Happy Thanksgiving to anyone that reads the blog. I have been thinking about starting a peer tutoring program during lunch in my classroom. I also want to start running a tournament for Sm4sh and MK8. That is AFTER I get other priorities straightened out. I will update the blog as soon as I hash out all of the details. So, what am I thankful for?
- I'm still alive
- My mother, brothers, sisters, nephews and nieces are still alive
- Finishing up school (only 1 semester remaining)
- Everything that I have
I hope all of my students are having a wonderful Thanksgiving with their families and if you're reading, happy Thanksgiving to you!
Thursday, November 27, 2014
Saturday, November 22, 2014
Parent Teacher Night 11-20
The first parent-teacher conference of the school year went (unsurprisingly) well!! I have been collecting a decent amount of test scores, important homeworks and classwork to show parents. This has been very helpful in addition to having Skedula handy. My biggest takeaways:
A) A decent (50%?) of parents showed up. This says a lot about their support and that they care for their children. I was happy to be able to see so many parents and discuss student progress and next steps.
B) Many of the students talk positively about me outside of school and a decent amount have commented that this is their favorite class. Great! This was a delight to hear, especially for the students who have had a difficult time with math in elementary school. Some of them have commented that now, they get it. I think this is a big thanks to visual models and trying my best to get students to feel safe enough to ask questions when they don't understand a concept.
C) Tokens are a big motivator and plenty of students talk about them outside of school or have shared how it works with their parents.
D) There is such a difference between Common Core and how parents (and even me) were taught math, so sometimes, there is little support at home for homework if a student is struggling. Parents are trying their best. I am not quite sure about what to do here.
MY next steps:
A) Find a way to balance homework. While I think it's okay to not give homework if students haven't fully understood the lesson (or we didn't get to complete the lesson for that day), that doesn't mean that they can't practice what they DO know. There should be some kind of backup homework or practice in case we don't finish the lesson for that day.
B) There should be some more signs around the room. Perhaps this can be done Wednesday?
Overall, it was a great experience. The next few units are not difficult compared to proportions and number sense. We will be done with number sense by the end of next week (or in two weeks depending on progress). We will finally move on to integers and we'll get to use our real-life coordinate plane!
A) A decent (50%?) of parents showed up. This says a lot about their support and that they care for their children. I was happy to be able to see so many parents and discuss student progress and next steps.
B) Many of the students talk positively about me outside of school and a decent amount have commented that this is their favorite class. Great! This was a delight to hear, especially for the students who have had a difficult time with math in elementary school. Some of them have commented that now, they get it. I think this is a big thanks to visual models and trying my best to get students to feel safe enough to ask questions when they don't understand a concept.
C) Tokens are a big motivator and plenty of students talk about them outside of school or have shared how it works with their parents.
D) There is such a difference between Common Core and how parents (and even me) were taught math, so sometimes, there is little support at home for homework if a student is struggling. Parents are trying their best. I am not quite sure about what to do here.
MY next steps:
A) Find a way to balance homework. While I think it's okay to not give homework if students haven't fully understood the lesson (or we didn't get to complete the lesson for that day), that doesn't mean that they can't practice what they DO know. There should be some kind of backup homework or practice in case we don't finish the lesson for that day.
B) There should be some more signs around the room. Perhaps this can be done Wednesday?
Overall, it was a great experience. The next few units are not difficult compared to proportions and number sense. We will be done with number sense by the end of next week (or in two weeks depending on progress). We will finally move on to integers and we'll get to use our real-life coordinate plane!
Saturday, November 15, 2014
Division with Fraction Word Problems
I've been spending a lot of time lately thinking about how I'm not hitting the skill cap there is for teaching. I am trying to increase my ability in facilitating math discussions. The students are now working on creating their own division (with fraction) word problems.
Division is a very rough topic, as many students do not understand the concept division and do not know when to apply it when given a word problem. I understand that this is quite challenging, but creating your own division problem means you understand what division is and why it's optimal to use it. Therefore, if a lesson like this is successful, that is a big breakthrough for my class. Some questions that were made:
With a topic like this, there is a lot of discussion that has to surface:
#1 - Does our question make sense?
#2 - Does our question require us to find how many (insert fraction) are in (insert fraction)?
