Drawing Pictures: Reflections On Work Solving
Wednesday, October 2, 2019
Activities,
algebra,
Algebra1,
Art,
bulletin boards,
Classroom Decor,
Common Core,
Creativity,
lessons,
Posters,
problem solving strategies,
proportions,
Reflection
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The to a greater extent than I teach, the to a greater extent than I learn. Eventually, I'm going to move pretty dandy at this job.
The summertime earlier my showtime twelvemonth of teaching, I made a laid of problem solving strategy posters to hang on the wall. My showtime twelvemonth of teaching, these posters had an entire bulletin board dedicated to them. I would occasionally reference them inward class, but I didn't actually produce anything substantial amongst them.
This summer, I redecorated as well as rearranged my classroom. In lodge to brand room for a Star Student bulletin board, I moved the work solving strategies to a novel dwelling underneath my SMART Board.
I don't fifty-fifty intend most of my students ever fifty-fifty noticed that they were there. Again, I did zilch to a greater extent than than postal service them on the wall.
If I actually as well as genuinely desire my students to prepare their work solving skills, I lead maintain to produce to a greater extent than than only postal service the strategies. I lead maintain to brand them produce the strategies. I lead maintain to brand them do the strategies. I lead maintain to remind them of the strategies. But, it's to a greater extent than than that. I lead maintain to make them challenging problems that volition forcefulness them to utilize the strategies. If I'm non challenging them, if I'm non asset to them to a high standard, thus it's pointless to fifty-fifty postal service the strategies.
This year, I opted to skip the unit of measurement on ratios as well as proportions inward Algebra 1. Under Common Core, ratios as well as proportions volition endure a middle schoolhouse unit. And, I knew that my students had seen these types of problems inward middle school. Since this is the final twelvemonth of testing our onetime standards inward Oklahoma, students were asked several problems involving ratios, proportions, as well as percents on their end-of-instruction exam. During our few weeks of EOI attempt out review, I threw these ratio/proportion problems upwards on the board to encounter how my students would lead maintain them.
Here's 1 of the problems I chose from questions released yesteryear the Oklahoma Department of Education:
At a candle store, the ratio of light-green candles to crimson candles is 2 to 5. The shop has 4,900 candles. How many candles are red?
This is a tricky question. When students encounter that 2 as well as 5, their gut instinct is to brand a ratio out of them as well as thus shape a proportion. 4,900 isn't the publish of light-green or crimson candles, though. It's the full publish of candles. So, nosotros demand a ratio that deals amongst the full publish of candles. We must stand upwards for the ratio of crimson candles to full candles equally 5/(2+5).
Knowing that students were probable to endure tripped upwards yesteryear this problem, I urged them to depict a motion-picture present earlier performing whatever calculations. It was a uncomplicated request. It was a asking that I should brand to a greater extent than often.
Draw me a picture.
A.K.A. Use a work solving strategy!
And, don't only role it. Use it, as well as thus present the degree how you lot used it.
Oh, you lot used a strategy but ended upwards doing something incorrectly? Awesome! You only provided me amongst insight to your idea process, as well as it's an first-class learning sense for the class.
I didn't realize only how powerful that inquiry would endure until students started asset upwards their dry out erase boards amongst their pictures.
Let's only nation that the agency I approached this work as well as the agency many of my students approached this work was differently. When I asked for a picture, I had a for sure motion-picture present already drawn inward my mind. So, when students started asset upwards pictures that were different what I expected, it was an awesome experience. I had to catch my photographic television set camera as well as document this experience!
I wasn't expecting a circle graph. But, it works! And, I virtually wishing I had idea of drawing my motion-picture present similar this.
Another educatee idea inward damage of writing the ratio using a colon. Many students inward the degree could relate to this. Again, it wasn't what I was going for. But, that doesn't acquire inward a feasible picture.
This educatee also used the colon format to write their ratios. She has made the mutual error that I predicted upon picking out this problem.
Of course, some students drew pictures that were creative but non precisely mathematical.
