Tag Archives: technology

Developing Division Skills

Pre-Lesson Information:

Teacher figures out what students know about division (basic and long) Students answer questions or complete assessment
This information helps guide future lessons and supports students who are struggling

 

Generate:

Teacher gets students to compare multiplication and division and their relationship Students create fact families, skip counting sequences, etc. to show relationship

Students create a relationship between the two concepts
When do we use multiplication and division? Division – Used for splitting items among groups, for sharing, for splitting bills at a restaurant, etc.

Multiplication – for purchasing more than one item, etc.

Understanding multiplication will create a solid understanding of division

 

Evaluate:

Teachers asks students to think about basic division and try and figure out how to solve more complex problems (long division) Students explore and evaluate questions. Can they figure out how to solve the questions?

Can students figure out what steps are required to different solve problems? 

 

Modify:

Teacher asks students how to figure out problems with remainders.

How can students use their existing knowledge to solve the problems?

 What happens when a number does not divide evenly?

What can be done with the “leftovers?” (decimals, remainders)

When would we use decimals vs remainders?

 

The concept that I chose to explore is long division. Using the T-Gem method, I’m hoping that integrating technology into the process will help students grasp the concept a little more easily. I will start with a bit of information about my class dynamics and what I have done before re-introducing these students to long division. In my math class, even though, I have a grade 7 class, I have only 8 students who are actually at a grade 7 level. This has caused our school to take a closer look at how we can best support our struggling learners, since the majority of them have not been tested and therefore, are not on an IEP. As teachers, we are not able to modify the curriculum, but rather, we must do our best to adapt it in a way that makes it accessible for these learners. As part of our PLC (professional learning community), we have created small groups that focus on mastering one or two concepts before moving on. Our goal is to try and fill some of the gaps that these students have so that they can feel a sense of success. At the beginning of the year, we administered an assessment to all the grade 7s so that we could see what concepts they had mastered and what concepts they needed to spend more time on. After working with our students and looking at this assessment, we discovered that there are quite a few students who do not understand how to do long division.

I believe the first problem with long division is that many of the students do not have a solid understanding of basic division. With these intervention groups at my school, this is where we began our lessons. We started with having the students use manipulatives and moving (dividing) these manipulatives into groups. The students were shown some videos to help explain the process (BrainPop, Khan Academy).  We also related division to multiplication and showed how they are related (fact families, etc.). Phet has a division simulation that helps show this relationship. The students played “games,” worked with partners, and used whiteboards to practice. Throughout the process, the teachers in the room observed the students and created formative assessments to make sure all of the students were grasping the concept successfully.

Once this small group of students had a deeper understanding of what division is, they moved onto long division (this is the stage they are at now). One strategy that was used had the students using post-it notes to show the relationship between the numbers. 

http://middleschoolocd.blogspot.ca/2013/09/throwdown-linky-post-it-note-division.html – Sorry, I couldn’t figure out how to get the visual in this document.

This helped students see where the numbers go, the relationship between the numbers and the importance of lining up columns (this was an issue for many of these learners). One colour is used for the divisor and one for the dividend. The quotient and product are the same colour as the divisor so students can see that they are related. The difference is a third colour (yellow). I am trying to figure out how I can make this digital. Does anyone have any suggestions? Once students have mastered the PROCESS of long division (I find this takes longer than expected), there a tons of games, programs, videos and apps that help students practice this skill to create a solid understanding of how to complete long division questions.  

Games:

Who Wants to Be a Millionaire: http://www.math-play.com/Division-Millionaire/division-millionaire.html

Snork’s Long Division Game:

http://kidsnumbers.com/long-division/

Math Mountain:

https://www.funbrain.com/games/math-mountain

Drag and Drop math:

http://mrnussbaum.com/drag-and-drop-math/

Long Division with Scratch

https://scratch.mit.edu/projects/1387273/

Programs:

Mathletics

http://ca.mathletics.com/

Apps:

Division!! (free)

https://itunes.apple.com/ca/app/division/id492164003?mt=8

Long Division Touch (free)

https://itunes.apple.com/ca/app/long-division-touch/id574226151?mt=8

Videos

Khan Academy

https://www.khanacademy.org/tag/long-division

Brainpop

https://www.brainpop.com/math/numbersandoperations/division/

One app that is great for getting students to show their understanding and thinking is Explain Everything. In the past, I have had students create a “how to” book so that they can teach others how to do long division. I find this to be a very helpful strategy.

