Tag Archives: mathematics

Reflections on Anchored Instruction Posts/Discussion

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After reading through the myriad of posts in the Anchored Instruction portion of module B several themes seemed to stand out. When discussing the Jasper Series videos the value of this type of teaching and learning was evident. My peers spoke to the abstract thinking that is an outcome of learning. In addition, the positive learning that occurs through collaboration, having an authentic purpose for learning, engaging students, a student centered and constructivist approach and scaffolded problem solving were all hilighted.

On the other hand, many also alluded to the possible drawbacks to using this style of teaching/learning. The lack of teacher understanding of how to use the videos effectively surfaced, as well as the problems with lack of technology training for educators, which may leave them at a disadvantage when attempting to incorporate anchored instruction using these videos or technology in general.Several peers also mentioned that these videoes were a bit outdated and that newer technology(ies) could provide the same type of anchored instruction. Virtual reality was suggested, as well as videos that are even more interactive and open-ended.

It was interesting to read that several peers were attempting to integrate anchored instruction in their own classrooms but tailoring it to meet both their own needs and the needs of their students. I think seeing the videos provided some with a springboard which they could then use to change or start to change their math program. If nothing else, the videos provided a new way to look at math instruction and although there would be a learning curve before fully integrating this type of instruction in a classroom, many felt that anchored instruction and using videos would be a valuable component of a student centered classroom.

I still have questions about evaluation/assessment as well as how to properly scaffold group work and collaboration. I believe in constructivist teaching/learning but I also understand that it is not a linear way to teach and learn and it takes a lot of work and flexibility in approach. This may not be comfortable for some educators and having a mentor to help them through developing a classroom with anchored instruction components would be beneficial.

Mathematics Instruction for Students with Learning Disabilities-Jasper and Reflections on my Teaching Practice

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The article, “Mathematics Instruction for Students with Learning Disabilities: A Meta-Analysis of Instructional Components”, helped me to further analyze the Jasper series and its goals. Within this study the researchers sorted the studies by major types of instructional variables. Their interest was in the detailed curriculum design and teaching practices that resulted in enhanced mathematics and they focussed on the essential attributes of effective practice. They went further and defined “explicit instruction”, which in previous research has shown positive effects in terms of increased understanding of mathematical skills for students with learning disabilities. The researchers broke it down into three components: (a) The teacher demonstrated a step-by-step plan (strategy) for solving the problem, (b) this step-by-step plan needed to be specific for a set of problems (as opposed to a general problem-solving heuristic strategy), and (c) students were asked to use the same procedure/steps demonstrated by the teacher to solve the problem (Gersten, Chard, Jayanthi, Baker, Morphy & Flojo, 2009). They also looked at the methods that exemplify a generic approach for solving a problem, student verbalizations of their mathematical reasoning, using visual representations while solving problems and range and sequence of examples. They further investigated providing ongoing formative assessment data and feedback to teachers on students’ mathematics performance, providing formative assessment data and feedback to students with LD on their mathematics performance and peer-assisted math instruction.

The results of the meta-analysis rendered some interesting data. Firstly, peer assisted learning did not provide much benefit, whereas being tutored by a well-trained older student or adult appears to help significantly (Gersten, et al., 2009). When assisting students with LD in my classroom, this finding is important, as I often pair my students with LD with their peers in order to provide more scaffolding or scaffolding when I am busy helping other students. I will need to rethink this approach.

In addition the two instructional components that provided significant benefits were teaching students to use heuristics (a process or method) to solve problems and explicit instruction (Gersten et al., 2009). When reflecting on these findings I still have some questions. I do teach my LD students a certain process or method to solving mathematical problems but I also don’t want to limit their strategies as we are being told to allow them to explore mathematical problems with a variety of strategies. Now that I think about this, perhaps students with LD do not benefit from a variety of strategies but are best served with a limited number of strategies to use, at least initially. In terms of explicit instruction, I do provide this to my students with LD, although they are also part of any open-ended problem solving that we do in class. I feel it is important to expose them to this type of mathematics as well, but perhaps they would be better served working on other math during this time. That being said, the researchers found that explicit instruction should not be the only form of instruction, so perhaps I should continue to expose the LD students to our open-ended problem solving discussions.

They also found that the sequence of examples is of importance when new skills are being taught, so scaffolding is critical for student success. Examples and problems should move from simple to increasing complexity (Gersten et al., 2009). When reflecting on my own teaching, I find that I do this naturally with all students, as it makes sense to me to move from simple to more complex problems. That being said, and reflecting on the Jasper series, perhaps introducing complex problems that students have to work through and problem solve through may be of more benefit.  The Jasper experiment believes that engaging students in real-world problems that are inherently interesting and important helps students understand why it is important to learn various sub skills and when they are useful. The Jasper adventures are purposely created to reflect the complexity of real world problems (Cognition and Technology Group at Vanderbilt, 1992).  As part of inquiry teaching (a method I use to teach some of the time in my classroom), I often introduce mathematical problems based on math explored in read-alouds. For example, when reading the book “Iron Man” we explored measurement as we explored how big we thought the Iron Man, the science fiction character in the story, would be compared to us as students. So in this way I attempt to introduce concepts that lead the students down possibly unexplored mathematical pathways and see what they can produce. I am left with the wondering: Do LD students benefit from this?

