Design the Life You Love by Ayse Birsel is a fabulous "self-help-ish" book. It offers a creative, interactive approach to helping readers create a life that is worth living. The book is divided into various steps:
1) Warm-up
2) Deconstruct
3) Inspiration
4) Today
5) Tomorrow
6) Design
7) Living
The author's little doodles and creative presentation inspire me to let loose and get into a state of flow while interacting with the text. The stylish, minimalistic layout of the pages and the books division into clear steps serves to prevent readers from feeling overwhelmed by the prospect of "redesigning" their lives.
I highly recommend this book to anyone who wishes to reevaluate their current lifestyle and design something he or she can enjoy passionately. This book is a great tool for self-reflection and creation. 4.5/5 stars.
-Mrs. Mundt
P.S. I received this book for reviewing purposes courtesy of Blogging for Books.
Saturday, November 21, 2015
Sunday, August 16, 2015
A Lofty Task: Setting up my 4th Grade Classroom!
I have been out of the blogging world for quite some time now, but I am back and ready to roll!
Update: I will be a 4th grade teacher at an IB PYP school in Minneapolis this school year, and I couldn't be more excited to get started.
Last week, I attended the "Making the PYP Happen" introductory workshop. The PYP (Primary Years Programme) framework is super intense and very inspiring. The PYP has five primary components: knowledge, skills, attitudes, concepts, and action. The goal of the program is to promote international mindedness through inquiry. The training merely scratched the surface of the PYP, and it was still so much! I am eager to apply what I've learned in the classroom and to document it all here on my blog!
I have moved some things into my classroom, but there is so much yet to be done. I want to create a classroom environment that is simple/streamlined yet engaging and invigorating...that allows opportunities for collaboration and exploration...that promotes students to grow into their identity as readers...that students can build upon and make their own. I believe the classroom environment has a HUGE impact on student learning, so I feel I have a lofty task ahead of me!
Another update with photos will come soon!
Mrs. Mundt
Update: I will be a 4th grade teacher at an IB PYP school in Minneapolis this school year, and I couldn't be more excited to get started.
Last week, I attended the "Making the PYP Happen" introductory workshop. The PYP (Primary Years Programme) framework is super intense and very inspiring. The PYP has five primary components: knowledge, skills, attitudes, concepts, and action. The goal of the program is to promote international mindedness through inquiry. The training merely scratched the surface of the PYP, and it was still so much! I am eager to apply what I've learned in the classroom and to document it all here on my blog!
I have moved some things into my classroom, but there is so much yet to be done. I want to create a classroom environment that is simple/streamlined yet engaging and invigorating...that allows opportunities for collaboration and exploration...that promotes students to grow into their identity as readers...that students can build upon and make their own. I believe the classroom environment has a HUGE impact on student learning, so I feel I have a lofty task ahead of me!
Another update with photos will come soon!
Mrs. Mundt
Sunday, February 16, 2014
The storm has come
Invisible body of readers,
I must apologize for my lack of blogging. School has begun, and it is taking me by storm. That said, it's a really beautiful storm with lots of radiant, illuminating lightning and refreshing rain that tastes like discovery! I am learning so much, and my mind is truly blooming with all of this new knowledge.
A few things I've been a'pondering…
1) The politics in education - topics of charter schools, accountability, high stakes testing, and more. I'm just overwhelmed. I don't know how to sort out what's real and what's not. Before starting my program, I read Wendy Kopp (founder of TFA) and Deborah Kenny's books and was totally in favor of their ideologies toward education. I decided to check out Reign of Error, in which Diane Ravitch questions the privatization movement toward charter schools and the idea of "school choice." Actually, she questions pretty much all of the ideas I felt I was in favor of after reading Kopp and Kenny's books. She suggests that these ideas will benefit big money and that what we need is significant societal reform to tackle the real culprits, poverty and social inequity. My textbook has left me even more overwhelmed as I read about Social Reproduction theory, which suggests that schools actually promote educational inequity by assuring that current class boundaries maintain intact. Woofta. I'm trying to let this all just sink in and not make any rash decisions on what I do or do not believe. That's hard for me to do. I want to know what I believe, so I can make informed decisions from those beliefs. I'm going to be reading Michelle Rhee's book Radical while finishing Reign of Error, so I'm sure my confusion will only surmount as I approach these two opposing perspectives at once.