What strategies, resources or technology do you use to teach your students long division?

Nicole

On a side note, I absolutely loved the interactive Periodic Table in the Chemland Interactive website and wish I was able to use this during my chemistry course. Even though many of the concepts within this website are beyond what my grade 7 students are learning, some students might like to explore it if they have an interest in this subject area. In grade 7, students are learning a very basic level of chemistry, but this does not mean that some would not like to extend their learning and use Chemland to do that. They can click on any of the elements to learn more (density, boiling point, melting point, etc.). I also like that the descriptions are clear and written in a way that students can understand.

Design of TELEs and Flexible Seating

According to David Jonassen (2000), “students [do not] learn from computers or teachers-which has been a traditional assumption of most schooling… students learn from thinking in meaningful ways.” This idea supports the new BC curriculum that encourages teachers to provide students with opportunities to creatively and critically think, as well as to collaborate and communicate with their peers. Our math and science (actually ALL!) learning spaces need to provide students with a variety of areas that contain flexible seating, as well as tools that encourage students to think critically. The reason for providing choice  is because not all students learn in the same way. Some students would prefer to stand, others sitting on the floor, others need to fidget and still some of our learners prefer desks and chairs. Students should have the freedom to move between these workstations freely (as long as they can handle this responsibility). Since many teachers are moving away from doing whole class lessons, students need areas to work on exploratory activities in small groups. The designer of these spaces should ensure that they contain a variety of technology tools (VR, iPads, laptops, 3D printers, etc.) and seating choices (hokki stools, tables, couches, rugs, standing desks, etc.). All of the materials, tools and furniture in the room should moveable so that it’s easy to create different learning areas, depending on the activities the students are engaging in.

This is would be the ideal classroom that I would teach in. I could change the room around based on my students’ needs, learning styles and curriculum activities. The problem is that many districts do not have a large budget for furniture and/or technology. How do we convince our districts of the importance of flexible seating and variety of technology tools?

Collaboration, Persistence, & Communication

I interviewed a colleague at a K – 8 school who is a Continuous Improvement Coach.  This is her first year in the role, as it is a new job in the division, but she has been in a coaching type of role in her six years in the division.  Prior to that, she worked in Ontario in administration for private school where she was part of the development and founding team and worked with gifted and talented students.  The reason I chose M is because her and I have worked closely together in the last few years on STEM, personalized learning, and technology related projects.  However, she has a more supportive and engaged administrator and teacher team and our projects often end up looking very different.

 

M and I had difficulty connecting for a face to face interview.  Between her illness and the tightness of our tech tools, our options were limited.  We ended chatting through todaysmeet.com, which is actually blocked through our school division.  The division will block sites to force us to use ones that they provide.  The teachers in the division have access to Office 365 but Microsoft Teams would not allow me to export the chat transcript or print it.  Secondly, we wanted to be able to speak freely about some of the divisional controls on a non-divisional tool.

 

M identified immediately that she used technology with staff and students for collaboration.  While technology use varies across the school, she explained that “For the most part the kids use technology for research and presentations.  I’ve been trying hard to get people to look beyond that and how it can be a tool to the actual project, as well as the collaboration.  The technology can also BE the project.  Or provide opportunities for them to create their own learning”.  She described that students wanted to know how to make a Snapchat filter and how much learning has to go into a project like that.  However, when I asked her what her favourite ways to use technology in the math and science classroom are I found the examples to be very surface level, symbolic learning.  Melissa described Mathletics, Khan Academy, Kahoot, and exit tickets via email. Are these authentic ways to use technology in a math and science classroom?  Do they provide true opportunities for collaboration?  I am skeptical that these tools do more than make learning fun and easy.  They are great entry points but not the whole story.

