I started watching these videos in the fall of 2014 when they were being created. I wrote a comment in the guest book on the website lovemath.org and Herb replied to my comment on the same day and then again a few days later he shared more. I am impressed with his passion for teaching math and appreciate his efforts to help elementary teachers understand math content. I also appreciate the connections he makes to literacy as he explains numbers to be adjectives that modify nouns such as units. Mathasasecondlanguage.com and adjectivenounmath.com are two other websites to explore as well. Both offer free math lessons along with various resources. I plan to watch this video series during the summer and will share my thoughts on a later post. Thanks Herb.
Tuesday, June 30, 2015
Monday, June 22, 2015
Introduction to Multiplication
A few years ago, I was perplexed by a class of fourth grade students who constantly counted by 2 to solve all of the multiplication facts of two. I listened to students count 2, 4, 6, 8, 10, 12, 14, 16, 18 to solve 2 x 9. I attempted to change student thinking about the concept of multiplying by 2 as it related to doubles facts. Although students could see that it is quicker to think doubles and they could draw to illustrate this understanding, when it came to a testing situation or independent practice they always resorted back to counting by twos. After an entire year, I was convinced that this particular group of students had first learned multiplication as skip counting and this was going to remain their thought pattern. As a teacher, I made a conscious decision to never teach students how to count by twos or to introduce multiplication as skip counting. In my opinion, skip counting is truly an inefficient way to solve multiplication and as teachers we have been mislead by the Math Expressions Teaching Manual. Below is a link to a presentation about how to integrate technology while introducing second grade students to the concept of multiplication. Please forward your comments and suggestions.
I believe the key to teaching students how to multiply is having them read the math symbol as "groups of" and then stop to visualize and draw the situation. Stating a problem as two times nine does not lend to any sort of mental picture to help students understand the concept of multiplication. I focus on just reading equations until it becomes a habit and then add drawings to support the problem. When students say two groups of nine, they also need to pause to understand what they just said. Just as with reading when we pause to comprehend, students need to pause to comprehend math as well. Groups can be drawn as circles and then either dots or numerals in each group. Once students can do this, they will never be confused with multiplication.
Introduction to Multiplication
I believe the key to teaching students how to multiply is having them read the math symbol as "groups of" and then stop to visualize and draw the situation. Stating a problem as two times nine does not lend to any sort of mental picture to help students understand the concept of multiplication. I focus on just reading equations until it becomes a habit and then add drawings to support the problem. When students say two groups of nine, they also need to pause to understand what they just said. Just as with reading when we pause to comprehend, students need to pause to comprehend math as well. Groups can be drawn as circles and then either dots or numerals in each group. Once students can do this, they will never be confused with multiplication.
Introduction to Multiplication
Monday, June 8, 2015
ScreenChomp
I started using the ScreenChomp app after I saw the icon listed on the Padagogy Wheel v3 under the create section. The app is very simple to use and intuitive. As I prepared to give some instructions to students on how to use this app, they quickly started creating and did not need help.
The app provides three pages of space for drawing along with three different colored pencils. The erase options include a small eraser or a quick wipe to clear the entire screen. There are options to take a photo or upload a picture from Dropbox or Library. The app limits one photo per video. Unfortunately, recordings do not save to the camera roll. Sharing options only include email, copy link, or Tweet this. Videos are automatically stored in the app with the option to give a title to each recording. Once a video is saved, it cannot be edited or given a title.
The options for this app are endless. Most all students comment that they do not like the sound of their voice which is common. Immediately after creating a video students were excited and eager to share and asked if they could email the video to parents, teachers, or the principal. The ability to quickly share this learning is amazing. Also, the possibility of students watching each others videos to learn new concepts transformed learning with new opportunities. When my students realized that their videos were stored in the app they were excited to see what other students were creating. I was surprised when students were asking me permission to view another student's video that included their name in the title. I guess this is a good example of digital citizenship. Next year, I will definitely continue to use ScreenChomp in the classroom. To make sharing with parents easier, I will need be more organized so that each student will have access to their parents email addresses.
