Technology, Technology, Technology

After reading through the article on Using Digital Resources to Support Math Instruction, it made me think of a few things that I could do differently in my classroom, but it is difficult to do when you have textbooks that are not teaching to the new "way".

I think that using technology to enhance math instruction is an awesome idea. William McDonald, discusses some important points that can help all students excel and grow in math concepts. He suggests that using technology can further all students understanding because they are able to manipulate on the computer and try multiple ways to solve a problem. I think that this is extremely important because each child can work and their own pace and the teacher is able to see and check understanding based on how far each child has got on the problem that they are working on. One example that McDonald uses is that students can lay geometric figures over a real world image and be able to adjust them accordingly on the computer screen to help them solve the problem.

Technology is a great resource for the classroom and is the way that the future of education seems to be heading, but what about those schools that don't have the funds for these types of programs. Are those children going to be "left behind" in the future or are schools going to make it possible for each child to have the same type of opportunities.

Technology and Real World Data Help Teach Math!

I have never taught in a classroom with computers/ iPads before. I am reading a lot of the blog posts and see a lot of talk about iPads in the classroom.  I would probably freak out if my teacher handed me an iPad and said, “Play the Math Busters game for 20 minutes!” I think games have so much more of a motivational pull than any other form of instruction… even hands on experiments.  When I was teaching the 4^th grade at CHIME Charter School in Woodland Hills, my students would froth at any hint of an up-coming game.  I would create renditions of common games like battleship, connect-4, chutes and ladders, and memory!  Most direct instruction lessons would follow with a game and the levels of enthusiasm in students, even those who “hate math,” is what always motivated me to keep things fresh, creative, and fun! I couldn’t even imagine the excitement in students using an iPad or a computer for learning new concepts.  I think it would really help the visual/spatial, interpersonal, logical, and even intrapersonal students! Being a teacher means that you need to target all learning types because every student is different. Learning through the use of technology opens the mind to a different type of learning that might be exactly what some students need to make everything “click.”

I loved watching the YouTube video “Adding Rigor to the Classroom.” I thought that everything Mrs. Weigle said made perfect sense.  Kids really can do more if you give them the opportunity and open window to do so. On most worksheets, I would pose a tricky challenge question at the end that students could work out if they finished early and if they wanted to exude a little extra brainpower.  This would always impress me because students would come up with the most magnificent procedures to solving these challenging questions.  

I also think that the short video on teaching students math through real world data just confirmed what I already believe.  When someone is trying to teach me something and I can relate it directly to something I already know a little bit about and an familiar with, comprehending that topic or concept is that much easier.  I think using money is such an effective way to teach students math concepts because it is something they will be dealing with for the rest of their lives.  Most concepts can be taught with money.  Coins and fake dollars make for such excellent math manipulatives/ artifacts for students to play with. Everything from addition to division to fractions to algebraic variables can be taught with money!

Learning Math in New Ways...Finally!

I watched Betsy Weigle's videos with ideas of how to easily push our students past the standard's expectations. Sounds difficult, but she makes it seem so easy. She uses charts for multiplying multiple digit numbers. I wish my teacher had taught me this! It makes it so much easier to multiply larger numbers such as 11 x 2,312. She breaks down the number into 2,000, 300, 10, 2. And multiplies each by 11. She mentions that students love doing this because once they get their math facts memorized they can complete it fairly easily and feel confident about it.

She also explains the importance of teaching algebraic reasoning with function boxes. This allows students to easily see the variable and then determine an equation from the function box. I totally agree with her that teachers should start teaching this method sooner than later because I can remember being in 6th grade and having no idea why I was mixing letter with numbers now. It was so confusing to me and I really struggled with understanding this new concept. However, if we can get students used to seeing equations and understand what variables mean and why we are mixing letters and numbers then our students will be more successful with math in later grades.

I also liked the use of ten blocks to help with subtraction. I could definitely see this method being useful, especially for hands on learners. I liked how he used the terms"borrowing" and "trading." These are terms that students are generally familiar with in life and can also be applied to math. Base ten blocks are a great visual aid for students to really understand why they are borrowing and trading when subtraction. It is much more beneficial to show students this versus just telling them this is what we do because we have to.

Using iPads in Math

I love using iPads during math lessons! I  have 6 iPads in my classroom, so the students work together in small groups. They get to use technology, advance their math knowledge, and learn to collaborate with others- it's a win-win!

A personal goal of mine this year was to start using the iPads as part of the actual lessons, not just filler or something to do for the early finishers. Right now in my 2nd grade class we are doing a unit on fractions. I am using the Book Creator app to create a class fraction book. Students use the iPads to take pictures, which turn into a fraction word problem. I try to do one iPad project a month in my classroom. I would love to hear any suggestions you have about how you incorporate iPads in your classroom! :)

Videos, iPads, & Google Classroom to Support MATH!