 

Part of the story I hoped to hear from M was about the misconceptions about technology and STEM that she hears from parents, staff, and/or students.  M stepped in right away to say “That it is floof, or a free for all – or even more so, that you need to be an expert to teach it.  You need persistence and patience – you do not need expertise”.  I think this is a great message for teachers and students.  STEM is not about having all of the answers, it is about being curious enough and determined to find them.  M continued, “Your students will figure it out.  There are tutorials for pretty much everything online.  We should not limit our students learning to our comfort zones – that is ridiculous – but often happens”.

 

Woven throughout the interview was M’s reference to Bring Your Own Device, and closer to the end of our discussion we addressed it when I asked her ‘In what ways has the school division helped and hindered the implementation of technology in your context?’.  To summarize, M said that students are prevented from using tools at school that they use at home.  She believes that “…for years they [the division] have been so terrified of privacy and protecting the children that we are super far behind”.   This is directly reflected in fact that for K-8 schools (she could not speak to 9-12 contexts) there are and have never been any BYOD plans or foundations started.  We both stated a belief regarding how important BYOD is to being able to successfully and authentically facilitate STEM which led me to a whole new question.

 

Ally:

If we were to make an argument, why is it important for students to have experience with technology in a STEM context?

 

M:

I would say that it is the absolute most important tool for all learning – these subjects included.  It can be used through the learning process in so many roles.  AND it’s essential to prepare 21st century learners ready for the workforce.  I can’t think of any job that doesn’t use technology in some form or fashion.

 

Ally:

It really is the door to so many opportunities!  Thank you for your candor and expertise, M!

 

M:

You are most welcome, Ally!

 

 

Reflecting on this interview, I wish I had asked a few more questions.

  • What does she wish she could do with technology?
  • What can’t technology do?
  • What assumptions do students/staff/parents make about STEM & technology?
  • Where is literacy in STEM?
  • Apple or PC? ????

 

As a parent and an educator, M also strongly advocates for better technological communication with parents.  It was a common thread throughout our interview and it led me to wonder if these stakeholders aren’t receiving enough information?  Are they getting everything they need regarding STEM and technology?

 

Ultimately, this interview magnified the importance of communication.

Interview: lack of support, lack of training, lack of funding and limited access to technology

Keywords: lack of support, lack of training, lack of funding and limited access to technology

The teacher that I chose to interview is a grade one/two teacher at a school with a high percentage of ELL students. She currently has 284 students in her school and 18 in her class. 16 out of 18 of her students are identified as ELL. She has access to a cart of iPads that contain enough iPads for every student to be able to have their own. There is also a computer lab that they are able to use. She has a projector in her classroom that she uses to display examples, videos and student work. She has been teaching for 14 years in a variety of grade one and two classes. This interview took place on Saturday, January 20 at 3:57pm at her house.

These are the questions that I chose to ask. I asked the sub questions (1a and 4a) when I wanted her to expand on some of her ideas.

  1. Research has indicated that teachers are hesitant to integrate technology into their practice due to the perceived lack of support and personal experience with technology.  How would you describe your experience in developing a sense of confidence when implementing technology into the classroom?
    1. Do you feel like you have other teachers that you can collaborate with?
  2. How do you think the school/district has helped or hindered your implementation of technology in the classroom? Some examples are funding, resources or support.
  3. Are 1:1 device programs necessary for integrating technology effectively in mathematics? Are students at an advantage if they do have their own device?
  4. Comparing last year when your students had their own devices versus this year where your students use school devices, what are the advantages and disadvantages to each?
    1. Did you find that your students did use their iPads at home for anything?
  5. How do you integrate technology into your math and science classroom?