2) Last night, I stayed up until 2:30am reading because I was completely RIVETED by my class reading assignment (see reference below to check out this fabulous reading - I believe it's taken from a textbook). Weird, right? It was on language in the classroom. The reading talked about how talking in the classroom revolves primarily around the teacher - 78% of class time on a given day is spent with either teacher talking or silent time - and his or her agenda. It made me question the way I speak with (and to) students and the purpose of my interactions with them. Are our interactions with students structured to coerce a specific answer out of them or to control student behavior? Or are they to facilitate genuine communication? I'd hope it's the second, but I don't think that is always the case. Further, the talking students are doing at school have very little in common with the talking they do at home and within their communities. There is a disconnect between their worlds of language, and this is a problem. What are we trying to teach students about the role of language??
Seriously, I could go on about a dozen more topics that are equally compelling to me, but I'd be here all night. I have some personal reading to go do. It's hard to make time for that with all of this beautiful class material, but I know how important independent reading is, so I'm intentionally making time for it. I'm big on Goodreads these days, and I've found it to be incredibly motivating. Check it out, and then pick up a book! :)
Keep those hearts and minds blooming,
Miss Elizabeth
Piper, T. (2007). Language & learning: The home & school years. Boston, MA; Pearson.
I must apologize for my lack of blogging. School has begun, and it is taking me by storm. That said, it's a really beautiful storm with lots of radiant, illuminating lightning and refreshing rain that tastes like discovery! I am learning so much, and my mind is truly blooming with all of this new knowledge.
A few things I've been a'pondering…
1) The politics in education - topics of charter schools, accountability, high stakes testing, and more. I'm just overwhelmed. I don't know how to sort out what's real and what's not. Before starting my program, I read Wendy Kopp (founder of TFA) and Deborah Kenny's books and was totally in favor of their ideologies toward education. I decided to check out Reign of Error, in which Diane Ravitch questions the privatization movement toward charter schools and the idea of "school choice." Actually, she questions pretty much all of the ideas I felt I was in favor of after reading Kopp and Kenny's books. She suggests that these ideas will benefit big money and that what we need is significant societal reform to tackle the real culprits, poverty and social inequity. My textbook has left me even more overwhelmed as I read about Social Reproduction theory, which suggests that schools actually promote educational inequity by assuring that current class boundaries maintain intact. Woofta. I'm trying to let this all just sink in and not make any rash decisions on what I do or do not believe. That's hard for me to do. I want to know what I believe, so I can make informed decisions from those beliefs. I'm going to be reading Michelle Rhee's book Radical while finishing Reign of Error, so I'm sure my confusion will only surmount as I approach these two opposing perspectives at once.
2) Last night, I stayed up until 2:30am reading because I was completely RIVETED by my class reading assignment (see reference below to check out this fabulous reading - I believe it's taken from a textbook). Weird, right? It was on language in the classroom. The reading talked about how talking in the classroom revolves primarily around the teacher - 78% of class time on a given day is spent with either teacher talking or silent time - and his or her agenda. It made me question the way I speak with (and to) students and the purpose of my interactions with them. Are our interactions with students structured to coerce a specific answer out of them or to control student behavior? Or are they to facilitate genuine communication? I'd hope it's the second, but I don't think that is always the case. Further, the talking students are doing at school have very little in common with the talking they do at home and within their communities. There is a disconnect between their worlds of language, and this is a problem. What are we trying to teach students about the role of language??
