 3-D shapes will benefit them in their understanding of geometry. By having this type of understanding as teachers, we will better be able to use hands-on activities to teach our own students how to better comprehend spatial sense and how it applies to different forms of geometry. When students use inquiry based learning such as the type given in this lesson, students get to explore different nets and models as well as incorporate technology into the curriculum. This overall will help students to develop spatial sense.

April Journal Article TCM

Treahy, D.L. and Gurganus, S.P. (2010). Models for special needs students. Teaching Children Mathematics (16)8, 484-490.

Co-teaching is a specific type of teaching where a special education teacher and a classroom teacher work collaboratively in order to develop a more cohesive progam for planning, teaching, and assessing/evaluating. By using collaborative efforts such as co-teaching, the classroom becomes unified and represented as a whole unit. In one specific classroom, a classroom teacher and special education teacher taught mathematics together. The classroom teacher would teach her mathematic concepts or lesson while the special education teacher would ask her to clarify specific points or to repeat important concepts that may need to be heard again. By doing this, the two teachers incorporate a strategy similar to the reading strategy, think-alouds. These two teachers also take turns teaching important concepts and share the role of instructing in the classroom such as a team-teaching role would present. By doing this, students are gaining a deeper understanding of difficult concepts. By repeating difficult material and clarifying it in different ways, students get to see different aspects of the problem. The article lists a number of different models for teaching a classroom of integrated learners; these include:

Team: shared role between the two teachers

Alternative:

• one teacher works with small groups for re-teaching, enrichment, pre-teaching, etc. while the other teacher works with the rest of the class
• teachers use think-alouds to clarify and to help train special needs students to work through the problems rather than applying a random formula or idea that they have learned; (lack of metacognitive skills)
• great for hands-on learning
• great for working one-on-on or in small groups to clarify concepts for struggling learners

One teach, one assist:

• allows one teacher to teach while the other teacher walks around and observes and helps students who need it
• can beneift students with behavior issues
• helps to focus more on special needs students; gifted learners, special needs, ELL
• allows individual assistance for students
• great way to monitor progress

Stations:

• content is divided into different stations and each teacher teaches a specific station
• great way to incorporate the NCTM standards
• teachers can focus on an area of their strength to benefit deeper understanding for students
• stations often incorporate real-life integration
• allows for monitoring and reinforcement
• can help prevent math anxieties early on

Parallel:

• the teachers plan cohesively but then each teacher teaches a half of the entire class
• teachers must plan for all areas of learners
• teachers must think about how all students learn and how to relate to all students

As a teacher, co-teaching would be something that would be benefical in the classroom. It provides rich learning experiences for all areas of learners. During these types of instruction mentioned in the article, teachers use models and clarification so that all students have the ability to understand concepts. Co-teaching helps create a common instructional language that all areas of learners can understand. This helps to unify the classroom and help students become more engaged in the materia. C0-teaching provides a rich learning opportunity for a wide-variety of students. The talents and energies of two teachers can be effective in a class of different types and styled learners.

Observations with Checklists

Cole, K.A. (1999). Walking around: getting more from informal assessment. Mathematics Teaching in the Middle School (4)4, 224-227.

This article describes how informal assessments such as observations with checklists can be used to gain, organize, and document information about students' performances and academic growth in order to produce coherent stories of student progress. Teachers walk around the room to gain types of informal assessments on student learning and progress. By doing this, it helps teachers to receive immediate feedback of how students are thinking and working on problems. For example, a teacher described in the article walked around the room in order to view students' thoughts about a math problem they had been working on. When she walked around to each group and talked with them about their thoughts/ideas, she round that come children had confused meters and feet in their problem they had been working on. By observing students informally, teachers can gain a lot of information about how students are working and certain misunderstandings students might have. Teachers can also introduce new ideas and pose more in-depth/higher-order thinking questions to students. The teacher in this article continued to walk around the room during different days throughout the weeks and found that her questions she had posed to certain groups had been effective toward their learning. Students were able to use their journals to further explain their mathematical reasonings. Using checklists can help us to organize our observations as we walk around the room. Checklists can focus on mathematical tasks, students' communication, using math language, and their ability to work well with others in the classroom. Checklists help to observe students and find out how well students are using the mathematical concepts and standards in the classroom.

