A Global Look at Math Instruction
Looking at the strategies and techniques that countries with students achievement in math leading far ahead, is beneficial for the United States so that we can adapt and help our students to progress into efficient math students. Within this focus, the studies and research the authors based this article, on centered on the achievement and understanding of fractions which seems to trouble American students, and even adults. The first comparison among curriculum in Japan and Korea with the United States is when fractions should be taught which seems to be third grade for both Korea and the U.S, although with closer look at their Focal Points and our NCTM curriculum, the whole concept of fractions, decimals and multiplication of fractions are taught earlier in Korea then in the U.S. Multiple areas of the teaching instruction of math is compared between the three countries, in an unbiased yet informative voice. Textbooks, use and choice of manipulatives and examples, time introduced and time spent on, and independent versus dependent learning is compared, leaving the reader with a new understanding about a sliver of math teaching in three cultures.
I was first curious about this article because of the title and the use of the word ‘culture’, since that is something I am constantly interested in learning about. As I started to get into the article I became even more interested because I realized it was comparing the United States with two Asian countries, but then I was corrected because this article is not set out to compare and criticize, but to compare for the purpose of gaining insight on how to best teach the concept of fractions. I was expected to read all about the long school days and years the students in Korea and Japan endure, and the strict structure their school system has adapted but I was happily surprised by this break from the “normal stereotype towards education”. I was also interested to read that we do have some similarities in curriculum with Korea, but that they introduce the entire concept in a short span of time, then we do. The adaption of textbooks to fit curriculum, through the seven times it has been updated, was interesting too. I think we have a lot to learn from countries that excel in mathematics training/teaching, they are our competition and we need to make sure in the future American children have a fair shot for those jobs, industries and academics.
Son, J. (2011, February). A global look at math instruction. Teaching Children
Mathematics, Retrieved from http://nctm.org/eresources/view_media.asp?
article_id=9602
Virtual Data Collection--For Real Understanding
As the push for technology incorporation increases, teachers look for academically challenging, safe and reasonably priced equipment, that still allows for some inquiry-based learning. The various tools examined in this article written by S. Asli Ozgun-Koca and Thomas G. Edwards, become great resources for teachers as they prove beneficial for all grade levels, altering intensity. In an activity given to eighth graders, TI-Nspire (calculators), GeoGebra or Geometer’s Sketchpad (virtual graph paper) were used. Instructions were provided and followed easily but students as they manipulated, tested, and set different radii, circumference and area of circles. They saw how changing the radius affected the circumference and the comparison between the two while also incorporating slope and pi. The virtual graphing devices were not necessary for the activity, student could have drawn out the diagrams, but the objectives for the lesson were not seeing if the students were good artists, but how they interpreted the data, used equations and translated the representations. Using the technology is a fast, effective, visually enhanced way of looking at the work being done by the students while engaging them with hands-on programs that they can use throughout schooling.
I think these programs are great, cost is the one thing I would be concerned with but in an ideal world I would hope each student would have a chance to work with them. I would hope these would not completely take the place of students drawing diagrams themselves, because I think that is a skill in itself that is highly important, but it’s amazing that technology has come this far to produce something like this. It is great visually for students to see instantly the transformation a circle makes when the radius is changed, in contrast to the slower connection it would be if students had to spend time drawing the circle in between each observation.
Ozgun-Koca, S, & Edwards, T. (2011, February). Virtual data collection: for real
understanding. Mathematics Teaching in the Middle School, 16(06), Retrieved
from http://nctm.org/eresources/view_media.asp?article_id=9589
Tuesday, February 15, 2011
Monday, February 7, 2011
Math Applet #2 How Many Under the Shell
Information: How many under the shell http://illuminations.nctm.org/ActivityDetail.aspx?ID=198
Summary: The menu allows players/students to select how many bubbles the game will start with, or a random number can be chosen. Students then pick if they would like subtraction or addition problems, a mixture of both can be choosen as well. After the initial set-up, a bubble with a number in it appears and covered by the shell. Numbered bubbles are added or taken away from the shell, but are all still hidden by the shell. The equation is in the top right corner for students to refer to, but no manupultives to count. The game repeats itself like this.