After listening to Tinashe Blanchet speak about her strategies for incorporating technology into her math class and getting kids excited about math. Her strategies reminded me about the different technology integrations we learned about last semester. She mentions making a rap video with her students explaining algorithm and submitting the video into a contest (and winning!). Her students were so excited about making this video that they were taking time out of lunch and other special areas to work on the video with her. As we learned last semester, incorporating video production in the classroom can be a very beneficial learning tool.

She also talks about the use of ipads in her classroom and having students use them as graphing calculators. She states that on an ipad you can really manipulate the graph with making it 2D or 3D, actually grabbing the graph and twisting it 360 degrees around. I could definitely see this being exciting for students and encouraging them to want to learn about graphs and making graphs on a calculator.

Additionally, she talks about using a "google classroom." Where each student has their own page and can communicate in a virtual classroom. She states that she notices that students get excited about projects they have ownership of. I believe this 100% true. I found when teaching, that my students produced awesome and memorable projects when they felt ownership of the project. It amazing to see what students can come up with with minimum direct instruction. Has anyone used any of these strategies for math in their classrooms?

Dylan's Guided Learning...Not Dictated Learning.

After reading and trying to understand Dylan's way of thinking (which took me a very long time!) it became so fascinating to me that a first grader who hadn't even begun learning subtraction could use his place value knowledge to figure out how to solve it. I am 24 years old and think to be educated and would have never thought of this strategy. It's amazing what our students can come up with! After learning this, it became apparent to me how truly important it is to provide our students with learning tools and vocabulary that guides their learning but doesn't dictate it. Often when I was a student, I felt that teachers taught us one way of figuring out a problem and that was it. There did seem to be much support for student's figuring out their own individual methods.
I think this article is a great eye opener for all to demonstrate just what our students are capable of. We must provide our students with the necessary tools for learning and then allow them to think creatively to find solutions to problems. Dylan's thinking is a great example of our students applying math knowledge to solving a problem.

Sue Lampkin's Lessons

Word problems are extremely fearful for students who have not received a solid foundation and/or influenced to believe that they are not as painful as they think. Moreover, word problems should be given at all ages so because the norm and as organic as reading a book. Upon reviewing Sue Lampkin's first grade class math lessons, I feel she used amazing strategies to help her students gain the insight needed to approach word problems. It is very detailed, properly scaffolded for the betterment of her students. I also like that she reflects on her own teaching. I feel that is something that we should all take time to do so we can grow as educators and be the best for our students. 

Dylan's Math Journey

I think the video clips and reading show that students can approach a problem in many ways and arrive at the correct answer. But, it is up to the educator to take the time to assess their student’s thought process in order to assist them. It also examines the importances of taking time to differentiate your instruction to meet the needs of all types of learners. Equally important, that when students have a strong foundation they are very much capable of excelling and solving algorithms that they were not even introduced to yet. Such as the young girl with the fraction problem. All and all, differentiation, proper assessments, and understanding are essential components for students in learning math. 

Thorough Understanding

Sue Lampkin's first grade class is very lucky. The process that she takes her students through to solve two step word problems is awesome. Her lesson's are very in depth and she reinforces past lessons to continue to develop concepts. Word problems can be so tricky for students to understand, especially two step problems. I have to walk many of my 3rd grade students through them still. If this emphasis is reinforced at every grade level, all students will have a better foundation to solve these difficult problems now and in the future.

Independent Thought Process

I was amazed to read Dylan's logic behind his strategy to subtract. What shocked me the most was his ability to solve a problem without any form of formal instruction. For many students such strategies just make much more sense to them, which is why I feel that as teachers, it is crucial to question critical thinking steps. Not only is questioning important to for us as teachers to understand the steps, but also serves as a teaching strategy for students. At times, students learn best from one another.

Dylan’s number sense, as he displayed, is at a mastery level. We can all learn plenty from students like Dylan. Way to go!  

Dylan is one smart cookie...

Wow, Dylan! This kid is one smart cookie.  After reading both articles about Dylan and his strategies on subtracting multidigit problems, it made me laugh.  I can only imagine how his teacher would have felt, having him explain his logic behind his strategy. As a teacher, I would ask myself, “Should we teach all students his method? Would they understand it better?” I was so excited about Dylan’s strategy, that I even tried doing several different problems myself; his way, and was so surprised that it worked every time. I even showed my husband and he thought it was so cool that a kid, who is only seven years old, can take the fundamentals of simple subtraction and take it into a more complex situation and get the correct answer.  His response was so cute when he was asked to do a subtraction problem with 3 digits and was able to get the correct answer, he knew he got it right.  I was proud of him and I don’t even know him.  Good work Dylan! Can’t wait to see what else you may come up with!

Number Sense Makes Sense!

I felt the common thread in all the articles and videos was the concept of number sense and how crucial it is that we, as teachers, spend a significant amount of time developing it with our students.  In Dylan's example, we were able to see how without any help, he came to an answer using a method he developed.  He was consistent in its usage and accuracy and was able to explain what he did.  The explaining is the best part.  I'm forcing myself to ask students to explain or justify their answers in all subjects these days.  It's time consuming, but it pays off.

