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Wednesday, April 19, 2017
Tuesday, January 31, 2017
SlamDunkMath: Replacing Unit Based teaching with Activity based ...
SlamDunkMath: Replacing Unit Based teaching with Activity based ...: Finally getting back to this blog after a while away. I am going to try and focus and publish a few posts about activity based teaching in m...
Sunday, January 29, 2017
Math Homework
Jon Orr (http://mrorr-isageek.com/spiralling-in-advanced-functions-mhf4u/) wrote this in his post and it is 'bang on'. We need to continue to search for creative ways to get to the same result while maintaining the focus and engagement level of all learners.
On Homework:
In the past I’ve given out homework in a very traditional way, “Tonight, complete page ___ Questions #__ to ___. Tomorrow we’ll take them up.” And what did homework take-up look like in a grade 12 course? Well, for me, it was always “What problems did you have trouble with? Number 8b? Ok, does anyone have that one completed? Kearra can you put that solution up on the board?” If no one had that question right, then I would put up a solution. And everyone watched, twiddling their thumbs (or more realistically — texted) while I put that solution up….or we all watched Kearra put the solution up. Not a great use our of time.
I’ve changed that process over the last year or so. For me, giving out homework comes in a homework set. I got the idea from Al Overwijk and Mary Bourassa. The sets not only have practice problems from the ideas from that day, but also practice problems from other areas of the course. Each night of homework they are practicing most strands of the course. It keeps concepts fresh in their minds and keeps practice going all semester.
When students come to class they get a playing card that randomly assigns them a partner. Instead of asking which question we should put up, I choose two or three from the set and the pair has to put them up on the vertical whiteboards/blackboards around the room. They are only allowed one piece of chalk or marker between them. I circulate around the room to give feedback and check for understanding/thinking. I’ll routinely yell out to “switch the marker” which forces students to communicate, error check, and defend their work. A better use of our 10 minute homework take-up time. After, students hand in their homework which allows me to check their understanding and gives me insight on what skills we need to improve on (I choose one or two questions to focus on). Gone are the days where I give out homework and I don’t find out what they really know until test time. Now, I know daily. Is it more work for me? Yes it is. But it’s worth it.
Wednesday, April 6, 2016
Monday, December 14, 2015
Parent Communication - A Key to Student Success
Bridget Stegman does a very nice job in pointing out some very easy ways in which we can keep our parents 'in the loop' by utilizing the various forms of technology available to us.
November 2015 | Volume 57 | Number 11
Seeing Beyond the Glass Half-Full
Seeing Beyond the Glass Half-Full
Road Tested / Supercharge Parent Communication
Bridget Stegman
Throughout my doctoral studies and work as an instructional coach, my observations have exposed me to a variety of best practices. One key to student success is the partnership between schools and families. Technology, I've observed, is a quick and often easy way to strengthen this connection. From apps that allow teachers to provide parents with reminders to blogs where students share projects and schoolwork with parents, the potential for engagement is limitless.
Keep parents up-to-date on homework and events. Websites like Remind, a free and secure messaging tool, let teachers create an account, set up a class, and send text messages to parents and students about school and classroom information. For example, a teacher might send parents a reminder that a project is due on Friday and then send another reminder that there is an art night at the school on Wednesday evening.
Give parents a window into the classroom. Elementary teachers can provide parents with a glimpse of what's going on in class by having students share what they are learning through electronic family message journals. In the 2014 anthology Using Technology to Enhance Writing: Innovative Approaches to Literacy Instruction, Victoria Seeger and Robin Johnson wrote a chapter explaining how it works: Students compose the first e-mail, and then parents respond and ask questions to help expand on the student's writing and to learn more about the student's day. This creates a dialogue that also promotes family literacy.
Seeger and Johnson recommend that teachers first discuss the process with students and their families. This includes modeling sample journal entries and outlining expectations. If parents do not speak English, use Google Translate to write an e-mail in the parent's native language. If a family lacks Internet access at home, take the low-tech approach by using notebooks that travel back and forth between the school and home.
Share student progress. Classroom websites and blogs not only enhance communication with parents but also provide an easy way to share student work. Edublogs is one of many platforms where teachers can post content ranging from pictures of projects that students are working on to videos of student presentations. Students can take an active role by commenting on teacher websites or creating their own blogs. Letting students be the reporters is an authentic way to promote the connection between the school and home. Platforms such as Kidblog allow teachers to moderate student blogs and comments.