March Journal Article TCM

Wallace, A. H., White, M.J., and Stone, R. (2010). Sand and water table play. Teaching Children Mathematics (16)7, 394-399.

Sand and water tables provide many educational opportunities for younger children. Social atmospheres and play time help students with their natural emotional and cognitive development. When teachers provide opportunities such as a sand and water table for play, students get to explore using different types of manipulatives. Teachers can help engage students in more valuable learning opportunities using different types of manipulatives at the play table in addition to creating different learning environments. For example, teachers can designate specific tasks at the table, but can also allow free exploration for students. By providing students with different beakers and 3-D shaped objects, students can explore different concepts such as equal values, volumes, shapes, etc. This article explains that it is important to allow free exploration first so that the children become socially comfortable as well as get used to some of the manipulatives. Once free exploration has been done, the teacher can introduce different concepts. This might mean that the teacher would point out the numbers on the side of a beaker and help guide the students to figure out what the numbers mean. After the concept introduction, the teacher can use application of the concept. Students then get to choose their own manipulatives/materials and explore concepts through concepts that have been introduced. The final stage is the evaluation stage. The teacher informally can evaluate students the entire process. Some teachers use checklists based on whether or not children are observed using different mathematical concepts. Other children are evaluated on specific concepts and whether or not they can complete specific objectives.

One of the activities described in the article was a dinosaur dig. Students got to play the role of archaeologists to dig for dinosaur bones and artifacts. The students then were asked to sort their artifacts based on what they believed 'fit together' by their characteristics. The students then created a graph based on their real artifacts and compared the data that they had dug from the sand/water table. We use this activity in the pre-school that I sub for and the students LOVE it. Students like getting to play the role of an dinosaur expert and love to dig up artifacts and dinosaur bones. This activity provides great mathematical concepts for children such as qualitative and quantitative data as well as sorting things based on their characteristics. Also, students get to use graphs to show the results of their data. Overall, I think that using the sand and water play table is a great idea because it opens up many opportunities to integrate the NCTM standards as well as a lot of inquiry-based teaching.

March Journal Article MTMS

Roberts, S.K. and Tayeh, C. (2010). Assessing understanding through reasoning books. Mathematics Teaching in the Middle School (15)7, 406-413.

Reasoning Books are very beneficial to students learning and understanding mathematics. Often times in math, students are most focused on finding the correct answers or quick solution to problems or questions rather than gaining understanding. As teachers, we can help guide students in the right direction by starting reasoning books with our students. Reasoning books should be started at the beginning of the year and teachers should model how to create reasoning books by going over good samples, adequate samples, and poor samples. Through modeling a good reasoning book, students will be able to better develop their reasoning book skills. These reasoning books are great for students' communication skills and helps students focus on the bigger pictures in mathematics. In these books, students will write responses and reasonings to specific mathematical problems. In these books, students will use data, drawings, reasonings, justifications, etc. to explain a mathematical argument. These reasonings should be able to be read by anyone and should explain exactly how the answer or solution was found. Reasoning books help students to answer the more in depth questions about math such as "how do we know?" and "will this always be true for every problem?" etc. The ideas in the book should focus on the important concepts in mathematics that students have difficulty understanding, concepts that provide a bigger picture, and ideas that relate to real-life context. By creating reasoning books, students will value mathematical learning through reasoning early on in the semester. This book will also help students focus on the conceptual side of mathematics rather than just formulas and correct answers for the entire semester/class.