Critique: I did not like this math applet as much as the "grouping and grazing" for a few reasons. There were not as many different oppurtunities for learning (only addition and subtraction) and the format was slightly confusing. Not being able to touch the screen and count the bubbles (having them hid under the shell) might be hard for Pre-K and K, although it might have been better for first and second grade, because they could more easily use the equation.
Summary: The menu allows players/students to select how many bubbles the game will start with, or a random number can be chosen. Students then pick if they would like subtraction or addition problems, a mixture of both can be choosen as well. After the initial set-up, a bubble with a number in it appears and covered by the shell. Numbered bubbles are added or taken away from the shell, but are all still hidden by the shell. The equation is in the top right corner for students to refer to, but no manupultives to count. The game repeats itself like this.
Critique: I did not like this math applet as much as the "grouping and grazing" for a few reasons. There were not as many different oppurtunities for learning (only addition and subtraction) and the format was slightly confusing. Not being able to touch the screen and count the bubbles (having them hid under the shell) might be hard for Pre-K and K, although it might have been better for first and second grade, because they could more easily use the equation.
Math Applet #1 Grouping and Grazing
Information: Grouping and Grazing http://illuminations.nctm.org/ActivityDetail.aspx?ID=218
Summary: This virtual manipulative uses the image of cows to teach children counting, place value, subtraction, addition and grouping using single and double-digit numbers. The player has the option of grouping the cows in fives or tens or to add or subtract them. At the end of each round, there is a button that tells the student if they were right or if they need to keep trying. During adding and subtraction the student inputs they number they think is there. A red barn is added to the bottom of the screen each time a player gets the answer correct.
Critique: I played first without looking at the directions, acting as if I were a pre-k or kindergarten aged student who didnt know how to read. It was easy enough for me to figure out through a little trial and error, and although directions should be gone over prior, a child Pre-K through 2nd, could figure it out. I liked that there were four skills to work on through this game allowing practice for those struggling and a challenge for those who are ahead. The motivational and positive red barns after each correct answer was appropraiate as was the box that read "try again", if needed. It had activities that ranged well between Pre-K and 2nd! I am brining this up to my co-teachers at my Preschool for the kids to use during computer time!
Summary: This virtual manipulative uses the image of cows to teach children counting, place value, subtraction, addition and grouping using single and double-digit numbers. The player has the option of grouping the cows in fives or tens or to add or subtract them. At the end of each round, there is a button that tells the student if they were right or if they need to keep trying. During adding and subtraction the student inputs they number they think is there. A red barn is added to the bottom of the screen each time a player gets the answer correct.
Critique: I played first without looking at the directions, acting as if I were a pre-k or kindergarten aged student who didnt know how to read. It was easy enough for me to figure out through a little trial and error, and although directions should be gone over prior, a child Pre-K through 2nd, could figure it out. I liked that there were four skills to work on through this game allowing practice for those struggling and a challenge for those who are ahead. The motivational and positive red barns after each correct answer was appropraiate as was the box that read "try again", if needed. It had activities that ranged well between Pre-K and 2nd! I am brining this up to my co-teachers at my Preschool for the kids to use during computer time!
Tuesday, February 1, 2011
Problem Based Learning Part 3
Hawaiian School Carnival: Sixth grade Students work with a budget and fundraising to plan a Hawaiian themed carnival that supports a technology center for the school. The problem the students face is how they will fundraise the rest of the money they need for the event. This problem incorporates different subject areas including math (numbers and operations, algebra, geometry, measurement, probability), language arts, social studies, and fine arts. An overview of the project was laid out along with questions that will help prompt the students and also for the teacher to use to assess and check progress of the kids along the way. There are lesson plans included that introduce and teach about each of the math sections mentioned above. As the students work through the problem, they will be assisted by the lesson taught. Adaptations for children with special needs and challenges for those who need something extra were stated and discussed. Students would be assessed by the provided materials.