Help tame the homework beast. Many times, when parents help children with homework at night, they hear the dreaded, "That's not how my teacher did it!" To alleviate this issue, teachers can use technology to record their teaching. They might simply use a mobile phone to record a lesson and post it to a YouTube channel that parents can access, or they can use screencasting apps like Educreations or whiteboard apps like ShowMe and Explain Everything to record their lessons and create video tutorials. Parents can watch these videos at their convenience, and students can use them to review lessons.
Communication is key for establishing the partnership between schools and families, but it has grown far beyond newsletters and written notes sent home. Teachers can embrace technology to give families new insight into their child's school day and help them feel like they are a welcome part of the classroom. 
Sunday, December 6, 2015
The Man Who Will Save Math
Dan Meyer, the most famous math teacher in America, wants to radically change the way we learn math.
BY BOYCE UPHOLT
The article has a number of hyperlinks that lead to numerous
other articles, etc...Great article.
Wednesday, October 15, 2014
Making Math Children Will Love
Making Math Children Will Love: Building Positive Mathitudes to Improve Student Achievement in Mathematics
Loving the Math!
“Instead of trying to make children love the math they hate, make a math they’ll love.”
Seymour Papert
Make no mistake...math is math. However, our individual approach to teaching math is sometimes not math. I think this is what Seymour Papert means with the above quote. The curriculum is something we all share but how we 'bring it to life' is very much up to the individual.
"We know that learning often begins with play."
Experiential learning via curiosity is at the core of student engagement. Kids do this naturally with their play every day. In 'bringing the curriculum to life' it is the talented teacher who can do this with all students each and every day. Initially this might seem a relatively easy task, however, once you begin to immerse yourself you will find the opposite true. The good news is that it does become easier as you begin to practice and change the way you think about planning/organizing your math program.
Have Fun with Math! ...
“... games and play have more positive effect on motivation and retention of knowledge than conventional instruction.”
Jonnavitula and Kinshuk
The key to planning/organizing is simply to 'have fun with math' as Jonnavitula & Kinshuk stated. One way to approach this is through 'macro' (yearly/monthly) planning. Macro planning allows for 'big picture' planning. You are able to set the pace, monitor the pace and thus effectively 'drive' the curriculum road. This 'drive' allows for periodic stops/breaks to delve deeper into the natural student inquiry as it arises without the pressure of feeling the need to 'plow' through textbook pages.
Another key to capturing that natural curiosity is to utilized innovative ways to engage. In today age of technology this is a relatively easy undertaking. The hardest part would be to choose from the vast possibilities (e.g.. educational TV, Youtube, vivid texts, the internet, etc…).
The Prime Radicals Shows
The Prime Radicals Pentomino App
(from App Store)
Mathemagic: Number Tricks
Furthermore, kids need to be 'freed' of the responsibility of the 'right answer'. The mathematical process (or how we get there) matters more than whether or not they produce the correct answer. It is the 'thinking' that needs the praise. Thus, designing activities that allow this to occur is key. Present a problem to solve (i.e. Dan Meyer style) and then let them spend time working through it.
"Before children can learn mathematics, they must become interested in it."
Overall, I believe making math 'come to life' is a realistic expectation for all classrooms. It requires a hard-working, caring and nurturing adult to plan, organize, preserve and provide an environment to allow students to be 'free' to take risks, inquiry and solve open-ended mathematical problems.
Loving the Math!
“Instead of trying to make children love the math they hate, make a math they’ll love.”
Seymour Papert
Make no mistake...math is math. However, our individual approach to teaching math is sometimes not math. I think this is what Seymour Papert means with the above quote. The curriculum is something we all share but how we 'bring it to life' is very much up to the individual.
"We know that learning often begins with play."
Experiential learning via curiosity is at the core of student engagement. Kids do this naturally with their play every day. In 'bringing the curriculum to life' it is the talented teacher who can do this with all students each and every day. Initially this might seem a relatively easy task, however, once you begin to immerse yourself you will find the opposite true. The good news is that it does become easier as you begin to practice and change the way you think about planning/organizing your math program.
Have Fun with Math! ...
“... games and play have more positive effect on motivation and retention of knowledge than conventional instruction.”