Seriously, I could go on about a dozen more topics that are equally compelling to me, but I'd be here all night. I have some personal reading to go do. It's hard to make time for that with all of this beautiful class material, but I know how important independent reading is, so I'm intentionally making time for it. I'm big on Goodreads these days, and I've found it to be incredibly motivating. Check it out, and then pick up a book! :)
Keep those hearts and minds blooming,
Miss Elizabeth
Piper, T. (2007). Language & learning: The home & school years. Boston, MA; Pearson.
Monday, January 20, 2014
Forthcoming adventures and where this girl is at
I am not sure if anyone is even reading this (I sort of doubt it), but that's truly okay. Just the idea of people reading my thoughts scares me some, so this is a big deal, even if nobody reads it. It's a form of personal development, a practice in bravery and commitment to (not-so-fearless) self-expression. I want to harvest the zesty truth telling I had as a girl and let the world know how I feel about things, even if that perspective is contrary to popular opinion.
Forthcoming adventures & where I'm at:
1) I am writing a book series? Eep, it feels odd to say that. It's not just any book series. It's targeted to a very particular population, and I think there is a very real need for it. It is close to my heart and stems from a life of experiences with a certain special someone. I've been meaning to begin for a few months now, and I finally started writing today. I have no idea how to do this, but I figure beginning is half the battle. Right?
2) I start classes in my Elementary Education Initial Licensure program on February 4th! While my heart is jumping to become a teacher, I think my brain still has a ways to go. While doing an assignment for one of my online math classes today, I realized there is still a lot I need to learn and even more importantly, remember. There are topics I've mastered a ridiculous amount of times (i.e. inductive and deductive reasoning, please just let me be) and still struggle with. My brain kicks in when I need it, but then my memory fails me. Thankfully, I will be teaching similar, if not the same, topics year after year, so I'm sure I'll come to master them in time. I'm glad that I have this perspective, as certainly many of my students will experience this, too.
Other things I'm really feeling:
-All things paper. Lovely paper products, particularly stationery, light up my heart in a weird sort of way. I love how paper, when brought to life with words and pictures, is capable of communicating love, expressing art, and embodying my current and past experiences. It just makes me so happy. Swear I'm not crazy.
-Feedly! Such a fab way to keep up with all of my sources of inspiration, particularly blogs. I probably follow 200+ now, and bookmarks were just NOT cutting it.
Questions for you all:
Regarding education: What are your thoughts on the Common Core State Standards? I am trying to learn more without identifying with a particular side of the issue. Above all, I'm for the kids, and whatever benefits them is what I will support.
Regarding spirituality: How do you incorporate your faith into your daily actions?
Keep those hearts and minds a blooming,
Miss Elizabeth
 |
| Fearless at 5: love her energy. |
1) I am writing a book series? Eep, it feels odd to say that. It's not just any book series. It's targeted to a very particular population, and I think there is a very real need for it. It is close to my heart and stems from a life of experiences with a certain special someone. I've been meaning to begin for a few months now, and I finally started writing today. I have no idea how to do this, but I figure beginning is half the battle. Right?
2) I start classes in my Elementary Education Initial Licensure program on February 4th! While my heart is jumping to become a teacher, I think my brain still has a ways to go. While doing an assignment for one of my online math classes today, I realized there is still a lot I need to learn and even more importantly, remember. There are topics I've mastered a ridiculous amount of times (i.e. inductive and deductive reasoning, please just let me be) and still struggle with. My brain kicks in when I need it, but then my memory fails me. Thankfully, I will be teaching similar, if not the same, topics year after year, so I'm sure I'll come to master them in time. I'm glad that I have this perspective, as certainly many of my students will experience this, too.
 |
| My heart is definitely in this. I love the kids. |
Other things I'm really feeling:
-All things paper. Lovely paper products, particularly stationery, light up my heart in a weird sort of way. I love how paper, when brought to life with words and pictures, is capable of communicating love, expressing art, and embodying my current and past experiences. It just makes me so happy. Swear I'm not crazy.
-Feedly! Such a fab way to keep up with all of my sources of inspiration, particularly blogs. I probably follow 200+ now, and bookmarks were just NOT cutting it.