Strengths: Good outline of what standards will be met, lessons that will be used to teach students the skills that go along with the problem and I appreciated the inventive solutions to challenges and adaptations. Tying in Hawaiian culture from textbooks, internet and discussions, creating a PR campaign, writing a business letter and being involved in their community through discussion and newspapers is a create way to incorporate language arts and social/emotional standards into this project. Adding art into the project will allow some students to be successful through that area.
Needs Improvement: problem not state entirely and does not clearly state what the goal or problem is for the students. Doesn’t make clear if students are planning, budgeting or fundraising.
Assessment: The rubric was very detailed and well thought out. There was a separate one for the portfolio part and the oral presentation. I think using a rubric is a good form of assessment because it allows students to be more successful. They can receive different points for different areas, so that if one part is bad, the entire grade doesn’t reflect that.
Building A Playground: Sixth grade students will build a playground which will require them to have knowledge and practice skills in the following areas; geometry, special reasoning, numeric thinking, statistical thinking and measurement. The community will be involved whether it is speakers coming in to talk about playgrounds and the town or students interviewing people to get more information.
Needs Improvement: The section on process standards could have been more specific to the problem at hand. There was no assessment created, just what could be done. I did not understand what the importance of the day five lesson was. It was an interesting idea but I thought it was slightly irrelevant and written poorly. At the same time day seven lesson seemed irrelevant as well. Each day was started with guiding questions, but I thought part of problem-based learning was for students to think of these questions when they stumbled upon them and thought of them themselves.
Strengths: The breakdown of each day of the lessons and problem solving time. The incorporations of other subjects in this problem were strong.
Assessment: I think looking at journals and logs is a good assessment but there was not formal way to assess them, where was the rubric or checklist. Without having a rubric, it does not provide clear expectations for the students, they won’t know how they can do well, or where they stand when they turn in their project.
Overall:I felt that the Hawaiian School Carnival was a more engaging problem than the playground for the grade level of kids. Both were relevant but I’m not sure how interested middle school aged students would be in playgrounds. Both problems allowed students to use prior knowledge but also gave them opportunities to learn new information through lesson, self-guided research and team work. In both problem sets, there were positive and challenging questions that would guide students to get to their solution. I thought overall it was in good form and structure of problem-based learning.
Strengths: Good outline of what standards will be met, lessons that will be used to teach students the skills that go along with the problem and I appreciated the inventive solutions to challenges and adaptations. Tying in Hawaiian culture from textbooks, internet and discussions, creating a PR campaign, writing a business letter and being involved in their community through discussion and newspapers is a create way to incorporate language arts and social/emotional standards into this project. Adding art into the project will allow some students to be successful through that area.
Needs Improvement: problem not state entirely and does not clearly state what the goal or problem is for the students. Doesn’t make clear if students are planning, budgeting or fundraising.
Assessment: The rubric was very detailed and well thought out. There was a separate one for the portfolio part and the oral presentation. I think using a rubric is a good form of assessment because it allows students to be more successful. They can receive different points for different areas, so that if one part is bad, the entire grade doesn’t reflect that.
Building A Playground: Sixth grade students will build a playground which will require them to have knowledge and practice skills in the following areas; geometry, special reasoning, numeric thinking, statistical thinking and measurement. The community will be involved whether it is speakers coming in to talk about playgrounds and the town or students interviewing people to get more information.
Needs Improvement: The section on process standards could have been more specific to the problem at hand. There was no assessment created, just what could be done. I did not understand what the importance of the day five lesson was. It was an interesting idea but I thought it was slightly irrelevant and written poorly. At the same time day seven lesson seemed irrelevant as well. Each day was started with guiding questions, but I thought part of problem-based learning was for students to think of these questions when they stumbled upon them and thought of them themselves.