Jonnavitula and Kinshuk
The key to planning/organizing is simply to 'have fun with math' as Jonnavitula & Kinshuk stated. One way to approach this is through 'macro' (yearly/monthly) planning. Macro planning allows for 'big picture' planning. You are able to set the pace, monitor the pace and thus effectively 'drive' the curriculum road. This 'drive' allows for periodic stops/breaks to delve deeper into the natural student inquiry as it arises without the pressure of feeling the need to 'plow' through textbook pages.
Another key to capturing that natural curiosity is to utilized innovative ways to engage. In today age of technology this is a relatively easy undertaking. The hardest part would be to choose from the vast possibilities (e.g.. educational TV, Youtube, vivid texts, the internet, etc…).
The Prime Radicals Shows
The Prime Radicals Pentomino App
(from App Store)
Mathemagic: Number Tricks
Furthermore, kids need to be 'freed' of the responsibility of the 'right answer'. The mathematical process (or how we get there) matters more than whether or not they produce the correct answer. It is the 'thinking' that needs the praise. Thus, designing activities that allow this to occur is key. Present a problem to solve (i.e. Dan Meyer style) and then let them spend time working through it.
"Before children can learn mathematics, they must become interested in it."
Overall, I believe making math 'come to life' is a realistic expectation for all classrooms. It requires a hard-working, caring and nurturing adult to plan, organize, preserve and provide an environment to allow students to be 'free' to take risks, inquiry and solve open-ended mathematical problems.
Tuesday, February 11, 2014
Voice Comment App
This App was highlighted at a Conference I recently attended. Using Kaizena to provide Voice 'descriptive feedback' has opened a whole new world. Students submit their work via Google Drive and you open and provide that rich descriptive feedback based on the success criteria that you and your students developed around your learning goal. Check it out....
Professional Self Reflection
Recently this blog post was shared with me. I find it very timely as we just completed Term 1 with a 'Celebration of Learning' (i.e. Student Led Conferences). At our next Divisional Meetings I would like to take some time to debrief and discuss the 'next steps' with respect to Assessment & Evaluation. Assessment & Evaluation is key to what we do each day as the expression goes, "Assessment drives Instruction".
This blog post really hits home for me. As professionals, we have a responsibility to our students (and ourselves) to continue to remain 'current' in our practice. To continuously self-reflect and hone our practice based on the most current research. Take some time to see if your 'heart is visible' in your classroom.
http://christopherlehman.wordpress.com/2014/02/10/wear-your-heart-on-your-sleeve-and-walls-and-actions-and/
This blog post really hits home for me. As professionals, we have a responsibility to our students (and ourselves) to continue to remain 'current' in our practice. To continuously self-reflect and hone our practice based on the most current research. Take some time to see if your 'heart is visible' in your classroom.
http://christopherlehman.wordpress.com/2014/02/10/wear-your-heart-on-your-sleeve-and-walls-and-actions-and/
Thursday, December 12, 2013
Classroom Independent Libraries
Timing is everything. I subscribe to a number of blogs and although I often simply skim & scan, I was drawn to go deeper inside this particular post.....and I wasn't disappointed. Follow the link and check out this teachers video describing her journey to reorganize her independent classroom library.
As we continue to upgrade our classroom libraries, I thought this was perfect timing. Also, check out the other individual blog posts across the top tool bar.
As we continue to upgrade our classroom libraries, I thought this was perfect timing. Also, check out the other individual blog posts across the top tool bar.
Monday, December 9, 2013
RCAC Symposium 2013
The Western Regional Computer Advisory Committee (RCAC) Symposium was held in London, Ontario on Thursday, December 5, 2013. Great Day!
Travis put into words my thinking. He began by stating that it is not about putting technology in place of what we are already doing in the classroom but we need to think differently and use technology to enhance what we do. Check out his initial Youtube video he made after using his first SMART phone in a class in his high school to help him keep organized
Gary highlighted that one good prompt is worth a thousand words (i.e. one good question). It is less about us and more about them (the student). The most powerful idea of all is the idea of powerful ideas. Gary went on to say there is an epidemic of whole class instruction (i.e. too much focus of teacher directed instruction). Check out his blog http://stager.tv/blog/?p=1857
Did a lunch & learn with Kyle Pearce (http://tapintoteenminds.com/about-me/). Very interesting. Anybody who references Dan Meyer (http://blog.mrmeyer.com/) can't be all bad.