Monday, June 1, 2015
The SAMR Model
As an assignment this week, I created a screen cast in effort to explain the SAMR model and to give some examples about how to apply this framework to math instruction, specifically multiplication. It was my intention to be brief and embed text within photos which made some of the text difficult to read. I also failed to mention during the video that this model is not a hierarchy that implies all of our teaching should be at the redefinition level. Flashcards are purposeful and in my mind necessary practice in order to achieve fluency. Instead, the idea is that at some point our instruction should reach all levels of technology integration. Redefinition may not happen on a daily basis, but is a demonstration of deeper understanding when students and teachers are ready.
I used Screencast-o-matic to create this video because it allowed me the most freedom. I was able to adjust the size of the screen capture and hide the movement on the desktop. I like the ability to just restart, but in the end I hated this option as I kept trying to perfect the video. In the end, my first recording was my best, but unfortunately I deleted it. I only saved this cast because I thought I would just upload it and then go back to see if I could make it better since I forgot to say a few things even though I had note cards. After multiple attempts, my computer was not able to upload the video to You Tube so I had to download the cast instead.
Next time I would like to try Camtasia. I wonder if one of the software programs would allow you to screen cast while using your iPad and Reflector. Screencast-o-matic would not allow me to use Reflector at the same time. I think screen cast are a nice way to quickly share information. I just need a lot more practice so that it is not so time consuming.
http://www.sartell.k12.mn.us/samr-model-explained
Friday, May 22, 2015
Number Rack
One of my favorite teaching tools is the number rack which can also be referred to as a bead rack, or Rekenrek. I was fortunate to win mine in a drawing at a workshop. Teachers have stopped me in the hallway to ask me about this interesting tool, how I use it with students, and if I really felt it was helpful. I too was skeptical of this teaching tool and really didn't appreciate all the ways this rack can help students with math. However, now after using the bead rack on a daily basis for about 2 years now, I couldn't imagine teaching without it. Students often ask if they can use the bead rack to help them solve math problems so they too have come to find this tool very useful.
The bead rack is perfect for developing and reinforcing one to one correspondence with counting objects. The rack I use has 100 beads and is a convenient way to carry around 100 objects. It is great for skip counting by 10's, 5's, and 2's. The rack provides a constant representation of quantity. I can quickly assess students understanding of quantities as I ask students to move say seven beads. Some students may count and move seven beads one at a time. Some students will first move five red beads and then two more white beads. Eventually, students will be able to visually find the seventh bead and move it with just one push. How students move the beads tells me a lot about where they are in their development of mathematical thinking.
In the classroom, the curriculum encourages teachers to use the base ten blocks to reinforce place value and quantity. These manipulatives work for some students, but I've noticed that many students have a difficult time just accepting the fact that a stick is equal to ten cubes. I watch students count from 1 to 10 all the time to verify that the ten stick truly equals ten. This is an algebraic idea which asks students to have faith that 1 stick represents 10 cubes. I now realize why this is such a challenge for students to internalize this concept. On the other hand, the bead rack structures the beads in rows of ten. We can move ten beads in one motion and when necessary students can recount and pull apart the ten beads to verify that each row is equal to ten. The beads also structure the number ten as five red beads and five white beads in each row. A downside to the base ten blocks is that the ten sticks cannot be pulled apart. Most base ten blocks have ridges to make the cube, but I have seem some that are just smooth ten sticks and student have to place ten cubes in a row to verify that yes it equals ten.
After working with students over the past four years in math, I have realized that one of the main difficulties that seems to affect all students is the ability to compose and decompose numbers. It seems that some students become stuck in their thinking about how to break apart say the number seven. All the various parts of the number seven seem to not exist for some students. The realization that seven has small numbers inside is a foreign idea and not easy accepted by students. When I ask students to show me seven fingers and they can only show three fingers on one hand and then four on the other hand. The inability to show me a different way is evidence that they are stuck in their thinking. They are stuck because they don't understand that two and five also makes seven. Keep in mind that some students are reverse of this example. Whatever the case, the bead rack can provide structure to these numbers. Very easily the bead rack displays various combinations of all numbers.