Importantly, the study showed that the process of encouraging students to verbalize their thinking or their strategies, or even the explicit strategies modeled by the teacher, was always effective (Gersten et al., 2009). In my teaching practice I often use verbal understandings to gain a better understanding of student understanding/misunderstanding and for ongoing assessment to move forward. I do this for all students, but particularly for students with LD.

It appears that teachers and students also benefit if the teachers are given specific guidance on addressing instructional needs or curricula so that they can immediately provide relevant instructional material to their student.  Teachers require support!!  This is an important point to discuss as educators are often expected to know what to do in all situations with a variety of different styles of learners, with a variety of curriculum and with a variety of learning abilities. As Schulman (1986) noted in his research, teacher training and the type of training provided needs to be revised to reflect both content and pedagogical knowledge.  The fact of the matter is that educators do not have all of these skills and cannot devote the amount of time required to meet the needs of all students. Teachers require the supports of special education teachers, administration, professional development, etc. in order to gain and implement these skills.  The research further disseminates this as the researchers recommend that providing specific instructional guidelines and curricular materials for teachers  and co-teachers or providing support services, peer tutors, cross-age tutors and/or adults providing extra support would be of direct benefit to students with LD (Gersten, et al., 2009).

Interestingly the researchers found at there seems to be no benefit in providing students with LD-specific feedback that is specifically linked to their goal attainment (Gersten et al., 2009). This seems to refute the feedback loop that we are encouraged to use as educators in order to help students to move forward in their learning. I will have to consider this when providing feedback to LD students. Perhaps spending more time on heuristics and explicit instruction and use of visuals would provide better scaffolding for their learning. I look forward to your thoughts on these points.

References

Cognition and Technology Group at Vanderbilt (1992). The jasper experiment: An exploration of issues in learning instructional design. Educational Technology Research and Development, 40(1). pp. 65–80.

Gersten, R., Chard., D.J., Jayanthi, M., Baker, S.K., Morphy, P., Flojo, J. (2009). Mathematics instruction for students with learning disabilities: A meta-analysis of instructional components. Review of Educational Research, 79(3), 1202-1242.

Shulman, Lee S. (1986). Those who understand: Knowledge growth in teaching.  Educational Researcher, 15(2)., pp. 4-14.

 

Integration of Technology to Support the Mathematics Program in a Grade 5 Classroom-Pros and Cons

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Abstract for Interview- Elementary Teacher Grade 5-Multi-Disciplinary Teacher-Interviewed Specifically about Math Programming 

Interview Length  22 minutes.  The teacher I interviewed is from a city of approximately  100, 000 people  in Northern Ontario, Canada. The interview took place during the lunch hour in the staff room in the elementary school where we both work.  The elementary school houses students from JK-8 and the school population is approximately 550 students. It is a relatively new school and it has several shared laptop carts, several shared I-Pad carts and an Interactive Whiteboard in every classroom. The interviewee is in her 40’s and has been teaching full time for for 5 years and had previously worked as an occassional teacher for 2 years. Prior to this she worked as an educational assistant for 7 years and prior to that worked as an early childhood educator for 12 years. She has taught grade 5, and worked as a primary planning teacher where she was responsible for teaching the music program from grades K-8.  She has a keen interest in technology tools. I asked questions specific to technology and her mathematics teaching.

Three themes came out of the interview:

  1. There is a need for teacher training and support in regards to technology

2. Technology is being used in the math program, but not to full effect

3. A BYOD (Bring your own device) strategic plan may alleviate some of the concerns about BYOD in the elementary school and  may provide students with more access to technology and more flexibility with the tools they are able to access and use in mathematics.

The integration of technology into the math programming in an elementary grade 5 classroom has many benefits but this also seems to go hand in hand with many issues. Most of these issues are around availability of technology, tech support and teacher training, but the risks inherant with students bringing their own devices to school was also apparent in the interview.

My colleague reported that she was incorporating technology in her math program across several of the elementary math strands including geometry, numeration, measurement and algebra. In addition, she reported enjoying incorporating the technology and a willingness to incorporate more as she learned about new applications. Although she mentioned that she often found out about new applications, websites etc through casual conversations in the school, she also noted that the training was lacking and that she felt that the training should be done in shorter sessions that concentrate on one topic or one tool to try instead of a longer session where too much information is given and teachers feel overwhelmed. She expressed that this type of training is often ineffective because either teachers don’t remember what they have learned or they do not have the proper technology or tools in order to practice what they have learned.