Strengths: The breakdown of each day of the lessons and problem solving time. The incorporations of other subjects in this problem were strong.
Assessment: I think looking at journals and logs is a good assessment but there was not formal way to assess them, where was the rubric or checklist. Without having a rubric, it does not provide clear expectations for the students, they won’t know how they can do well, or where they stand when they turn in their project.
Overall:I felt that the Hawaiian School Carnival was a more engaging problem than the playground for the grade level of kids. Both were relevant but I’m not sure how interested middle school aged students would be in playgrounds. Both problems allowed students to use prior knowledge but also gave them opportunities to learn new information through lesson, self-guided research and team work. In both problem sets, there were positive and challenging questions that would guide students to get to their solution. I thought overall it was in good form and structure of problem-based learning.
Problem Based Learning Part 2
Summary: A teacher saw the love for a book through her students interest in Harry Potter. To make a math lesson more engaging, she linked budgeting, checks and balances, and purchasing. The teacher created a list of materials students at Hogwarts needed or would want for school, along with their prices. She assigned each student a character in the book that had a budget. The problem set forth was to see how they could budget their money to get the most, get the best, get what they wanted for school.
Review: I though this was a great way to study the idea of budgeting. There are many fun ways to do this, grocery lists, allowances, shopping etc but this teacher saw an outstanding and already existing passion her students had and incorporated it. I appreciated that she did not assume each child had read the story before, and therefore created a language arts activity in the room as well, allowing each child to read aloud. Not all student had the same budget, the result of pairing each student with a Hogwarts student, which allowed them to work through their own budget. It was mentioned that students helped each other periodically, but each person still felt individuality this way. Two class periods were used to do this lesson, which I thought was appropriate. This gave enough time for a structured introduction and reflective debrief which created a full-circle experience for the students.
Citation:
Beaton, Tisha. (2004). Harry potter in the mathematics classroom. Mathematics in the Middle School, 10(1), Retrieved from http://www.nctm.org/eresources/view_media.asp?article_id=6672
Review: I though this was a great way to study the idea of budgeting. There are many fun ways to do this, grocery lists, allowances, shopping etc but this teacher saw an outstanding and already existing passion her students had and incorporated it. I appreciated that she did not assume each child had read the story before, and therefore created a language arts activity in the room as well, allowing each child to read aloud. Not all student had the same budget, the result of pairing each student with a Hogwarts student, which allowed them to work through their own budget. It was mentioned that students helped each other periodically, but each person still felt individuality this way. Two class periods were used to do this lesson, which I thought was appropriate. This gave enough time for a structured introduction and reflective debrief which created a full-circle experience for the students.
Citation:
Beaton, Tisha. (2004). Harry potter in the mathematics classroom. Mathematics in the Middle School, 10(1), Retrieved from http://www.nctm.org/eresources/view_media.asp?article_id=6672
Problem Based Learning Part 1
I am somewhat familiar with problem-based learning from earlier math education classes, and was involved in a few of them. I remember getting a problem and a back bone of instructions and structure and told to find a solution. At first it was a little overwhelming but as my group and I started to brainstorm we really got into it and almost a little competitive to make our solution better than the others. It was a lot of team work but also some individual work. This is what I walked away from the activity realizing and I am glad to see through reading some of the materials on Problem-based learning that I got the right information from that activity. We talked in class yesterday about challenging your students and letting them struggle a little bit so that they can problem solve and become confident in their abilities to do so. Through these real-life problems there is brainstorming, sketching, crumbling up and throwing away ideas, setbacks and achievements with group and their individual work. They learn to use outside resources, teachers, community, classmates etc. Teachers are involved, but minimally. They are there for support, facilitating and debriefing. One of the documents I looked at, broke down the process and definition of problem-based learning in a very clear, direct and structured way. That document was great for someone who wants to start incorporating problem-based learning to their classroom effectively.
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