Math racks can be purchased online at http://mathrack.com/.
There is a free app and web version of the number rack at the link below.
http://www.mathlearningcenter.org/web-apps/number-rack/
Below is a video I created to help students learn doubles addition facts. The red and white beads help to provide structure to the numbers so that students can quickly perform mental math.
Math Recovery emphasizes teaching math with a bead rack. Below is a video that illustrates how to use the bead rack with students.
Click here for more math lesson activities using the Rekenrek.
The bead rack is perfect for developing and reinforcing one to one correspondence with counting objects. The rack I use has 100 beads and is a convenient way to carry around 100 objects. It is great for skip counting by 10's, 5's, and 2's. The rack provides a constant representation of quantity. I can quickly assess students understanding of quantities as I ask students to move say seven beads. Some students may count and move seven beads one at a time. Some students will first move five red beads and then two more white beads. Eventually, students will be able to visually find the seventh bead and move it with just one push. How students move the beads tells me a lot about where they are in their development of mathematical thinking.
In the classroom, the curriculum encourages teachers to use the base ten blocks to reinforce place value and quantity. These manipulatives work for some students, but I've noticed that many students have a difficult time just accepting the fact that a stick is equal to ten cubes. I watch students count from 1 to 10 all the time to verify that the ten stick truly equals ten. This is an algebraic idea which asks students to have faith that 1 stick represents 10 cubes. I now realize why this is such a challenge for students to internalize this concept. On the other hand, the bead rack structures the beads in rows of ten. We can move ten beads in one motion and when necessary students can recount and pull apart the ten beads to verify that each row is equal to ten. The beads also structure the number ten as five red beads and five white beads in each row. A downside to the base ten blocks is that the ten sticks cannot be pulled apart. Most base ten blocks have ridges to make the cube, but I have seem some that are just smooth ten sticks and student have to place ten cubes in a row to verify that yes it equals ten.
After working with students over the past four years in math, I have realized that one of the main difficulties that seems to affect all students is the ability to compose and decompose numbers. It seems that some students become stuck in their thinking about how to break apart say the number seven. All the various parts of the number seven seem to not exist for some students. The realization that seven has small numbers inside is a foreign idea and not easy accepted by students. When I ask students to show me seven fingers and they can only show three fingers on one hand and then four on the other hand. The inability to show me a different way is evidence that they are stuck in their thinking. They are stuck because they don't understand that two and five also makes seven. Keep in mind that some students are reverse of this example. Whatever the case, the bead rack can provide structure to these numbers. Very easily the bead rack displays various combinations of all numbers.
Math racks can be purchased online at http://mathrack.com/.
There is a free app and web version of the number rack at the link below.
http://www.mathlearningcenter.org/web-apps/number-rack/
Below is a video I created to help students learn doubles addition facts. The red and white beads help to provide structure to the numbers so that students can quickly perform mental math.
Math Recovery emphasizes teaching math with a bead rack. Below is a video that illustrates how to use the bead rack with students.
Click here for more math lesson activities using the Rekenrek.
Quick Formative Assessment App
Plickers is a free app that allows you to create your own question sets and easily poll an entire group of students while they use QR codes to select an answer. I was super excited when I first heard about this free technology, but I also questioned whether or not primary students would be able to easily respond correctly with the QR codes. I was surprised by my second graders when they quickly understood how to use this technology and how excited they were to use Plickers. After the first session, they continue to ask every day if we could use the Plickers. I used Plickers as a warm-up or a closure to math lessons. Within five minutes, I quickly assessed math concepts that informed the lesson for the next day. I thought the initial excitement would fade, but after a few months of occasional use, students were still excited to use Plickers. Active engagement of learning is unavoidable when you use Plickers as each student is accountable for responding to every question. There is no daydreaming allowed.