Travis put into words my thinking. He began by stating that it is not about putting technology in place of what we are already doing in the classroom but we need to think differently and use technology to enhance what we do. Check out his initial Youtube video he made after using his first SMART phone in a class in his high school to help him keep organized
Gary highlighted that one good prompt is worth a thousand words (i.e. one good question). It is less about us and more about them (the student). The most powerful idea of all is the idea of powerful ideas. Gary went on to say there is an epidemic of whole class instruction (i.e. too much focus of teacher directed instruction). Check out his blog http://stager.tv/blog/?p=1857
Did a lunch & learn with Kyle Pearce (http://tapintoteenminds.com/about-me/). Very interesting. Anybody who references Dan Meyer (http://blog.mrmeyer.com/) can't be all bad.
Kyle Pearce is a Secondary Math Teacher and Intermediate Math Coach with the
Greater Essex County District School Board leading a Ministry funded part-time,
one-to-one iPad project. He is an Apple Distinguished Educator and Authorized
Apple Education Trainer who leads professional development in both math and
technology in his district and beyond. Teaching secondary mathematics at
Tecumseh Vista Academy K-12 in the morning, Kyle shifts his focus to the Middle
Years Collaborative Inquiry (MYCI) Project in the afternoon.
Join Kyle as he shares his journey of creating a digital learning environment. In Kyle’s secondary one-to-one iPad math class, the goal was to effectively deliver a 3 -part math lesson while eliminating wasted time copying useless facts. This resulted in increased student engagement and high levels of student
success. Positive results from the one-to-one iPad math classroom have led to the introduction of a One iPad Classroom model for instructional use through the Middle Years Collaborative Inquiry Project for intermediate teachers in 29 schools. Both one-to-one and One iPad Classroom models continue to grow as GECDSB educators strive to redefine digital learning in mathematics.
Join Kyle as he shares his journey of creating a digital learning environment. In Kyle’s secondary one-to-one iPad math class, the goal was to effectively deliver a 3 -part math lesson while eliminating wasted time copying useless facts. This resulted in increased student engagement and high levels of student
success. Positive results from the one-to-one iPad math classroom have led to the introduction of a One iPad Classroom model for instructional use through the Middle Years Collaborative Inquiry Project for intermediate teachers in 29 schools. Both one-to-one and One iPad Classroom models continue to grow as GECDSB educators strive to redefine digital learning in mathematics.
Monday, November 25, 2013
When Do I Move Students to the 'next' Guided Reading Group?
If we already haven't done so, guided reading groups should be 'on the move' as the students gain more consistency at their current level. In Debbie Diller's book, Making the Most of Small Groups - Differentiation for All (I have a copy if you would like to borrow), she gives some 'things to consider' to assist us in making good decisions about when is the correct time to move students (see below).
Moving students to the 'next group' is different in Primary grades compared to Junior/Intermediate grades. As Nelson Literacy is our main resource in Junior/Intermediate, moving students occurs as you change reading strategies. Moreover, our CASI scores also help us determine 'areas of focus' and thus appropriate groupings. In the Primary grades, we rely on our Running Records, Flexible Small Group Folder & PM Benchmarks to guide our instruction and form our guided reading groups. However, what is good in one area of the school (eg. Primary, Junior or Intermediate) can also be good in other areas (i.e. it is only the size of the students that changes).
Moving students to the 'next group' is different in Primary grades compared to Junior/Intermediate grades. As Nelson Literacy is our main resource in Junior/Intermediate, moving students occurs as you change reading strategies. Moreover, our CASI scores also help us determine 'areas of focus' and thus appropriate groupings. In the Primary grades, we rely on our Running Records, Flexible Small Group Folder & PM Benchmarks to guide our instruction and form our guided reading groups. However, what is good in one area of the school (eg. Primary, Junior or Intermediate) can also be good in other areas (i.e. it is only the size of the students that changes).
| Flexible Small Group Folder - "Reading Levels & What to Focus on in Lessons |
3 Part Math
We had our 2nd in a 6 part series of CILM (Collaborative Inquiry & Learning in Mathematics) this week. In essence what we do is co-plan, co-teach & co-debrief. A very positive way to develop the 'collective strength' as a school. The unanimous comments from all involved were, "It wasn't so bad. I wish we could do this more often."