Lack of Support and Training

The interviewee, Lesley, states that the biggest obstacles that she faced when she first began integrating technology into her classroom were a lack of support and training. When she began integrating technology into her classroom a few years ago, she relied on social media platforms to find support and ideas from other teachers. “I relied a lot on Twitter and following people who were using it in their classrooms and I was taking ideas and trying to implement them into my own classroom.” She describes her experience as somewhat of a solo one and she felt like she needed to discover ways to make it work for her students. “Initially, I was left to my own devices to try and figure out how to make it work in the classroom… when we were first told to implement technology, we were given no support or training on how to do it effectively.” In her new school, she feels more supported as she is able to collaborate with a couple of new teachers, and they have a technology mentor that supports them when needed and provides workshops for interested in teachers. “We have a couple of new teachers at my school who are very into using technology and our tech mentor is a good resource person to talk to… He has put on a couple of different workshops about coding and about our e-portfolio program that we use in the district that have been quite helpful.” Unfortunately, many of the older teachers in her particular school are not interested in learning how to use technology with their students. “A lot of the older teachers at my school are a bit more hesitant or don’t like using technology.”

Lack of Funding and Limited Access to Technology

Along with a lack of support and training, Lesley believes funding to be an issue. When there is a lack of funding for technology, this limits the amount of technology that can be purchased for the classroom. She feels very fortunate because at her new school she has access to a set of iPads that contain enough iPads so that her students can each use one. She assigns the students the same iPad so that they continue working on projects the previous day. “Our iPad cart initially only had 20 devices, but having a class of 18, I was able to jump into using technology without a lot of difficulty. My kids could still be 1:1, and they could be assigned to the same device and because a lot of the teachers don’t use it, it’s been fairly easy to book and get time with the iPads whenever I have wanted to.” Some of the teachers with larger class sizes were not as fortunate. Just recently, her school was able to find funding to purchase more iPads, but sadly this didn’t happen until almost half of the school year was over. “We recently used a bit of our learning grant money and our school has bought some additional iPads. So now our carts are full so that the older grades that have higher class numbers are now able to go 1:1 on the devices and [students are] not having to share. So I think for those teachers it was kind of a big hindrance.” Lesley does worry that as more teachers start integrating technology into the classroom, this will make it harder to find available times to use technology. “Funding definitely is going to be an ongoing issue as more and more teachers get used to using more technology and it becomes harder to find times [available] to use it; this will be a bit of a hindrance.” Even though she usually has access to technology, she still wishes that she had her own class set. Her reasoning is that it would be nice to have for those teachable moments that arise in the classroom. No matter how much we plan as teachers, our students will often take us down a different path. These are the times when it would be nice to have unlimited access to technology. ”Not having them in the classroom all the time is kind of a pain. Sometimes you think, oh if they were here, I could grab them and do this. You have to be much more planned and organized and you can’t use technology as kind of a spur of the moment thing, which sometimes naturally comes out of an activity – oh I wish we could’ve done this on the iPad. I think in that way, not having your own set for your class is bit of a hindrance. Given the funding concerns in the public school system that probably will never happen.”

I’ve had a very similar experience to this teacher. I have found that there doesn’t seem to be a lot of training and support to encourage teachers to integrate technology. I think the overarching reason for this is that there is a lack of funding, which makes it difficult for school districts to provide opportunities for teachers to get training and it also prevents each classroom from having enough technology to access. These obstacles deter many teachers from attempting to use technology with their students. What this teacher shows us is that there are ways to find support and training, even if you have to discover it on your own. I truly believe that if teachers are truly passionate about integrating technology into their classroom and see the value of it, they will find a way to overcome these obstacles.

If you’re interested in reading the entire interview, I have posted the transcript on my E-Folio (along with this abstract). https://blogs.ubc.ca/nicolemoxey/2018/01/21/interview-transcript/

Nicole

Video 5 and video 8

I chose to watch video 5 and video 8 as they were dealing with technology use in upper intermediate classrooms and I am currently teaching grade 7. In video 5, the first teacher interviewed was very positive about technology use in the classroom. She stated that she uses it in her classroom almost everyday as it challenges the students, compensates for language barriers for her ESL students and it levels the playing field since her students are all tech savvy. The students interviewed were very excited to share the video about hurricanes they were creating. The professor in the video 8 was also very passionate about technology use and helping teacher candidates learn how integrate it into their practice and make sure that it is enhancing student learning. It appears that both of these teachers understand the benefits of using technology and how to integrate it to deepen student understanding.