#3 - Is it realistic and does the unit we chose make sense considering the quotient? (e.g. we can't have 1.5 people)
#4 - Working on problems that don't make sense and understanding why, and possibly changing it so that it does make sense.
Some misconceptions some of the kids have had so far when making their own problems:
A) The question does not make sense
B) The question does not require us to divide to solve
C) The question is not clear
D) Divisor and dividend have different units
As a teacher, it's been hard clearing up the misconceptions. You have to get students to understand why their own question doesn't make sense. Lastly, when they are finally successful in creating their own questions (like the ones I posted in the pic above), they tend to stick to the same format or don't change the scenario (I'm still happy though!).
A hands-on activity is far better for something like this, or at least should be done before this lesson (note for the future). While this reminds me much more of a lesson for a science class, I have been thinking about purchasing multiple different cups of different measurements and having students solve these types of division word problems in real life.
A question like "Mr. E has 1/3 (cup, gallon, quart) of milk. He wants to share it equally between 2 students. How much milk will each student get?" or "how many 1/5 cups of milk are in 3 cups of milk? Students will actually take the 1/5 cup and continue to fill the container/measuring cup until they find their quotient. The kids would appreciate this as they did with the last chance lesson.
A lesson like this is also good for teaching conversions i.e. finding how many cups are in a quart, converting quarts to gallons, etc. I'll probably do something like this before this unit is over.
Division is a very rough topic, as many students do not understand the concept division and do not know when to apply it when given a word problem. I understand that this is quite challenging, but creating your own division problem means you understand what division is and why it's optimal to use it. Therefore, if a lesson like this is successful, that is a big breakthrough for my class. Some questions that were made:
#1 - Does our question make sense?
#2 - Does our question require us to find how many (insert fraction) are in (insert fraction)?
#3 - Is it realistic and does the unit we chose make sense considering the quotient? (e.g. we can't have 1.5 people)
#4 - Working on problems that don't make sense and understanding why, and possibly changing it so that it does make sense.
Some misconceptions some of the kids have had so far when making their own problems:
A) The question does not make sense
B) The question does not require us to divide to solve
C) The question is not clear
D) Divisor and dividend have different units
As a teacher, it's been hard clearing up the misconceptions. You have to get students to understand why their own question doesn't make sense. Lastly, when they are finally successful in creating their own questions (like the ones I posted in the pic above), they tend to stick to the same format or don't change the scenario (I'm still happy though!).
A hands-on activity is far better for something like this, or at least should be done before this lesson (note for the future). While this reminds me much more of a lesson for a science class, I have been thinking about purchasing multiple different cups of different measurements and having students solve these types of division word problems in real life.
A question like "Mr. E has 1/3 (cup, gallon, quart) of milk. He wants to share it equally between 2 students. How much milk will each student get?" or "how many 1/5 cups of milk are in 3 cups of milk? Students will actually take the 1/5 cup and continue to fill the container/measuring cup until they find their quotient. The kids would appreciate this as they did with the last chance lesson.
A lesson like this is also good for teaching conversions i.e. finding how many cups are in a quart, converting quarts to gallons, etc. I'll probably do something like this before this unit is over.
Saturday, November 8, 2014
Visual Models vs Algorithms
There has been a substantial increase in the use of visual models in my class compared to last year. As a beginner teacher with no experience, I taught like how I was taught. This year however, I understand how important conceptual knowledge can be, and what a better way than to visualize it. It's the reason why some of the weaker classes can keep up. Visual models are good for everyone. Just because a student is in the algorithmic stage (as in, they can solve a problem algorithmically), doesn't mean that they have the conceptual knowledge.
I have been wondering lately though, when should I take students off of visual models and move them onto the division w/ fraction algorithm? Some higher level students are annoyed with drawing models, but I want them to understand that this is a tool they have in their disposal at any point in time, not something that's disposable just because there is a faster way.
We have been doing a lot of division with fractions lately, and we've gone as far as division with fractions with uncommon denominators. And I must say, it did occur to me that the model for division with fractions is a piece of extra work when the algorithm is so easy to follow.
The downside to the algorithm is that it literally conveys no conceptual knowledge at all. I want to make sure students have a solid foundation of what division is before moving onto the next topics (long division/GCF/LCM). In the long run, I'd rather be safe than sorry. I think when students have shown that they can compute or solve word problems fluently with the visual model, then I can teach the algorithm and we can move on.