Questions for you all:
Regarding education: What are your thoughts on the Common Core State Standards? I am trying to learn more without identifying with a particular side of the issue. Above all, I'm for the kids, and whatever benefits them is what I will support.
Regarding spirituality: How do you incorporate your faith into your daily actions?
Keep those hearts and minds a blooming,
Miss Elizabeth
Wednesday, January 8, 2014
Half inspired, half reluctant
I am writing. This post is half inspired, half reluctant. I have so many words inside that just rush throughout me all day long, yet I find releasing them to be such a harrowing task. They never seem to come out right. However, being as I am going to be a teacher and encouraging my students day in and day out to write, I may as well practice what I preach and put a few words down on paper.
I am currently reading Emily Freeman's A Million Little Ways, and boy, has it inspired me. I've always been all for discovering my God-given passions and connecting with those truths that have always been there, inside of me. In college, I read Parker Palmer's Let Your Life Speak and struggled, like really struggled, trying to understand what my calling was. We did all these fancy practices to uncover them, "figure them out," and I just couldn't. I wanted to know my path so badly. The harder I tried to find it, I think the less success I had.
Now, here I am reading Emily's words, and I realize that at some point in the past year of, I did it. I found that thing that makes me come alive. The story of how that happened is another post entirely, but somehow, after years of having no idea of who I was, I figured I want to teach. I don't just want to lecture in front of a class and grade papers. I want to teach hearts and minds to bloom, just like mine has upon connecting with this massive, awesome love of mine.
Of course, upon figuring this all out, I am faced with a period of intensive waiting. Waiting at home to get a sub license (to fill time during my wait), waiting for sub jobs to appear. Waiting to get into a teaching preparation program, waiting for classes to begin (February 3rd). I've spent many a day of waiting alongside my twitter feed - an awesome yet horrible source of inspiration that taunts me with this teaching world I'm not quite part of. #edchatnotyet
Emily, on waiting:
"You are in a season of waiting. When you finally show up ready to release your art by being the person you believe you are created to be, there may be nothing more disheartening than to be asked to wait. The waiting can drive us mad if we let it. It can become a merciless dictator, shoving us into shapes we aren’t made for, shapes of worry and doubt and short tempers."
As I wait, I sub. These experiences are both enlightening and frustrating. I am so pumped to finally be in a classroom that I do not realize it is not at all what my teaching career will be like. I am told, "it will be different when you have your own classroom." I am told, "subbing is way harder than teaching." I am told, "the kids act way differently when their with their classroom teacher." After a particularly challenging day of subbing, I decide to take a little break. These challenging days cue self doubt. I ask my boyfriend, a teacher himself, if I'm really cut out for teaching. I want to be. I so want to be.
In A Million Little Ways, Emily quotes Steven Pressfield:
“Self-doubt can be an ally. This is because it serves as an indicator of aspiration. It reflects love, love of something we dream of doing, and desire, desire to do it. If you find yourself asking yourself . . . ‘Am I really a writer? Am I really an artist?’ Chances are you are. The counterfeit innovator is wildly self-confident. The real one is scared to death.”
This resonates with me and fills me up with such great hope. One day I'm all, "I'm made to connect with these kiddos" and "I will give all I have to ensure that they succeed" and the next day I'm feeling slightly crazy and am sure that I can't handle the politics and high stress environment that is teaching. Then I read this, and I think, or rather know, that all of these thoughts are an indication of just how much this all means to me. I come alive when I talk about teaching and education and children's futures. It's just all so big and scary, which is the reason I've shied away from it in the past. There's so much at stake when you're a teacher.
Okay, one more Emily quote because I am just so inspired and ready to get out there and DO THIS:
"Sometimes inspiration toward that thing that makes you come alive follows after you so hard and so loud that you look around to see how everyone else is reacting to this most obvious explosion of creativity happening right here in this room. It is bright and tangible and full."