I also viewed Jane's thinking on the Mountain View, Slater School site.  I like the questioning process and how Jane recorded the question, the data - the teacher suggested she look at an old worksheet to remind herself what "data" meant- the problem, the answer, and finally putting a check mark at the end to indicate that she had checked her work.  You can see that this is process they use daily in that math class that elicits detailed and thoughtful responses.  It was interesting to see how quickly Jane added the two numbers 12 + 2 to get 14.  That part was the fastest and she did not speak while doing it.  What was key was the way that she could explain "why" she did what she did and she was able to say "why" subtracting would not get you to the correct answer.  (The teacher asked that question at the very end.)

I was pleased to hear, from the Spark's article, that counting (or the speed at which a child can count and solve arithmetic problems) is not the best indicator for success in math later in life.  Rather understanding sets of numbers and how to manipulate them is more important and a better indicator.  In my own room, I have seen tremendous growth with students who struggled with counting (and still do) when it comes to their overall number sense.  I feel that the accessibility of manipulatives, ten frames, part-part-whole mats and other tools has increased my students' ability to see sets of numbers and to understand equations.  I also spend a great deal of time on math vocabulary, ensuring that they know equal means same, sum is the answer when adding, etc. While counting is important - number sense, or better, set sense is more valuable for long term growth.

Three Cheers for Dylan!

I was blown away in reading about Dylan’s subtraction victories! For a student to create their own strategies and apply it to all different subtraction problems is exactly the outcome that we as teachers want for our students. He used thinking skills to develop his own method for subtraction that makes sense for him, although he needed support in explaining his process. In essence, this is what the common core standards are aiming to do-allow students to work out problems in different ways and then explaining their work. However, our math curriculum has not caught up to this yet. Our math curriculum is very narrow-sighted when it comes to methods and procedures, often forcing students to use the curriculum’s specified way to solve problems on tests. Another obstacle is the number of students we have in class. It would take a tremendous amount of time to sit down with each student and examine and analyze their methods-especially if the student was unable to understand a way to arrive at a correct answer. With lower class sizes teachers would be able to offer students more personalized attention and instruction. If we were able to offer students the freedom to explore and invent their own strategies I believe students would have a more solid foundation of math and number sense. 

Dylan's Strategy and Pedagogy

Dylan's incredible way to solve two digit and three digit subtraction and his teacher understanding what a monumentous event this was,

Today we must differentiate instruction to every student, but to do that we must understand what the students know, understands, and how the student knows. The conversation with Dylan started because the teacher noticed he always got the right answer, but he never wrote the process. Because Dylan was at the time, the explanation had to be talked out. The teacher asked Dylan to go through his thought process. Through the interview, the teacher found out what Dylan did know (that you must start with the ones column). Dylan also knew that you must subtract the smaller number from the larger number in the one's column (Dylan did not understand regrouping). However, the rest of his thinking was logical. Yet this seven year old found out a different way to arrive at the correct answer, showing divergent thinking. I am old school, so I will not use his method because I find more complicated than the algorithm in which regrouping is used.

The teacher learned about how her student solved problems, the misconceptions he had (regrouping), and he had the correct answers. Even though Dylan discovered a new way to subtract, Dylan will need to learn how to solve two-digit and three-digit subtraction. 

Students need to learn various ways to solve a mathematical problem because it encourages mental flexibility, and a thorough understanding of the math, and logic behind the problem. 

If teachers are to individualize instruction, you must also listen to the thinking behind the computations that the students do.

DYLAN’S SUBTRACTION STRATEGY HAS ME STUMPED

Maybe I am thinking too deeply about trying to decipher “Dylan’s multi digit subtraction strategy” and the answer is actually very simple, but I am completely lost. I read it a few times and even tried some problems of my own but the logic for me just isn’t there. I must be so old fashioned with my blinders up that my mind wont even accept anything new as far as strategy’s go.  Subtraction has been engrained in my brain to always go from right to left and borrow from the left side if the numerator is too small. Dylan’s way of thinking is a powerful example of how apt children are of adapting original and factual methods for mathematics.  It is so necessary to allow children the ability and power to develop their own ideas before telling and teaching them the “right way” of doing something.  Reading this article confirmed the notion that there is never just one single way of doing something.  There are multiple outlets for almost anything and if there is logic behind a method and it can be proven to work in any condition then it should be validated and accepted.  Some children see things differently than others.  Some might instantly understand the old fashioned method of subtraction while others may not.  Some may instantly understand “Dylan’s multi digit subtraction strategy” and others may not.  That’s why I think it is so beneficial to show children many different ways of doing something and then decide which way works best for them.  I am a very hands-on learner…  I can read all the directions in the world and look at illustrations and maybe even watch a video on the topic of “how to change a flat tire,” but it is not until I physically change that flat tire myself that it all makes sense! Everything I have read finally “clicks!”  I feel as if young learners are the same way J