I have been wondering lately though, when should I take students off of visual models and move them onto the division w/ fraction algorithm? Some higher level students are annoyed with drawing models, but I want them to understand that this is a tool they have in their disposal at any point in time, not something that's disposable just because there is a faster way.
We have been doing a lot of division with fractions lately, and we've gone as far as division with fractions with uncommon denominators. And I must say, it did occur to me that the model for division with fractions is a piece of extra work when the algorithm is so easy to follow.
VS.
The downside to the algorithm is that it literally conveys no conceptual knowledge at all. I want to make sure students have a solid foundation of what division is before moving onto the next topics (long division/GCF/LCM). In the long run, I'd rather be safe than sorry. I think when students have shown that they can compute or solve word problems fluently with the visual model, then I can teach the algorithm and we can move on.
Congratulations to Class 604!
I wanted to give a special shot-out to class 604 on the blog! Their math skills have been on such a SHARP increase lately! They are experts at Mathematical Practice #1:
Because this class NEVER gives up when given a problem, we have been able to struggle for some time, and learn new math. I am very impressed by their ability to try their hardest and to ask questions. They will become expert mathematicians in no time!!! In addition to coming so far with math, they are also now an ALL gold token class! Congratulations 604, I am proud of you all.
Signed,
Mr. E
Being a Leader
As someone who genuinely wants to be the best (or at least one of the best) math teachers, but at the same time is quite shy, being a leader can be a troublesome thing. I have always ran away from these types of things in the past. "Why don't you lead the ________ team?" "You can be a leader on this whole campus!" "When you talk, everyone turns around and listens to you". I have always turned these types of things down for:
A) Fear of failure
B) High level of responsibility
With teaching, it does not seem like I can escape this anymore. It's like the adage "you can't run from who you are". My classmates have taken somewhat of a liking to my blog, and even some co workers read it. We also have new staff now, and I am starting to think that they are genuinely looking towards me for suggestions, advice, and to watch what I do. In fact, one is coming to observe me for the next few weeks and two have already done so last month. I think I've made it clear that I don't like being the center of attention. But if you are always doing great things, or thinking outside of the box, you are always going to draw attention.
Classmates and staff expectations of me are now very high and I'm quite nervous about it. As it's only my 2nd year, I am still learning as well. I prefer to just be a valuable resource for them.
A) Fear of failure
B) High level of responsibility
With teaching, it does not seem like I can escape this anymore. It's like the adage "you can't run from who you are". My classmates have taken somewhat of a liking to my blog, and even some co workers read it. We also have new staff now, and I am starting to think that they are genuinely looking towards me for suggestions, advice, and to watch what I do. In fact, one is coming to observe me for the next few weeks and two have already done so last month. I think I've made it clear that I don't like being the center of attention. But if you are always doing great things, or thinking outside of the box, you are always going to draw attention.
Classmates and staff expectations of me are now very high and I'm quite nervous about it. As it's only my 2nd year, I am still learning as well. I prefer to just be a valuable resource for them.
One Year Wiser!
I haven't posted in a few days due to being so busy and sick. The end of the first marking period was yesterday, Friday November 7, 2014. My birthday was November 2nd. Due to some of my students snooping around the blog from time to time, I'll keep my age hidden although it's obvious that I'm still not that quite old!
My mother called and began to weep for how much the both of us have had to go through, with me not growing up in the best of environments nor a two-parent home, like much of my students. I knew that her tears were those of joy, tears that I haven't gotten a chance to quite experience yet.
It reminded me of how hard I've had to work to get where I am, and it let me know how much of an example I may be for some of my students. I share my life with them all of the time, and they probe and ask more questions when they realize that I am not much different. I became a teacher because I wanted to be a role model for students that I never had growing up. It has been an extremely difficult road.
Teaching is one of the hardest jobs in the world if you actually care about the children. And I do, deeply. At the very least, I want to finish this master's program (I graduate in June) and close out the year to see how far I can take them this year, and leave them with a positive example of math, and a human being.
On the bright side, I went shopping galore for myself, and my co workers have been treating me to meals and drinks!
My birthday resolution: Continue to stay focused on my current goals
Create new goals
My mother called and began to weep for how much the both of us have had to go through, with me not growing up in the best of environments nor a two-parent home, like much of my students. I knew that her tears were those of joy, tears that I haven't gotten a chance to quite experience yet.