This is beautiful and so YES. I feel this. I feel that inspiration.
xo
I am currently reading Emily Freeman's A Million Little Ways, and boy, has it inspired me. I've always been all for discovering my God-given passions and connecting with those truths that have always been there, inside of me. In college, I read Parker Palmer's Let Your Life Speak and struggled, like really struggled, trying to understand what my calling was. We did all these fancy practices to uncover them, "figure them out," and I just couldn't. I wanted to know my path so badly. The harder I tried to find it, I think the less success I had.
Now, here I am reading Emily's words, and I realize that at some point in the past year of, I did it. I found that thing that makes me come alive. The story of how that happened is another post entirely, but somehow, after years of having no idea of who I was, I figured I want to teach. I don't just want to lecture in front of a class and grade papers. I want to teach hearts and minds to bloom, just like mine has upon connecting with this massive, awesome love of mine.
Of course, upon figuring this all out, I am faced with a period of intensive waiting. Waiting at home to get a sub license (to fill time during my wait), waiting for sub jobs to appear. Waiting to get into a teaching preparation program, waiting for classes to begin (February 3rd). I've spent many a day of waiting alongside my twitter feed - an awesome yet horrible source of inspiration that taunts me with this teaching world I'm not quite part of. #edchatnotyet
Emily, on waiting:
"You are in a season of waiting. When you finally show up ready to release your art by being the person you believe you are created to be, there may be nothing more disheartening than to be asked to wait. The waiting can drive us mad if we let it. It can become a merciless dictator, shoving us into shapes we aren’t made for, shapes of worry and doubt and short tempers."
As I wait, I sub. These experiences are both enlightening and frustrating. I am so pumped to finally be in a classroom that I do not realize it is not at all what my teaching career will be like. I am told, "it will be different when you have your own classroom." I am told, "subbing is way harder than teaching." I am told, "the kids act way differently when their with their classroom teacher." After a particularly challenging day of subbing, I decide to take a little break. These challenging days cue self doubt. I ask my boyfriend, a teacher himself, if I'm really cut out for teaching. I want to be. I so want to be.
In A Million Little Ways, Emily quotes Steven Pressfield:
“Self-doubt can be an ally. This is because it serves as an indicator of aspiration. It reflects love, love of something we dream of doing, and desire, desire to do it. If you find yourself asking yourself . . . ‘Am I really a writer? Am I really an artist?’ Chances are you are. The counterfeit innovator is wildly self-confident. The real one is scared to death.”
This resonates with me and fills me up with such great hope. One day I'm all, "I'm made to connect with these kiddos" and "I will give all I have to ensure that they succeed" and the next day I'm feeling slightly crazy and am sure that I can't handle the politics and high stress environment that is teaching. Then I read this, and I think, or rather know, that all of these thoughts are an indication of just how much this all means to me. I come alive when I talk about teaching and education and children's futures. It's just all so big and scary, which is the reason I've shied away from it in the past. There's so much at stake when you're a teacher.
Okay, one more Emily quote because I am just so inspired and ready to get out there and DO THIS:
"Sometimes inspiration toward that thing that makes you come alive follows after you so hard and so loud that you look around to see how everyone else is reacting to this most obvious explosion of creativity happening right here in this room. It is bright and tangible and full."
This is beautiful and so YES. I feel this. I feel that inspiration.
xo
Miss Elizabeth
P.S. I ordered 192 teacher stationery cards because I'm just crazy like that and they are cheaper in mass quants. Oh, and a $100 off coupon code (courtesy of my new obsession with entering online giveaways) helps. Check out Pear Tree Greetings for some super cute stuff. Can't wait to use them in…20 months?? Boo time just pass please.
Thursday, November 14, 2013
Khan Academy Idaho | Shelby Harris & Kuna, ID
This is the teacher I mentioned in my previous post. Thoughts?
Fractions are FUN...
...and teaching them is even more fun! Teaching them so students truly understand can also be quite difficult, so it is important that we as teachers approach this topic carefully. I learned today how much of an impact language can have on student understanding of math concepts.