The 3 Part Math strategy begins with a Learning Goal derived from a Big Idea. Using our planning template we then began to 'fill in the blanks' of our 3 Part Lesson. The lesson begins with 'Minds-On' to get the students engaged with the upcoming lesson (i.e. getting in the right frame of 'mind'). This is followed by the 'Action' (i.e. the 'getting messy' of the lesson). The teacher moves around the room making observations (i.e. eves dropping) to gain important 'next steps'. The final stage is called the 'Consolidation' in which the learning (from the students) is highlighted by the teacher. Also during this stage the Success Criteria are co-created on an Anchor Chart to aid with the independent work. The entire process doesn't have a specific time frame (i.e. it could be done in one day or take multiple days to complete the 3 parts).
During the Consolidation stage there are a number of 'Questions to consider'...
The 3 Part Math strategy begins with a Learning Goal derived from a Big Idea. Using our planning template we then began to 'fill in the blanks' of our 3 Part Lesson. The lesson begins with 'Minds-On' to get the students engaged with the upcoming lesson (i.e. getting in the right frame of 'mind'). This is followed by the 'Action' (i.e. the 'getting messy' of the lesson). The teacher moves around the room making observations (i.e. eves dropping) to gain important 'next steps'. The final stage is called the 'Consolidation' in which the learning (from the students) is highlighted by the teacher. Also during this stage the Success Criteria are co-created on an Anchor Chart to aid with the independent work. The entire process doesn't have a specific time frame (i.e. it could be done in one day or take multiple days to complete the 3 parts).
During the Consolidation stage there are a number of 'Questions to consider'...
- What were the learning goals and big ideas of the lesson?
- Stay focussed even if some students are 'working ahead'...
- What mathematics is evident in students communication (oral, written & modeled)?
- observation/notes
- What language was used to show the mathematics? What vocabulary requires reinforcement?
- Word Wall, Math Journal, Anchor Chart, etc...
- How are the solutions linked?
- What misconceptions are present in the student work?
- key piece to independent success
- What are the next steps in instruction?
- assessment drives instruction
adapted from "Communication in the Mathematics Classroom", September 2010, Capacity Building Series.
Overall, our planning template & curriculum document (over time) will be our greatest resource as it becomes the 'road to student success'. For example, if we had a copy of the curriculum for our particular grade along with the Planning Template, then we could 'highlight' the specific expectations as we move from lesson to lesson. If you combine this highlighting and our notes on our planning templates, then the real strength comes to the surface as we move from week to week, month to month and term to term. Looking back and utilizing these resources as our 'assessment for, as & of learning' we will see how this then 'drives our future instruction' and precision teaching.
Resources:
http://teachingrocks.ca/three-part-lessons-teaching-math-through-problem-solving/
Resources:
http://teachingrocks.ca/three-part-lessons-teaching-math-through-problem-solving/
Friday, November 15, 2013
Debriefing the Thinking Process
At our next Divisional Meetings, we will go through the student-led 'night' in preparation for the Term 1 Report Cards. Basically, the 'How to' of Student-led (i.e. the script). We already have a big 'piece of the puzzle' complete with all students having a Portfolio. The next 'piece of the puzzle' is metacognition (thinking about their thinking).
The students just completed one form of metacognition activity with the student reflection on the Progress Reports. Why wait for the next reporting period for the students to show their thinking. Let's practice, practice & practice. The article 'linked' to metacognition outlines 6 strategies for developing students 'thinking about their thinking'. There are many good and practical ideas to help us teach our students the 'how to' of 'learning about your learning'.
As educators, we all have an innate ability to demonstrate metacognitive strategies. Modeling these strategies with our students on a consistent basis is the key to success. Students need to be able to not only describe the learning goals (i.e. the target(s) they are aiming for) but also how they plan to achieve the goals (i.e. the co-created success criteria). Afterwards, the learning needs to be 'debriefed' so the students can internalize the learning. It's not about the 'grade/mark' (i.e. once we put a grade on the page, then learning stops) but the learning that took place achieving that mark/grade that matters. This is apart of a bigger conversation around Assessment FOR, AS & OF learning (future blog topic).