I acquaint to you: Sherrie's Candle Store
When I drew my motion-picture present on the board, I drew 2 light-green candles as well as 5 crimson candles within a lovely store. (You tin tell me only how awesome of an creative somebody I am inward the comments!) Realizing that crimson as well as light-green candles were the colouring of Christmas candles, I changed the lift of my shop to the "Christmas Candle Store."
Next, I drew the sideways squiggly bracket, as well as I asked students how many candles were represented yesteryear the motion-picture present I drew. 4900 candles. How many candles did I draw? 7 candles. So, how many actual candles must each drawn candle represent? 700 candles! Once this regain was made, my students were quick to betoken out that the right respond was (d) 3,500 crimson candles. Why? After a satisfactory respond was given, I drew the circle graph that 1 of my students had drawn on their board on the SMART Board.
What if your motion-picture present looked similar this? What would you lot produce next? We walked through the same solution procedure using a different picture.
Why lead maintain I never done this before? I depict pictures on the board all the time. But, I don't lead maintain my students produce the same. I've been cheating them out of a learning sense yesteryear drawing the motion-picture present for them. I've been cheating myself out of a learning sense yesteryear non letting them depict their ain pictures. I gauge I've ever been afraid that their pictures would endure wrong. I've been afraid that they would brand mistakes.
This stops now. Will they brand mistakes? Certainly. Mistakes are how nosotros learn. I've ever idea that, but my actions haven't been reflecting that inward my classroom.
I'm currently reading a mass on how to organize my house/life yesteryear setting upwards daily/weekly/monthly routines. Maybe the best affair to come upwards out of this mass was a quote from the author's husband's geometry teacher: "Anything worth doing is worth doing wrong."
Do I actually believe that? Do I learn similar that is true? Because it definitely is. And, I demand to brand this my mantra. If a work is genuinely worth doing, thus it is worth it for my students to produce it wrong. There is something to endure gleaned inward the procedure of analyzing errors.
To sweat side yesteryear side year:
Problem Solving Strategy Gallery Walk
1. Pick an awesome, thought-provoking work for which the respond is non straightaway apparent.
2. List diverse (applicable) problem-solving strategies on strips of paper.
3. Let each educatee depict a strip of paper. Give them 3/5/10 minutes to apply that strategy to the problem.
4. On a sail of paper, they must illustrate how the strategy tin endure used. However, they CANNOT solve the problem. They should depict the picture, brand the table, write the equation. They should non respond the question. That volition come upwards later.
5. Hang the papers some the classroom.
6. Give each educatee 3/4/5 post-it notes.
7. Students must walk some the room as well as move out constructive feedback on the strategies employed yesteryear their classmates.
8. Once feedback has been given, grouping students yesteryear strategy. All of the students who drew a motion-picture present sit down together. All of the students who made a tabular array sit down together. All of the students who wrote an equation sit down together.
9. Each grouping takes the feedback provided yesteryear their classmates as well as plant the work together, coming to a singular solution. (Students may operate problems individually showtime as well as thus come upwards together for a grouping solution.)
10. Each grouping presents their solution as well as explains how they used their work solving strategy.
Why I intend I volition similar this:
* Emphasis on multiple avenues available to solve a problem
* Students giving students feedback - there's non plenty of this inward my classroom
* It volition forcefulness me to inquire to a greater extent than deeper, to a greater extent than complex, to a greater extent than thought-provoking questions
Thoughts? Feedback?
I realize that problems are going to accept longer this way. We powerfulness pass an entire 50-minute catamenia on 1 question. But, is that a bad thing? I've spent the final 2 years rushing through degree catamenia after degree catamenia to brand for sure I "cover" everything. No wonder they forget everything from the showtime semester yesteryear the fourth dimension the goal of twelvemonth attempt out comes around. Students larn as well as internalize what nosotros dwell on. And, work solving strategies is something I demand to dwell on. Few of my students volition ever ingredient polynomials or graph exponentials equally business office of their daily lives. But, they volition all human face upwards problems that demand to endure solved, as well as they volition demand tools to aid them variety through the many options available to them. If they move out my classroom equally critical thinkers as well as work solvers who persevere until a solution is found, I lead maintain done my job.