I have often used the words "out of" to explain fractions: 1/4 is one out of four, 3/8 is three out of eight, 6/10 is six out of ten. This leaves students thinking that 1/4 is greater than 3/4 because 1/4 has just one piece taken out of it (leaving 3 pieces), while 3/4 has three pieces taken out of it (leaving one piece). You "take more out" with 3/4, so it most be smaller, students reason. The teachers language leaves them with the opposite answer. Fancy that! I never would have realized this on my own - what an awesome opportunity to get into the minds of my future students. Understanding a student's thought processes when making an error is the first step toward helping him or her correct that error.
As a substitute teacher, I have helped several students with problems involving fractions. Just last week, a student told me to talk in "kid language" while explaining fractions. This was humbling, as I felt I was using very clear, easy-to-understand terms. Looking back on this experience, I realize I used "out of" in my explanation. Oops.
I was trying to explain how mixed numbers and improper fractions can be used interchangeably. This student was puzzled by mixed numbers. We worked with 1 1/4. He pointed to the first 1 and then the second, very confused. "How can we have more than a whole? We have one already." I made some silly putty pies to demonstrate. By the end of our conversation, he recognized we had one whole pie and that the 1/4 was part of a second pie. This was definitely an "a-ha!" moment.
Next, I partitioned the first pie into four pieces (imagine in my graphic - I'm new to Canva and am still struggling some, though it's awesome), so we could count five total pieces to get to the improper fraction 5/4. I didn't get too far on this explanation. I could tell the student was drained from all of the hard thinking we had done. Plus, I had been so totally "in the zone" talking to this student that I had neglected the numerous raised hands and "Miss Harrison's" throughout the rest of the classroom. I decided to call it a day and went to answer the other student questions. I faced a teacher's dilemma that day: I could either focus on truly and fully explaining concepts to this one student who was struggling so, or I could brush the topic's surface while assuring everyone in the class got his or her questions at least partially answered.
Khan Academy has some amazing videos explaining fractions in a straightforward, easy-to-understand way. In the documentary Teach, a math teacher implements a model of blended learning in which students work on Khan Academy on individual computers. I think this is an awesome way for students to work at their own pace and develop a solid understanding of topics before moving on. It would, however, be hard as a teacher to relinquish this "control," as this model isn't generally what we picture when we think of teaching. As great as this program seems, I would still be sure to pull struggling students aside in order to enhance their understanding with manipulatives, especially for a fundamental topic like fractions.
I am happy my struggling student understood at least a fraction (punny, I know) of what he needed to know the other day, but I am frustrated that I couldn't help him more. Has anyone else been in this boat? Please share!
Saturday, November 9, 2013
The sea of zeros...adding and subtracting integers with colored counters!
Adding and subtracting integers with counters is such a fantastic idea. The woman in this video uses little pieces of paper as counters, which works also. She puts numerous positive-negative counter pairs together to create a "Sea of Zeros" that students can access when doing integer addition and subtraction.
This blogger places the "Sea of Zeros" on an organized "work mat" template for students. The work mat also includes 1) a place for positive and negative counters not in zero pairs and 2) a number line. Students can see clearly that the result is the same whether obtained through number line or integer counters. I really like the organized format:
Unfortunately, I haven't had the opportunity to watch this method in action while subbing. I've gotten to teach equivalent fractions (multiple times), so hopefully this will be covered in future chapters so I can discuss this some.
Subbing has been challenging. Fortunately, I was able to sub in the same second grade class for four days. It was so helpful getting to know the students. It's near to impossible to run a classroom without knowing student names. On the first day, I used a lot of "Hey buddy," and "Dear, can you ____." The third day was the best. I used a "magic wand" to give out points for attentiveness, kindness, respect, etc. and take away points for talking out of turn, being off talk, disrespect, etc. Whole class points were available, as well, for outstanding behavior. These were exciting to give.
I subbed in Kindergarten again, although I had previously decided Kindergarten wasn't for me. This experience was better but wasn't without its share of challenges. Math time consisted of counting songs 1-100 and numbers in the teens. Love the energy these little guys produce.
That's all for now! Keep those hearts and minds a'bloomin'!