As a teacher, this provides a valuable context for student learning and teacher assessment. By viewing the reasoning books, teachers can clearly see exactly how the child was thinking and where they need help at in their thinking. As teachers, we often overlook ideas that we assume our students know. When reasoning books are introduced, students have the opportunity to explain their understanding of the concepts and how they got to their final conclusion/answer. We can guide students by modeling examples of good reasoning entries, showing them adequate examples of reasonings, and also reasonings that need extra work. When students understand how to write clear reasoning entries, it will greatly benefit their conceptual knowledge for math. This provides a great context for teachers at the beginning of the year and will provide students with higher expectations for learning rather than just 'finding the correct solution.'

Video Analysis #2

http://my.nctm.org/eresources/reflections/index.htm




1) tell the purpose of the activities in the video

The purpose of these videos is to explore and strengthen the relationship between graphs and tables with seventh grade students. By exploring meaning behind graphs and tables, it will help students strengthen relationships among ordered pairs, linear patterns, and the rules that accompany these patterns. The teacher starts out by having them explore relationships between graphs and tables. Students make up stories to go along with their graphs. Then the students explore making tables from graphs and creating tables based on linear functions. Once students have an understanding of the linear functions, they try to create their own.



2) answer at least 3 of the questions posed

• Describe how appropriate you think the primary task in this lesson is for developing an understanding of the mathematics being taught.

I think that the primary task in the lesson is very appropriate for developing an understanding of the math that is being taught (functions). Obviously the teacher wants to have her students investigate graphs and the different values that graphs can represent. Rather than giving her students a table and having them graph the values, she starts backwards and has her class create a story based on the graph given to them. From there, the students present the material to the class and explain their stories. The teacher's goal is to have her students understand the relationship behind the graph so that they can form a table using the values and reasoning behind the graph. This is very appropriate because it leads her in to teaching students how to look at x and y values and find unknown values as well. She goes right into teaching students about sequencing and infinite values through increasing and decreasing numbers in a sequence. The method she uses in teaching is investigative and her goal is to have her students creating sequences by the end of the class to stump either her or the other students. Students will gain a valuable concept understanding when they use communication, representation, reasoning and proof, problem solving, and connections. The teacher is using all of the standards through teaching her lesson.

• What specific actions could the teacher have taken to improve the effectiveness of learning when students are working in groups?

The teacher could have provided a guide sheet so that the students stayed more on task. These could have listed things such as the 'subject,' what method they were using, what dollar amount they were starting with, etc. Instead, when she discusses these things with the groups, it seems as if it is a little chaotic and they do not have a complete understanding of the 'subject' of their problem and their methods for application. If the students had written them down when she came to discuss their problems with them, she would not have had to lead or guide them so much in the questions that she was asking. Also, rather than have them work with their friends, ability grouping sometimes aids in difficult concepts such as sequencing. Students could also have had the opportunity to communicate with other groups to find out the methods they were using to solve their problems/create their problems.

• Describe how you use the evidence you collect about what students have learned to modify your teaching

If students do not seem to be grasping the ideas and concepts for a specific subject matter, I would have to modify my teaching to adapt to their needs. If most of the children in the classroom do not understand a subject, it may be beneficial to start again where they are having difficulty and review areas where they are having trouble, or provide a more valuable learning opportunity through an activity, exploration of ideas, communication, etc. Students may need hands-on materials, visualizations, etc. to aid them in the develpment of difficult concepts. I really liked how the teacher put the error up on the board and exploring why that error is wrong. I think that by doing this, students get a more in depth understanding of where they went wrong, how they can fix it, and the method for correctly solving problems.

3) explain your thoughts on the overall use of the video
The overall use of the video was important because it showed a good example of teaching graphs and linear functions to seventh grade students. Rather than throwing equations and formulas out at the students, they explored the meaning behind graphs and tables and the functions that accompanied them. Through group work, communication, and problem solving, students were able to create problems of their own at the end of the lesson. This shows how I can better structure my teaching as I enter into the teacher education world. Using strategies that focus on the standards really benefits students in their learning process and provides a strong foundation for meaning behind concepts.