It reminded me of how hard I've had to work to get where I am, and it let me know how much of an example I may be for some of my students. I share my life with them all of the time, and they probe and ask more questions when they realize that I am not much different. I became a teacher because I wanted to be a role model for students that I never had growing up. It has been an extremely difficult road.
Teaching is one of the hardest jobs in the world if you actually care about the children. And I do, deeply. At the very least, I want to finish this master's program (I graduate in June) and close out the year to see how far I can take them this year, and leave them with a positive example of math, and a human being.
On the bright side, I went shopping galore for myself, and my co workers have been treating me to meals and drinks!
My birthday resolution: Continue to stay focused on my current goals
Create new goals
Monday, November 3, 2014
Response to Intervention in Math
The following posts below are for an assignment of my current college course
CBSE 7402T. They are summaries of chapter 8 and 9 of "Response to
Intervention in Math". They outline the main ideas of three specific
math intervention programs targeted towards elementary and middle school
students with special needs. The final post outlines particular
interventions for building vocabulary in young students deficient in
mathematical language.
RTI - The Importance of Mathematical Vocabulary
Chapter 9 of Response Intervention in Mathematics is focused on the importance of teaching mathematical vocabulary. This is what I feel to be an unnecessarily long chapter. Therefore, I will try to briefly summarize this chapter and some include good takeaways.
The authors make a sound argument that the lower a students understand of mathematical language, the less proficient they will be in mathematics. Students with a low level of mathematical vocabulary (that is, they have mathematical terminology, understand the terminology and the contexts in which it is applied, and are proficient in using/applying it) have difficulties learning whatever it is being taught. I learned this last year, where most of my students were very deficient in mathematical language. It made it hard to teach new concepts and it was difficult for them to understand new things. This chapter includes seven recommendations for teaching vocabulary in math class. The following four resonated with me the most:
A) Establish a list of essential vocabulary words for each chapter or grade level
B) Evaluate student comprehension of mathematical vocabulary on a periodic basis
C) Develop an environment where mathematical vocabulary is a normal part of mathematics class.
D) Probe students' previous knowledge and usage of important terms before they are introduced during instruction.
Incorporating even a few of these recommendations will allow students to view mathematical vocabulary as important and not just a sidekick to what is being taught. Instead, they go hand in hand.
The book argues that teachers should devote instructional time to developing students' mathematical vocabulary. I certainly agree, but there is such little time to begin with. As such, one of the wonderful ideas that I found in this chapter included creating a list of mathematical words for students and sending it home (kind of like what is done for language arts). Here is an example of a vocabulary sheet taken from the book:
Let's face it: There's simply not enough time in a 45 minute period to teach concepts, procedures and vocabulary, all heavily dependent on the students in your classroom and the range of their abilities. However this is a great tool that can be used for students to study on their own time, and you can evaluate how useful it has been.
Another great tool that was presented in this chapter is an online math dictionary for kids. It can be found here: Children's Math Dictionary
It is an online interactive dictionary that students can use to learn new mathematical terms, along with a visual representation or interactive way to learn its meaning.
Another idea that resonated with me in this chapter is the use of graphic organizers. Graphic organizers are a great way for all students to organize information and help them see the connections between concepts and their application.
Another interesting one that I found (and is inspiring me to make one for my students as I type this):
Lastly, to evaluate students knowledge (and the usefulness of explicit vocabulary instruction), teachers can put vocabulary questions on quizzes/tests, or timed assessments in which teachers pick a few random words from their created list of words students should know (by the end of the year). The idea is that as the year progresses, students vocabulary will also progress, therefore, students should score higher on these types of progress-monitored assessments over time. Using the book again as a resource, the following photo is an example of the "progress-monitoring probe" discussed in the textbook:
To summarize, many students do not learn fundamental mathematical vocabulary, and therefore, have difficulties become strong students in math. Strong students in math have excellent mathematical vocabulary and understand the meaning of many different math terms and know when they are applied. This chapter went over many different ways to help students gain the vocabulary fluency in math.
Edit: Here is a prime example of why mathematical vocabulary is important. I went over some home work with a student. While he was able to get the correct answer, his articulation of his reasoning is low (due to a low level of mathematical vocabulary).