By modelling and 'debriefing the thinking process' we will instill true 21st century skills in our students. Check out the 2 resources below (located in the bookroom) for some good starting ideas.
| Great ready made resources...or get an idea & create your own. |
Thursday, November 7, 2013
Open Response Questions
Sunday, September 8, 2013
Math Journals
Right v. Wrong
Last year we talked about developing a 'collective strength' in the building to maintain the learning continuum from grade to grade. After all, learning doesn't start and stop from one grade to the next. Learning moves along each individual persons 'continuum of learning' (smooth and gradual). Thus, it is vital that we be able to provide smooth transitions to learning from year to year. This doesn't mean everyone doing exactly the same things, however, there are a few things that are proven 'result oriented' best -practices. For example, we all need to understand the Literacy & Numeracy Block, Small Group Instruction, Differentiated Instruction, etc...
In math the goal is to foster the thinking via a problem solving perspective. It's not about 'correct' or 'incorrect' answers (i.e. not black & white). For example, the correct thinking/procedures can be followed but still get an incorrect answer. As a result, a Math Journal is a very good strategy to use for all. Below is an excerpt from the Guide to Effective Instruction in Mathematics K-6 that talks about the 'big picture' in math...student self-assessment.
Student Self-Assessment
Students should have frequent opportunities to reflect on their own learning, to identifytheir strengths and those areas requiring growth, and to set appropriate goals. Student
self-assessment can be accomplished through the use of journals; rubrics, checklists,
and rating scales; portfolios; and surveys and questionnaires.
JOURNALS (LEARNING LOGS)
Journal writing helps students think about what they are learning. Students canrecord in their journals using written work, pictures, diagrams, stamps, and charts.
Through these forms students often communicate mathematical ideas that they
cannot express orally. In their journals students also have opportunities to express
how they feel about a particular learning activity or about mathematics in general.
Teachers can provide prompts to help students focus on what they did and learned
in a mathematics activity:
• Sentence stems:
– In math, I am learning . . .
– I understand . . .
– I don’t understand . . .
– I find it easy to . . .
– I find it difficult to . . .
– My favourite part of math is . . .
– I do best in math when . . .
• Other journal prompts:
– Write everything you know about . . . (e.g., 50; a cube; multiplication).
– Imagine that a classmate is absent today. Write a letter to explain what we
did and what we learned in math class today.
– Explain how you could . . . (e.g., find the most popular flavour of ice cream
in the class; find the answer to 3 x 6 if you didn’t know the answer by heart;
find the area of the classroom floor).
– Write a story that . . . (e.g., uses the fraction one-half or one-third; is about a
symmetrical object; uses division).
– Write a math problem about . . . (e.g., telling time; subtraction; the graph that
the class created this morning; percent).
– Measurement is . . . ; Symmetry is . . . ; Division is . . .
Check out the Guide to Effective Instruction in Math K-6 V4 for more information.
Thursday, August 1, 2013
Moving Beyond the Worksheet
I think this article does a nice job of encapsulating some of our own feelings. I can relate to this article as I reflect on my own career. I know how I taught when I first started and the progression I saw in my own practices. I have come to realize that the cliche that there is 'only one right answer' in math might be true (a topic for another conversation), however, there are certainly numerous ways to get there.
The Math Standards and Moving
Beyond the Worksheet
Teaching the common standards in math
http://www.edweek.org/ew/articles/2013/03/27/26crowley.h32.html
By Alison Crowley
When I started teaching
algebra 12 years ago, I was given a textbook, a day-by-day plan listing the
sections in the textbook that I was expected to teach, and a roster of
students. I attended various trainings the summer before about state
assessments, technology, and special education laws, and boom! I was off and
running.
One of the things I
remember most from those early years was a laminated poster I had that listed
all of the state standards for algebra. I was instructed to cross them off as
the year progressed so it would be very clear to myself, my students, and any
visitors exactly what was happening in my classroom.
I have to admit that, as a
math person, I loved my standards chart. It gave me a sense of accomplishment
at the end of each lesson to cross off that related standard, confident that I
was doing exactly what I was supposed to be doing. It gave me a sense of
reassurance. If I graded a set of assessments with surprisingly low scores, I
would be able to look at my chart and say to myself, "Huh, I wonder why
they missed that question about exponents on the test. I mean, I can see right
there on my chart that I covered the material. And I remember that I assigned
all of the problems in the book. My students really need to spend more time on
homework." Just like that, the responsibility had shifted from me to my
students.
"The good news is that the common-core standards
provide an open playing field that encourages teachers to move away from the
step-by-step model."
It wasn't until much later that I realized that
"teaching math" and "covering textbook sections" were not
synonymous.