Recently, Plickers added the option to upload images to use as part of the question. Below is an example of how I used images with Plickers.
Plickers archives questions along with student responses under the report tab. Items are stored chronologically and filtered by class.
Each question that you create is stored under the library tab. My only wish is that I would be able to organize the questions into folders. I emailed this request to Plicker and they replied that they are currently working on this feature as they have heard from many other about this same request. It is great to know that they are open to suggestions and are trying to create a very useful tool.
All of my second grade students are so familiar with using Plickers that they could create their own questions. Next year, I will plan to continue to use Plickers and allow more opportunities for students to be the teacher. This could become part of a daily routine as students create a question of the day. Most students love the opportunity to be the teacher and Plickers makes it easy.
Visit plickers.com to learn more.
This photo is posted on the Plickers website. When I was cutting out the codes, I just cut them in half as they print two codes to each page. After thinking about this, I cut the codes into squares because I really want students to respond based on their own thoughts, not other classmates. If codes are printed on rectangle paper, students may start to look around the room before they respond. In my opinion, the best think about this technology is the anonymity and I believe this photo is just an oversight by Plickers.
Recently, Plickers added the option to upload images to use as part of the question. Below is an example of how I used images with Plickers.
Plickers archives questions along with student responses under the report tab. Items are stored chronologically and filtered by class.
Each question that you create is stored under the library tab. My only wish is that I would be able to organize the questions into folders. I emailed this request to Plicker and they replied that they are currently working on this feature as they have heard from many other about this same request. It is great to know that they are open to suggestions and are trying to create a very useful tool.
All of my second grade students are so familiar with using Plickers that they could create their own questions. Next year, I will plan to continue to use Plickers and allow more opportunities for students to be the teacher. This could become part of a daily routine as students create a question of the day. Most students love the opportunity to be the teacher and Plickers makes it easy.
 |
| Plickers App |
Visit plickers.com to learn more.
This photo is posted on the Plickers website. When I was cutting out the codes, I just cut them in half as they print two codes to each page. After thinking about this, I cut the codes into squares because I really want students to respond based on their own thoughts, not other classmates. If codes are printed on rectangle paper, students may start to look around the room before they respond. In my opinion, the best think about this technology is the anonymity and I believe this photo is just an oversight by Plickers.
Sunday, May 17, 2015
SMILING MIND
Students who struggle to learn math seem to have difficulty with learning in general. I question how to help them. I have often thought so many of my students just need to relax and calm down so that they can learn. As a society that is constantly multi-tasking, mindfulness has become the new buzz word. What does mindfulness mean and how could this help my students? In search of yoga and mediation practice for young children, I came across an elementary curriculum specifically for mediation. So far, I have just printed the materials and listened to some of the breathing exercises. I have also downloaded the app. I am excited to try this with a few of my students. I believe many of my students live with chronic stress and I am hopeful that this could help them focus to learn math.
Below is a photo and caption from the Smiling Mind website.
As much as I am excited to begin to use this program, this photo gives me some concern as it appears students are praying. I am somewhat concerned that parents might become upset as meditation could be viewed as crossing the line with spirituality. So far, the audio recordings that I have previewed just focus on breathing and finding calmness within. In any case, I plan to get prior approval from my district before I implement this program. Below is a parent letter that I will share with my building principal and parents.
The intent of this program is to help children learn how to manage stress and live a healthier life. I have experimented with playing various types of music in the classroom. When the music stops, students always ask for me to play more. I have witnessed the positive affect of music. If music can help students to focus, I am interested to learn more about the possibilities of meditation. The Smiling Mind program also claims that children may display an increase in levels of empathy with fellow students. As I plan to implement this program in full next year, I am thinking about how to monitor the levels of empathy with my students. Teaching empathy has been a long time goal of educators without specific lesson plans. How do we teach empathy and could this program really increase empathy? I am hopeful that self-reflection could lead to greater compassion for others.
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