The authors make a sound argument that the lower a students understand of mathematical language, the less proficient they will be in mathematics. Students with a low level of mathematical vocabulary (that is, they have mathematical terminology, understand the terminology and the contexts in which it is applied, and are proficient in using/applying it) have difficulties learning whatever it is being taught. I learned this last year, where most of my students were very deficient in mathematical language. It made it hard to teach new concepts and it was difficult for them to understand new things. This chapter includes seven recommendations for teaching vocabulary in math class. The following four resonated with me the most:
A) Establish a list of essential vocabulary words for each chapter or grade level
B) Evaluate student comprehension of mathematical vocabulary on a periodic basis
C) Develop an environment where mathematical vocabulary is a normal part of mathematics class.
D) Probe students' previous knowledge and usage of important terms before they are introduced during instruction.
Incorporating even a few of these recommendations will allow students to view mathematical vocabulary as important and not just a sidekick to what is being taught. Instead, they go hand in hand.
The book argues that teachers should devote instructional time to developing students' mathematical vocabulary. I certainly agree, but there is such little time to begin with. As such, one of the wonderful ideas that I found in this chapter included creating a list of mathematical words for students and sending it home (kind of like what is done for language arts). Here is an example of a vocabulary sheet taken from the book:
Another great tool that was presented in this chapter is an online math dictionary for kids. It can be found here: Children's Math Dictionary
It is an online interactive dictionary that students can use to learn new mathematical terms, along with a visual representation or interactive way to learn its meaning.
Another idea that resonated with me in this chapter is the use of graphic organizers. Graphic organizers are a great way for all students to organize information and help them see the connections between concepts and their application.
Edit: Here is a prime example of why mathematical vocabulary is important. I went over some home work with a student. While he was able to get the correct answer, his articulation of his reasoning is low (due to a low level of mathematical vocabulary).
RTI In Mathematics - Solving Math Word Problems
The third and last intervention program outlined in chapter 8 is called the "Solving Math Word Problems" program. It is targeted towards students with disabilities in elementary and middle school. The program is comprised of eight units, five of which are addition & subtraction problems, and the remaining are multiplication and division problems). Lessons are 30-60 minutes long. There are four major components to this program.
First -To start, like the other programs, there is a big emphasis on teaching students to recognize different types of word problems. In this program, they are called "change", "group" and "compare" (these correspond to addition & subtraction word problems), "multiplicative compare" and "vary" for division & multiplication word problems.
Secondly - There is a diagram that accompanies each problem type, and students are to extract information from each problem and translate this information into the diagram. Each of the problem types has a corresponding diagram, showcasing the biggest aspects of those particular types of word problems. Teachers model how to use the diagrams, and students are given opportunities to practice transferring information from story situations and word problems onto the corresponding diagram.
Third - Students are to use a series of rules they learn to determine the correct operation necessary in solving the problem. Lastly, students must actually solve the problem. These four steps have been broken down into a Mnemonic called "FOPS". That is:
Find the problem type
Organize the information in the problem (using the diagram)
Plan to solve the problem
Solve the problem
Lastly - Compute/Solve the problem!
A key component of the program is that it starts out by giving students story situations instead of questions, making it easier for students to blend and understand the mathematical concepts behind the situations presented in future problems.
Example of a story situation (from the textbook): "Tyler has 37 Star Wars cards on Tuesday. He gives his sister 5 cards on Wednesday. Tyler now has 32 Star Wards cards". This is to get students to focus solely on the math behind the problem. No question is asked.
When students are able to accurately categorize story situations and the correct operation, story situations end and the lessons move on to actual questions.
Example of a question (based off of example from the textbook): "Ku has some cookies; he gives 5 to his sister. Now, he has 32 cookies. How many cookies did he have before he gave his sister cookies?
Likewise, when students progress further through the lessons, the use of the diagrams also stops. This gives students the chance to solve problems independently without any scaffolds.
First -To start, like the other programs, there is a big emphasis on teaching students to recognize different types of word problems. In this program, they are called "change", "group" and "compare" (these correspond to addition & subtraction word problems), "multiplicative compare" and "vary" for division & multiplication word problems.