However, the rest of the teachers interviewed were not so excited, or positive about technology use in the classroom. One retired teacher and one new teacher (video 5) both stated that technology is frustrating as there is not enough time to use it, not enough training, they are not equipped to problem solve issues, and they don’t feel comfortable using it. I think both of these teacher highlighted one of the main reasons as to why technology is not integrated into some classrooms (What I found interesting is that the new teacher was not integrating technology it into her classroom) These teachers do not feel like they receive enough professional development time to comfortably introduce technology into the classroom. How do we overcome this? Even when professional development does happen, the new teacher stated that she doesn’t have time to reflect upon this new knowledge and then she quickly forgets it before she has a chance to try it out with her students. Unfortunately, some teachers do not see the value in technology use and therefore, refuse to integrate it into their daily lessons. I think the best way to overcome this is to start with the teacher education programs. I think these programs should be integrating technology into all of the courses offered. Each year, new teachers will be graduating ready and excited to use technology in their new classrooms. Most of the teacher candidates in video 8 spoke positively about technology use in the classroom stating that it creates more engaged learning, helps visual learners see the process, and helps ESL and struggling learners.

Many teachers are very excited to integrate technology into their classrooms, but others still see it as a hindrance. How can we change this? What can we do to better support these teachers? Should we focus on the teachers who are interested in hopes that this will “snowball” and get others excited once they see positive examples of technology use? Is it fair that some students are able to explore some of their conceptual misconceptions with technology and others are not?

Technology use in the classroom

 

  • What is a good use of digital technology in the math and science classroom?
    • This is an excellent question and probably one of the main reasons that I chose to take this course. I struggle with authentically integrating technology into my grade 7 math and science classroom. In the past, I have used iPads extensively in my primary classrooms. We used the iPad to find math in the environment. If we were learning about 2D or 3D shapes (angles, arrays, etc.), the students would go around and take pictures of actual items. They would then create a pic collage (or other visual) with labels. However, now that I am teaching grade 7, I find it more difficult to integrate technology into my math and science lessons. Part of this is because we have very little technology available to us (one laptop cart to share between 10 grade 7 classes). The best ways that I have found to use technology is to show videos of the concepts that I am teaching for my visual learners (this works great for both math and science). We also create videos to help explain our understanding to others. I prefer for my students to work in partners or small groups that are randomly chosen. This way they are engaging and conversing while using technology. This provides the students opportunities to learn from each other. Another way to integrate technology is to allow students to further explore topics that they find particularly interesting. They can do this with other students who have the same interest.
    • In my previous school, we followed the SAMR model (substitution, augmentation, modification and redefinition). This was a good model and our goal was always to aim for modification and redefinition. The first two stages enhance the learning, but the last two transform it.
    • Technology provides students with the opportunity to converse and engage in conversations with other classes, as well as experts in a particular field. We have a class Twitter account that has been a great way for us to see how other students are learning different concepts and we are able to tweet out questions that we may have.
  • What would such a learning experience and environment look like?
    • This type of environment would have the students working in small groups at a table with a variety of device (tablets, laptops, etc.). The students would be able to move around the classroom (and possibly school) freely to explore their environment. Students would have choice in what they are learning based on their interests and knowledge.
  • What would be some characteristics of what it is and what it isn’t?
    • Technology should not be a replacement tool for paper and pencil/pen activities. It should be used to extend and further the learning process in the classroom. It should be a way for students to explore a concept in a way that fits their learning style and interests.
  • How might a learning experience with technology address a conceptual challenge, such as the one you researched in the last lesson?
    • Technology can help address conceptual challenge through the use of videos so that students can see the process. It can also be a way for students to show their thinking to their peers and teachers and open up a discussion. So much learning happens in the classroom when students are given time to explore and converse with their peers. Students can research up to date articles on specific topics and this is more easily acquired with technology.
  • Is this a vision or is it possible in real classrooms?
    • I think that many classrooms are well setup up with technology and many have flexible seating and open concept floor plans with lots of learning stations. However, some classrooms still lack the proper funding to provide up to date technology for all students.
  • What makes this vision a challenge to implement and what might be needed to actualize it?
    • The challenges that arise are funding, professional development and teacher interest and passion in regards to technology use. Some teachers have access to technology, but because of a lack of training or a fear, they do not implement it into the classroom. In order for teachers to feel comfortable, the need to be given access to technology and time to learn and feel confident using it with their students. Other classrooms have very little technology, but they have teachers that are passionate about integrating it.