The summertime earlier my showtime twelvemonth of teaching, I made a laid of problem solving strategy posters to hang on the wall. My showtime twelvemonth of teaching, these posters had an entire bulletin board dedicated to them. I would occasionally reference them inward class, but I didn't actually produce anything substantial amongst them.
 |
| Problem Solving Strategies Bulletin Board |
 |
| New Home for Problem Solving Strategy Posters |
If I actually as well as genuinely desire my students to prepare their work solving skills, I lead maintain to produce to a greater extent than than only postal service the strategies. I lead maintain to brand them produce the strategies. I lead maintain to brand them do the strategies. I lead maintain to remind them of the strategies. But, it's to a greater extent than than that. I lead maintain to make them challenging problems that volition forcefulness them to utilize the strategies. If I'm non challenging them, if I'm non asset to them to a high standard, thus it's pointless to fifty-fifty postal service the strategies.
This year, I opted to skip the unit of measurement on ratios as well as proportions inward Algebra 1. Under Common Core, ratios as well as proportions volition endure a middle schoolhouse unit. And, I knew that my students had seen these types of problems inward middle school. Since this is the final twelvemonth of testing our onetime standards inward Oklahoma, students were asked several problems involving ratios, proportions, as well as percents on their end-of-instruction exam. During our few weeks of EOI attempt out review, I threw these ratio/proportion problems upwards on the board to encounter how my students would lead maintain them.
Here's 1 of the problems I chose from questions released yesteryear the Oklahoma Department of Education:
At a candle store, the ratio of light-green candles to crimson candles is 2 to 5. The shop has 4,900 candles. How many candles are red?
This is a tricky question. When students encounter that 2 as well as 5, their gut instinct is to brand a ratio out of them as well as thus shape a proportion. 4,900 isn't the publish of light-green or crimson candles, though. It's the full publish of candles. So, nosotros demand a ratio that deals amongst the full publish of candles. We must stand upwards for the ratio of crimson candles to full candles equally 5/(2+5).
Knowing that students were probable to endure tripped upwards yesteryear this problem, I urged them to depict a motion-picture present earlier performing whatever calculations. It was a uncomplicated request. It was a asking that I should brand to a greater extent than often.
Draw me a picture.
A.K.A. Use a work solving strategy!
And, don't only role it. Use it, as well as thus present the degree how you lot used it.
Oh, you lot used a strategy but ended upwards doing something incorrectly? Awesome! You only provided me amongst insight to your idea process, as well as it's an first-class learning sense for the class.
I didn't realize only how powerful that inquiry would endure until students started asset upwards their dry out erase boards amongst their pictures.
Let's only nation that the agency I approached this work as well as the agency many of my students approached this work was differently. When I asked for a picture, I had a for sure motion-picture present already drawn inward my mind. So, when students started asset upwards pictures that were different what I expected, it was an awesome experience. I had to catch my photographic television set camera as well as document this experience!
I wasn't expecting a circle graph. But, it works! And, I virtually wishing I had idea of drawing my motion-picture present similar this.
 |
| Circle Graph |
Another educatee idea inward damage of writing the ratio using a colon. Many students inward the degree could relate to this. Again, it wasn't what I was going for. But, that doesn't acquire inward a feasible picture.
 |
| Ratio |
This educatee also used the colon format to write their ratios. She has made the mutual error that I predicted upon picking out this problem.
 |
| Ratios |
Of course, some students drew pictures that were creative but non precisely mathematical.
I acquaint to you: Sherrie's Candle Store
 |
| Picture of Candle Store |
When I drew my motion-picture present on the board, I drew 2 light-green candles as well as 5 crimson candles within a lovely store. (You tin tell me only how awesome of an creative somebody I am inward the comments!) Realizing that crimson as well as light-green candles were the colouring of Christmas candles, I changed the lift of my shop to the "Christmas Candle Store."