-Miss Elizabeth
That's all for now! Keep those hearts and minds a'bloomin'!
-Miss Elizabeth
Tuesday, October 22, 2013
Place Value Cups
I'm going to devote today's blog to a topic I struggle greatly with: Place Value. In our elementary math class, we have learned of a few different number systems: Egyptian, Babylonian, and Mayan, to name a few. Understanding these numbers systems greatly enhanced my understanding of our number system and its use of place value. It also helped me understand the struggle students may undergo when trying to comprehend our own Base 10 system. Although I won't look at these other number systems in today's blog post, I highly recommend examining them and sharing them with your students.
Minnesota's Math Standards regularly refer to the importance of understanding place value. This basic understanding, which feels not-so-basic when you're new to it, is crucial in efficiently undergoing mathematical operations. A student must understand place value in order to truly understand and utilize common short algorithms used for addition, subtraction, multiplication, and division.
The following tool is a neat manipulative to help to students understand place value (from http://suedowning.blogspot.com):
Sue Downing cites many uses of the cups:
"We use the cups to:
understand place value
practice counting forward and backward
learn the names of large numbers
decompose numbers to expanded form"
I made my own set of cups to try this out, and I found they were most useful for decomposing numbers to expanding form, which allows for a greater understanding of relationship between digits and their place value. By pulling out the thousands cup, I understood that a 1 in the thousands place is not 1 but rather 1,000.
However, the cups do not permit students to experiment with different representations of the same numbers as readily as other manipulatives do.
For example, we know that ten ones are equivalent to one ten. Twelve tens are the same as one hundred and two tens. Four hundred can also be expressed as 40 tens. Base 10 blocks are far more useful for demonstrating this than place value cups, as students are able to actually, physically "trade in" ten ones for one ten (or whatever the exchange is). Developing this knowledge is necessary for understanding and using algorithms.
With the cups, once students reach "10," they have to change the tens digit to 1 and the ones digit to 0. We know that ten ones is the same as one ten, but students may not understand this relationship. Nor are they able to understand and explore more abstract representations of numbers that base ten blocks allow.
Thoughts? Does anyone know of other unique manipulative for learning about place value? Have those manipulatives been effective with students?
Minnesota's Math Standards regularly refer to the importance of understanding place value. This basic understanding, which feels not-so-basic when you're new to it, is crucial in efficiently undergoing mathematical operations. A student must understand place value in order to truly understand and utilize common short algorithms used for addition, subtraction, multiplication, and division.
The following tool is a neat manipulative to help to students understand place value (from http://suedowning.blogspot.com):
Sue Downing cites many uses of the cups:
"We use the cups to:
understand place value
practice counting forward and backward
learn the names of large numbers
decompose numbers to expanded form"
I made my own set of cups to try this out, and I found they were most useful for decomposing numbers to expanding form, which allows for a greater understanding of relationship between digits and their place value. By pulling out the thousands cup, I understood that a 1 in the thousands place is not 1 but rather 1,000.
However, the cups do not permit students to experiment with different representations of the same numbers as readily as other manipulatives do.
For example, we know that ten ones are equivalent to one ten. Twelve tens are the same as one hundred and two tens. Four hundred can also be expressed as 40 tens. Base 10 blocks are far more useful for demonstrating this than place value cups, as students are able to actually, physically "trade in" ten ones for one ten (or whatever the exchange is). Developing this knowledge is necessary for understanding and using algorithms.
With the cups, once students reach "10," they have to change the tens digit to 1 and the ones digit to 0. We know that ten ones is the same as one ten, but students may not understand this relationship. Nor are they able to understand and explore more abstract representations of numbers that base ten blocks allow.
Thoughts? Does anyone know of other unique manipulative for learning about place value? Have those manipulatives been effective with students?
"The day i passed maths"
A boy who has long struggled with math shares his passing grade with his father. He knew his father would be happy, so he set up a camera to catch his reaction. So incredibly uplifting. Every child and parent should feel this kind of joy through success in school!
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