Conceptual Challenges: Cloud Formation and Precipitation

In the video, Heather has a misinformed understanding of the moon’s phases and the seasons. However, her teacher was not aware of these misconceptions before she introduced the unit of study. During her lessons, Heather was trying to merge her existing knowledge with the new information the teacher was introducing. The teacher needed to understand her students’ background knowledge before she began the new unit of study. Only through her understanding of her students’ prior knowledge, will she be able to help scaffold her students’ learning.

As we can see in this video, there are many misconceptions around scientific understandings. This may be because new scientific discoveries have been made that contradict existing theories or that the learner only understood part of the concept and tried to fill in the gaps. Many scientific theories are abstract and therefore, difficult for students to visually see the process. The use of models in science can help with the visualization process. Teachers also need to understand students’ prior knowledge and misconceptions on any given topic before they begin to teach it. This will help guide the teaching process and activities based on what the students already know, what they think they understand, but really don’t, and what they are interested in learning. If students are not interested in a topic, it will be more difficult for them to learn. If they do not see the relevance of the concept to their daily life, they will not take an interest in learning more about it.

When I was teaching primary grades, one of the topics that my students always had a difficult time understanding was cloud formation and precipitation. I often wondered if the difficulty arose because the students couldn’t actually see the process or touch it. The best we could do was create diagrams or models to help with this. However, some of the students still had a difficult time explaining the process. Often times, they would appear to understand, but as time would pass their understanding would diminish. In the Thompson and Logue article, the students ranged in age from six to twelve years old. Most of the students were able to describe how clouds were formed, but had strong misconceptions about precipitation. According to the authors in both articles, scientific misconceptions come from a variety of sources, including misunderstanding information from parents or teachers, as well as from sources, such as mass-media that provide inaccurate information. Misconceptions are often difficult to change and these can impact the learning process. According to the article, Children’s Ideas and the Learning of Science, people who attend the same lecture or read the same book will not necessarily understand it in the same way. Individuals internalize the experience and construct their own meanings. The authors argue that student beliefs are reviewed or revised when a more persuasive or a better theory is introduced, but sometimes “even if students are confronted with what appear to be contradictions to the teacher, they will not necessarily recognize them” (Driver, et. al., 1985, p. 3). Thompson and Logue believe that teachers need to figure out their students misconceptions so that students do not continue to build their knowledge upon these misunderstandings. The issue is not where these misconceptions come from, but rather how we identify them and overcome them in the classroom when teaching our students.

The best way for students to understand many of the scientific concepts being taught is in a constructivist learning environment that encourages students to take risks and explore through hands-on experiments. The teacher acts as a facilitator or guide and supports the students throughout the learning process. It would not be an effective teaching style for a teacher to simply tell the students that their existing understanding or beliefs about a given topic are incorrect, but rather he or she needs to provide students with exploratory lessons that “show” the students. Technology is a great tool to help support the science lessons and curriculum in the classroom. Some of the simple ways that it can be used is to watch (up to date) videos or have students create their own videos on a given (or chosen topic). There are some great interactive whiteboard applications that allow students to draw and record their learning and thinking. This gives the teacher another way to identify any misconceptions that may exist.

Driver, R., Guesne, E., & Tiberghien, A. (1985). Children’s ideas and the learning of science. Children’s ideas in science, 1-9.

Thompson, F., & Logue, S. (2006). An Exploration of Common Student Misconceptions in Science. ERIC, 553-559. Retrieved January 8, 2018, from https://eric.ed.gov/?id=EJ854310.