Next, I drew the sideways squiggly bracket, as well as I asked students how many candles were represented yesteryear the motion-picture present I drew. 4900 candles. How many candles did I draw? 7 candles. So, how many actual candles must each drawn candle represent? 700 candles! Once this regain was made, my students were quick to betoken out that the right respond was (d) 3,500 crimson candles. Why? After a satisfactory respond was given, I drew the circle graph that 1 of my students had drawn on their board on the SMART Board.
What if your motion-picture present looked similar this? What would you lot produce next? We walked through the same solution procedure using a different picture.
 |
| Illustrating the Question |
Why lead maintain I never done this before? I depict pictures on the board all the time. But, I don't lead maintain my students produce the same. I've been cheating them out of a learning sense yesteryear drawing the motion-picture present for them. I've been cheating myself out of a learning sense yesteryear non letting them depict their ain pictures. I gauge I've ever been afraid that their pictures would endure wrong. I've been afraid that they would brand mistakes.
This stops now. Will they brand mistakes? Certainly. Mistakes are how nosotros learn. I've ever idea that, but my actions haven't been reflecting that inward my classroom.
I'm currently reading a mass on how to organize my house/life yesteryear setting upwards daily/weekly/monthly routines. Maybe the best affair to come upwards out of this mass was a quote from the author's husband's geometry teacher: "Anything worth doing is worth doing wrong."
Do I actually believe that? Do I learn similar that is true? Because it definitely is. And, I demand to brand this my mantra. If a work is genuinely worth doing, thus it is worth it for my students to produce it wrong. There is something to endure gleaned inward the procedure of analyzing errors.
To sweat side yesteryear side year:
Problem Solving Strategy Gallery Walk
1. Pick an awesome, thought-provoking work for which the respond is non straightaway apparent.
2. List diverse (applicable) problem-solving strategies on strips of paper.
3. Let each educatee depict a strip of paper. Give them 3/5/10 minutes to apply that strategy to the problem.
4. On a sail of paper, they must illustrate how the strategy tin endure used. However, they CANNOT solve the problem. They should depict the picture, brand the table, write the equation. They should non respond the question. That volition come upwards later.
5. Hang the papers some the classroom.
6. Give each educatee 3/4/5 post-it notes.
7. Students must walk some the room as well as move out constructive feedback on the strategies employed yesteryear their classmates.
8. Once feedback has been given, grouping students yesteryear strategy. All of the students who drew a motion-picture present sit down together. All of the students who made a tabular array sit down together. All of the students who wrote an equation sit down together.
9. Each grouping takes the feedback provided yesteryear their classmates as well as plant the work together, coming to a singular solution. (Students may operate problems individually showtime as well as thus come upwards together for a grouping solution.)
10. Each grouping presents their solution as well as explains how they used their work solving strategy.
Why I intend I volition similar this:
* Emphasis on multiple avenues available to solve a problem
* Students giving students feedback - there's non plenty of this inward my classroom
* It volition forcefulness me to inquire to a greater extent than deeper, to a greater extent than complex, to a greater extent than thought-provoking questions
Thoughts? Feedback?
I realize that problems are going to accept longer this way. We powerfulness pass an entire 50-minute catamenia on 1 question. But, is that a bad thing? I've spent the final 2 years rushing through degree catamenia after degree catamenia to brand for sure I "cover" everything. No wonder they forget everything from the showtime semester yesteryear the fourth dimension the goal of twelvemonth attempt out comes around. Students larn as well as internalize what nosotros dwell on. And, work solving strategies is something I demand to dwell on. Few of my students volition ever ingredient polynomials or graph exponentials equally business office of their daily lives. But, they volition all human face upwards problems that demand to endure solved, as well as they volition demand tools to aid them variety through the many options available to them. If they move out my classroom equally critical thinkers as well as work solvers who persevere until a solution is found, I lead maintain done my job.
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