Secondly - There is a diagram that accompanies each problem type, and students are to extract information from each problem and translate this information into the diagram. Each of the problem types has a corresponding diagram, showcasing the biggest aspects of those particular types of word problems. Teachers model how to use the diagrams, and students are given opportunities to practice transferring information from story situations and word problems onto the corresponding diagram.
Third - Students are to use a series of rules they learn to determine the correct operation necessary in solving the problem. Lastly, students must actually solve the problem. These four steps have been broken down into a Mnemonic called "FOPS". That is:
Find the problem type
Organize the information in the problem (using the diagram)
Plan to solve the problem
Solve the problem
Lastly - Compute/Solve the problem!
A key component of the program is that it starts out by giving students story situations instead of questions, making it easier for students to blend and understand the mathematical concepts behind the situations presented in future problems.
Example of a story situation (from the textbook): "Tyler has 37 Star Wars cards on Tuesday. He gives his sister 5 cards on Wednesday. Tyler now has 32 Star Wards cards". This is to get students to focus solely on the math behind the problem. No question is asked.
When students are able to accurately categorize story situations and the correct operation, story situations end and the lessons move on to actual questions.
Example of a question (based off of example from the textbook): "Ku has some cookies; he gives 5 to his sister. Now, he has 32 cookies. How many cookies did he have before he gave his sister cookies?
Likewise, when students progress further through the lessons, the use of the diagrams also stops. This gives students the chance to solve problems independently without any scaffolds.
RTI In Mathematics - Pirate Math
The second of the intervention programs outlined in chapter 8 is called "Pirate Math". This program is a 16 week tutoring program targeted towards second and third grade students. Lessons are organized into five activities and the central theme is one of "pirates".
For the first activity, students are given a set of addition and subtraction flash cards and are taught to "count up". For addition, students start from the larger number and count up to reach the sum. For subtraction, students start from the number being subtracted, and count up to find the difference. Then, students play with a tutor to try to beat their previous score (of flash cards answered correctly). As this program continues, students are taught how to recognize three different problem types. They are:
A) Total - Combining two numbers to find a sum
B) Difference - Finding the difference between a bigger number and a smaller number
C) Change - A problem in which there is a starting amount, and something in the problem increases or decreases this amount (students must find the ending amount).
The second activity is called "Word Problem Warm-Up". Students are asked to explain the correct way to solve a word problem from a previous lesson. It allows students to display their thinking, as well as re-teach/review things that have been taught previously.
To classify the problem type, students are asked to follow an acronym called "RUN" which stands for:
Read the problem
Underline the question
Name the problem type
After students figure out the problem type, they work their way through three questions that guide them to set up the correct number sentence to solve the problem.
Lastly, there are "Sorting Cards" which students use to continue practice in classifying problem types. The flash cards contain word problems that are read by the tutor and the student is to identify the problem type, and places the flash card on a sorting mat. Cards that are sorted incorrectly are reviewed at the end of the lesson. Teachers circulate and give feedback to student pairs.
There is an incorporated behavior management system in which students rewarded with "treasure coins" for exhibiting student-like behaviors such as: listening, following directions, completing assigned work, and improving their skills. Students color in a treasure map at the end of a lesson (based on the number of coins earned). When the map is fully colored, students earn a prize.
For the first activity, students are given a set of addition and subtraction flash cards and are taught to "count up". For addition, students start from the larger number and count up to reach the sum. For subtraction, students start from the number being subtracted, and count up to find the difference. Then, students play with a tutor to try to beat their previous score (of flash cards answered correctly). As this program continues, students are taught how to recognize three different problem types. They are:
A) Total - Combining two numbers to find a sum
B) Difference - Finding the difference between a bigger number and a smaller number
C) Change - A problem in which there is a starting amount, and something in the problem increases or decreases this amount (students must find the ending amount).
The second activity is called "Word Problem Warm-Up". Students are asked to explain the correct way to solve a word problem from a previous lesson. It allows students to display their thinking, as well as re-teach/review things that have been taught previously.
To classify the problem type, students are asked to follow an acronym called "RUN" which stands for:
Read the problem
Underline the question
Name the problem type
After students figure out the problem type, they work their way through three questions that guide them to set up the correct number sentence to solve the problem.
Lastly, there are "Sorting Cards" which students use to continue practice in classifying problem types. The flash cards contain word problems that are read by the tutor and the student is to identify the problem type, and places the flash card on a sorting mat. Cards that are sorted incorrectly are reviewed at the end of the lesson. Teachers circulate and give feedback to student pairs.