Before I started
implementing, or had even heard about, the Common Core State Standards, I had
already begun shifting my instructional practices to include more hands-on
activities and group work, and less book work. Project-based learning began
trending in my math-teacher circles, and pursuing national-board certification
forced me to rethink my instructional practices. Were my students actually
learning the material for mastery, or were they just good at following
directions and memorizing steps?
Fast forward to the 2011-12
school year, when I heard Ann Shannon, a mathematics educator and consultant
then working with the Bill & Melinda Gates Foundation, describe what she
refers to as math
teachers' tendency to "GPS" students.
Think about it: If a
teacher is explaining how to solve a system of equations using the substitution
method, she might list on the board a set of steps for students to follow. Step
1: Solve one of the equations for one of the variables; Step 2: Substitute the
value or equation found in Step 1 into the other equation. If you peeked
inside her classroom on this particular day, you would likely see all the
students copying notes, and then probably completing a worksheet with problems
similar to the example. From an observer's perspective, you might think the
lesson was going well.
But do the students really have a solid understanding of
the mathematics they are using? And, more importantly, do they understand why they're using it?
Do they have a graphical understanding of what it means to solve a system of
equations? Can they explain their methodology to another student? Can they
apply it to real-world situations? Is
their knowledge transferable so that they will be able to draw upon it
when they are solving more difficult systems of equations in future math
classes?
My guess is that the answer
to most of these questions is no. What Ann Shannon would say is that in this
particular situation, the students
have been "GPS'ed" from problem to solution. Just as when I
drive in a new city using my global positioning system, I can follow the
directions and get to where I need to go. But I can't replicate the journey on
my own. I don't have a real understanding of the layout of the city. If a road
were blocked because of a parade, for example, I would be in trouble because I
have no real understanding of the city's geography.
So, how can we keep from
GPS-ing our students, so that they understand the mathematics behind a series
of steps? How can teachers help them grasp the why, instead of just the how?
The good news is that the
common-core standards provide an open playing field that encourages teachers to
move away from the step-by-step model.
Explain
why the x-coordinates of the points where the graphs of the equations y=f(x) and y=g(x) intersect are the solutions
of the equations f(x)=g(x); find the solutions approximately, e.g.,
using technology to graph the functions, make tables of values, or find successive
approximations. Include cases where f(x) and g(x) are linear,
polynomial, rational, absolute value, exponential, and logarithmic functions.
Remember the earlier
example about the teacher showing the students how to solve a system of
equations using a set of steps? The first sentence of the new standard, "Explain why the x-coordinates
where the graphs intersect are the solutions," really pushes the teacher to introduce
and explain a new concept in a way that goes beyond one-dimensional instruction.
What is an x-intercept, and what does it look like on a graph? How is
that related to the algebraic equation? Perhaps rather than starting a lesson
with the steps for solving the equations, the teacher might first have students
consider graphs of related equations, or better yet, a real-world example of a
system of equations and what the values of the x-intercepts mean in that
situation. This standard also challenges the teacher to present multiple types
of equations from the beginning of the lesson so that the students can apply
the concept of an x-intercept to many types of functions.
For many teachers, myself
included, this is a fairly
significant change in instructional practice. Although I have taught
lessons on solving systems of equations using real-world applications and
emphasizing graphical connections, I have not yet truly focused my instruction
on the "why"
behind the mathematics or given students opportunities to create their own
understanding.
So how do math teachers
make that shift away from GPS-ing students a reality? It won't be easy, and we
can't do it alone. We need opportunities to collaborate, plan, and reflect with
colleagues, both in our buildings and nationwide. We need quality resources and
relevant, engaging professional development. We need time to learn from
teachers who are already successfully implementing the common core, like Kansas
educator Marsha Ratzel, who recently shared insights in her essay "The Talking
Cure: Mathematical Discourse"
(Education Week Teacher online, Dec. 31, 2012), on how her students' mathematical-thinking skills
evolved when she gave the students time and space to have conversations about
math. We need administrators and parents to support us and play an
active role in helping us transform our classrooms into places where students
are truly engaged in what they are learning.
In my daily classroom instruction,
I am still sometimes guilty of GPS-ing students. But I am hopeful that as I
learn how to fully implement the common standards, I will become less and less
dependent on steps and crossing standards off a poster. After all, my students
really deserve to navigate themselves.