Although my colleague discussed the way she was incorporating technology in the math program, after reflecting on her comments I noticed that much of the technology use was for demonstration purposes or practice and review. If more training specifically focussed on ways that technology could be used for problem solving, creating or sharing and communicating amongst students perhaps this could also be explored in the classroom.

She also spoke about the BYOD (Bring your own device) situation in her classroom. Her concerns were around the students’ lack of responsibility when using technology, including inappropriate use and not thinking critically about their online behaviour. In addition, she was concerned about the students losing their devices and having both of these situations cause her to have to deal with issues that may get her into professional trouble.

The uniqueness of this interview lies in the fact that elementary educators are multidisciplinary educators yet in our school the science component is given to planning teachers to teach, so the homeroom teacher does not teach her own science. In this way, the integration of math/science/technology/engineering may happen less often. So the natural fit between STEM may be stifled. In addition, in the elementary school setting the educators are often the ones responsible for ensuring that the technology students bring to school is not lost, stolen or broken and if this happens the teacher often has to deal with this. This may be different in upper grades, a highschool setting and definitely in higher education settings. In addition, young students may not have an understanding of what it means to be a responsible digital citizen, and this should be explored along with technology so that the students can make informed and reasonable decisions about its use.

Transcript of Interview

Interviewer will be bolded throughout

How do currently utilize technology in your math program?

Well…I use the Smart Board regularly to demonstrate thinking and so that I can record their math strategies and so that we have a visual way to discuss them. I record number talk strategies as they are shared in class. I also use the I-Pads to, for example, practice elapsed time. Actually….I use the Porter website for that! I go on their website and pick a flight and then I tell the kids, “If I leave at 1:00 and land at 8:00 how much time has elapsed? They like that.
I also use the laptops and I-Pads for different games…I use “Math is Fun” and Prodigy.

So, when you are using these applications, are they aligned with the curriculum you are teaching?

Yes. So when we are doing multiplication the students went on “Grand Prix Auto” racing game for some reinforcing. I also use them for teaching concepts.

What are the differences in student engagement between using technology in math and not using technology?

Well….it depends on the student. Some think it is fun and some find it boring. I think overall they are more engaged.

Why do you think this is?

Well….I think they like the independence, and also the sounds, colors and action in the games.

Do you see any roadblocks to using technology in the math programming in your classroom?

Yes! Wifi is a big problem. The laptops themselves…well there’s not enough and when I sign them out a lot of them are broken.  They are hard to book as well. I prefer I-Pads for quick learning and laptops have certain applications that can’t be used properly on the I-Pads so the laptops are helpful then.
Also some students bring in a device and then it won’t work and I don’t have the know-how to troubleshoot and there is no tech support so the student gets upset. Then some devices get stolen and then I have a crying student on my hands and an angry parent.

How do you think technology could be integrated more fully in the math programming in our school?

Well first of all training. Hands-on training in small steps. I have started inviting people to my class after school on Tuesdays for 30 minutes tops. They try some new technology and then get a chance to use it. When you throw everything at someone in one big course it is too overwhelming. Tech needs to be available when they are learning and the applications need to be available to teachers if they are being trained in their use.

Do you think ideas about how to use technology tools are being shared with the staff?

Well, I am open to learning anything new about technology. I love it. I don’t have anyone sharing with me, or if it is shared it is shared one-on-one informally…like in a hallway or over the lunch hour. Then I will try these “tips” out. But for many people it is in one ear and out the other because they don’t even know where to start.

Why did you take the initiative to voluntarily invite staff to technology training in your classroom after school?

Well…my friend (colleague) didn’t know how to use the Smart Board and I knew that I could be helpful. I’m excited about using technology in my classroom!

Do you allow students in your class to bring their own devices to school?  

I haven’t started that yet. I usually wait until after Christmas.

Is there a reason that you wait and what are some of the perceived drawbacks of BYOD?

Well one time a kid in my class went on porn at home, saved it and then shared it at school. Also one student took a picture of another student and posted it on Facebook and then I got in trouble. The students need to learn responsibility and be held accountable which is hard to control.

What strands of math do you currently support with technology?

Geometry-looking at shapes and building 3-D objects and viewing these objects virtually.
Patterning-I use the “Patterns to Algebra” program on the Smart Board. It is found in the Smart Notebook program.
Number Sense-We use Grand Prix Auto
Measurement- I like using the Smart Board tools for this. The ruler that shouts out numbers is great!
I use the Smartboard for teaching and I use the I-Pad more for practice and consolidation.

Are the students using any of this math technology at home?

Well, I use the e-learning website to link to websites at home, but this year there are far more students not even accessing the e-learning.

Why do you think this is?   

I think parents and kids are just too busy.

How do you see technology tools in the math program being of assistance to students who are struggling?

I really like “Prodigy” for that. It can be set up for the whole class or individualized for the grade level of the student. Two students I had last year, “A” and “D” were performing math below grade level so I used the I-Pad or laptop and they could practice math at their level.

Thank you for the interview! There are some really good discussion points here!
Interview Ended