There is an incorporated behavior management system in which students rewarded with "treasure coins" for exhibiting student-like behaviors such as: listening, following directions, completing assigned work, and improving their skills. Students color in a treasure map at the end of a lesson (based on the number of coins earned). When the map is fully colored, students earn a prize.
RTI In Mathematics - Hot Math
Hello classmates! My presentation is focused on chapter 8 and 9 of "Response to Intervention in Math" by Paul Riccomini and Bradley Witzel. Chapter 8 is comprised of three different programs that are centered around teaching problem solving strategies to students with disabilities.
As we all know, what is essential for strong problem solving includes an understanding of the problem, a repertoire of skills and strategies, and a strong level of fluency in computation.
These three programs were designed with teaching students these essential problem solving traits, and the book includes brief anecdotes of their successful implementation. There will be separate blog posts for each one. This is the first!
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The first of the three programs outlined in chapter 8 is called "Hot Math" it is called "Hot Math" because students hold onto five thermometers per skill and shade in points on these thermometers. As the thermometers get higher and higher the students become more "hot" in math. This program lasts 15 weeks (five 3-week units). It is targeted towards 3rd-grade students with disabilities, and each lesson within each unit ranges between 25 and 40 minutes. Problems are broken down into 4 different categories, and students are taught the rules for solving problems in each category. The problem types are:
Shopping List - teaches students to solve multi-step problems when buying a variety of things at different prices.
Half - teaches students ways to find half of a group of objects
Pictograph - teaches students how to solve pictograph type questions and use the data to solve other questions.
Buying bags - teaches students how to deal with word problems that deal with purchasing items in groups
The first unit focuses on teaching students the following: the reasonableness of an answer (does it make sense?), aligning numbers correctly to solve computational problems, and labeling answers with the "appropriate symbols" (units?). Students are also taught how to interpret what the question is asking them along with how to solve it After unit 1, each unit focuses on one of the above mentioned problem solving types.
A big central theme of the "Hot Math" program is a skill called "transfer". Students are taught what transferring means and why it's important. In this particular case, teachers teach students that problems can change in different ways without changing in solution. Transfer allows students to categorize/classify problems depending on which part of the problem has changed, and solve them using experience, skills and strategies gained from solving prior problems.
At the end of class, students work independently on a problem and check their answers along with an answer key. Students do not have to get every question correct, but they get points for each part of a problem they get correct. As such, self-regulation is also apart of this program due to the goal-setting
and self-monitoring of students through their thermometers.
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As we all know, what is essential for strong problem solving includes an understanding of the problem, a repertoire of skills and strategies, and a strong level of fluency in computation.
These three programs were designed with teaching students these essential problem solving traits, and the book includes brief anecdotes of their successful implementation. There will be separate blog posts for each one. This is the first!
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The first of the three programs outlined in chapter 8 is called "Hot Math" it is called "Hot Math" because students hold onto five thermometers per skill and shade in points on these thermometers. As the thermometers get higher and higher the students become more "hot" in math. This program lasts 15 weeks (five 3-week units). It is targeted towards 3rd-grade students with disabilities, and each lesson within each unit ranges between 25 and 40 minutes. Problems are broken down into 4 different categories, and students are taught the rules for solving problems in each category. The problem types are:
Shopping List - teaches students to solve multi-step problems when buying a variety of things at different prices.
Half - teaches students ways to find half of a group of objects
Pictograph - teaches students how to solve pictograph type questions and use the data to solve other questions.
Buying bags - teaches students how to deal with word problems that deal with purchasing items in groups
A big central theme of the "Hot Math" program is a skill called "transfer". Students are taught what transferring means and why it's important. In this particular case, teachers teach students that problems can change in different ways without changing in solution. Transfer allows students to categorize/classify problems depending on which part of the problem has changed, and solve them using experience, skills and strategies gained from solving prior problems.
In each lesson, teachers model their thinking with a think aloud, along with modeling the solution through a think-aloud. This gives students a chance to hear (and see) solid reasoning and model the problem solving strategies taught in unit 1. As students become more proficient, they are able to work in pairs to solve problems with a peer of higher ability that provides feedback along with the teacher.
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