Alison Crowley teaches Algebra 2 and Advanced Placement
Calculus at Lafayette High School in Lexington, Ky. A national-board-certified
teacher with 12 years of experience, she is also a member of the Center for
Teaching Quality's Common Core Lab. For more stories on teachers' efforts to
adapt to the common standards, see Education
Week Teacher's new online package, "Common-Core Instructional
Opportunities."
Vol.
32, Issue 26, Pages 29,31
Metacognition
Metacognition
What is a Portfolio?
S. Colautti May 2013 Student-Led Conferences PLC
What is a Portfolio?
A portfolio is a purposeful collection of selective significant samples of student work accompanied by clear criteria for performance which evidence student effort, progress or achievement. A portfolio is different from a folder in that it includes:
o Explicit guidelines for selection
o success criteria
o Clear objectives for each task
o Selective and significant pieces (evidence of progress, favourite work, etc.)
o Students’ self-reflection pieces
o Evidence of student participation in selection of some of the content
A portfolio exhibits the student's progress and achievement in several subject areas, but should focus on reading, writing, and mathematical problem solving. The contents can be varied. Some suggestions are: work samples, journals, compositions/essays, photographs, checklists, projects, videos, audio clips, self assessments, student reflections, summative evaluations, etc.
There are many online resources that can support teachers starting the journey towards portfolios and student-led conferences. Here are some for you to peruse:
1. Various types of portfolios, pedagogy, information for teachers
2. Portfolios for student growth for all grade levels http://www.gallaudet.edu/clerc_center/information_and_resources/info_to_go/transition_to_adulthood/portfolios_for_student_growth.html
3. How to build a portfolio for elementary students
September Readiness
September Readiness
I want to put out a 'list' (for lack of better term) of some things to keep in mind as we prepare for the upcoming school year. This 'list' is by no means an exhaustive/complete 'all encompassing' list but only a group of ideas to help guide our collective efforts. Like we have talked about many times, we are all individually extremely strong at what we do. However, it is our collective strength that makes the most impact on our students. As a result, we need to collectively be 'on the same page' to allow the 'big picture' to materialize. Please allow this 'list' to help guide your September Readiness.
I want to put out a 'list' (for lack of better term) of some things to keep in mind as we prepare for the upcoming school year. This 'list' is by no means an exhaustive/complete 'all encompassing' list but only a group of ideas to help guide our collective efforts. Like we have talked about many times, we are all individually extremely strong at what we do. However, it is our collective strength that makes the most impact on our students. As a result, we need to collectively be 'on the same page' to allow the 'big picture' to materialize. Please allow this 'list' to help guide your September Readiness.
- Planning (i.e. long-range, unit, short-term)... intentional & purposeful professional facilitation of year long road map of learning is key to student achievement...What teachers do in the classroom is the #1 predictor to Student Achievement. Some students come to us with less than others which only means we need to be more deliberate in our practice.
- School Supplies (student purchased supplies) - list out with June Report Card
- Data driven instruction - classlists, IEP's, most current data all provided by end of June. Most Data has been inputted into the document in Google. If you have 'lost' your link, please let me know and I will resend.
- Early Intervention (Goal/Priority) - We need to do everything we can early on in a students career to insure then can read. The majority of our school level support will be spent trying to achieve this goal. The research is clear that students who are not at grade level by Gr 1/2 will probably never be there.
- Classroom teaching practices have definitely moved to focused small group instruction (i.e. Guided Reading/Math). All kids learn at different levels. You might like to take the Spec Ed model literally (i.e. IEP - Individual Education Plan). Some students require the officially paperwork but all kids require the concept of individualized teaching.
- LSST 'blitz' first couple of weeks - JK staggered entry, IEP 'touch ups' & Guided Reading schedules will consume our LSST's over the first couple of weeks. The goal is to be in 'full swing' by the third week.
- Class schedule...has guided reading time this year. You will be getting a template to fill in and submit with your regular class schedule.
- Student-led Conference - meta-cognition. The only thing you need to begin with is some form of student portfolio for each student. Our first Divisional Meeting will cover the 'next steps'. If you have any questions, please ask.
- Math from a problem solving perspective. Last year was great and we would like to continue our growth in this area. Open & Parallel questions (see Marian Small resource). Giving students an open/parallel question allows them to attack the problem at their level and showcase their math knowledge. This allows us to meet them at their level and move them to the next level (i.e. the curriculum is a continuum) and thus meets a goal previously stated regarding Individual learning.
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