1512-Week 4

Common Core State Standards

        Common Core State Standard Initiative is a wonderful initiative working toward more specific standards not fewer standards. They want to make sure that the standards are clear for not only teachers but the students and parents as well. They also focus on a consistent framework. They are designed to be relevant to the real world to help in their success in the future. 

        Minnesota sadly has not yet adopted the Common Core State Standards. Although it is a relatively new initiative, MN is only one of eight states that have not yet joined the initiative. I think it would be a great thing to have for the students of MN. It would be nice to see all 50 states united in this initiative.

Rockin' the Standards=Awesome!
        Tim Bedley is amazing. What will he think of next?? I think this is great way to not only get kids interested in math but to have fun learning it at the same time. My favorite song is the Quadrilateral Dance and The Angles song is pretty catchy as well. If you haven't noticed kids love to sing! I have heard many students singing such songs as "Pray for You" by Jaron and The Long Road to Love and "Rain is a Good Thing"by Luke Bryan, among many other pop songs. If you have heard the lyrics to these songs and others on the radio, I would much rather hear students sing to RTS than some of these pop songs. I definitely think this CD is a great investment for any teacher or parent.

1510-Week 4

Math and Art :)

Circle Limit III by M.C. Escher (1959)

        Math and Art have a long history together going as far back as the great pyramid. When we think of great artists of the past many incorporated math into their work. The great Leonardo Da Vinci incorporated many mathematical concepts into his artwork. M.C Esher was known for his mathematically inspired work, for example his tessellation work (right).
        The video, Cool Multiplication Technique for Large Numbers (below), is a great Math Art video. It is a Stop-motion animation. The artist that created it did a great job connecting art and math. This clip makes math fun with its irony.
        For those students who are interested in art, and not so much in math, doing interdisciplinary lessons that connect Math with art is a great way to get those kids interested in Math. Connecting the lesson to another subject that they show interest in is a great hook to reel them in. Without mathematics we wouldn't have our family favorite animated movies, for example, (my favorites) Toy Story, Lion King, Wall-E, etc. The DreamBox Learning Blog post, Helping Young Animation Lovers Appreciate Math, is a great resource to use for connecting math with animation. It links to many other great articles and resources that make learning math and animation fun.

1512-Week 3

What are the odds? 
        Have you ever heard the phrase "what are the odds of that happening?" The odds may seem greatly outweighed but it could happen, like the odds of being struck by lightning in a given year (reported deaths + injuries) is 1 in a million. The odds you will be affected by someone that has been struck by lightning are far less. Probability is everywhere in our daily lives. The NCTM Principles and Standards for School Mathematics (2000) states that the curriculum for pre-k to 8th grade should include the study of probability so that students can understand and apply the basic concepts of probability.
        In the textbook, Mathematics for Elementary School Teachers, on page 529 refers to a game on Odds and Fairness. It explains a game called Multiplication Toss. This game is for 2 players, one being “odd” and one “even.” They are give two number cubes (die) to roll for their turn and are to find the product of the numbers rolled. If the product is odd the odd player gets a point if it is even the even person gets a point. Students are to play the game up to 10 rolls and then switch roles. They would then be asked: Is it a fair game? Why/why not? If we look at the odds, we find that "finding the product" is an unfair game as the odds of the product being “odd” is ¼. If you change the game to the sum being “prime” or “not prime, we find the sum being “prime or not” unfair as well, as we find the sum being prime 42% of the time. If you changed the game to finding the "sum of the numbers" rather than the product, we would find the sum of the cubes with the odds of rolling “odd” or “even” is 50/50, a fair game.

Why is studying about the topic of fairness of games an important school topic? 

        It is important to teach fairness of games in school because we don’t want students to feel they are at a disadvantage, but we have to teach them that life is not always fair. We can’t always change the rules in life like in a math game, but we can choose to be fair. Fairness goes along with student’s character development in teaching them right from wrong. Fairness means playing by the rules, taking turns, sharing, and listening. Fair people do not take advantage of others. The topic of fairness promotes better decisions made by students when interacting with others at school.
         Usually children learn about fairness at a young age. Having siblings and when out with friends, if one child gets a treat everyone wants a treat. Parents say you must share your treat to be fair, so everyone gets some. Once they enter school for the first time, they are not used to being with so many children their same age. Sharing becomes a big issue. Who wants to share their snack with 20 other kids!? 
         Teaching fairness greatly connects to teaching being a responsible citizen. We as teachers need to teach students that you shouldn't leave anyone out in certain situations. Along with Math, there are many other ways we can teach fairness. A great resource for teaching fairness is AtoZTeacher Stuff.com: Teaching Fairness. It lists a variety of useful books and lessons/mottos teachers use. Another great publication comes from the West Virginia University Extension Service. It is called Family Times Newsletter and is for adults with children ages 5-8. This particular issue is on developing Fairness. This newsletter is a great resource for those needing help in the teaching of fairness.

1510-Week 3

Let's Do It Together!
       Having students work out problems on their own in groups is very useful learning activity. Cooperative Learning is a very useful strategies that should be used in every classroom. This strategies allows students to interact with and learn about other students. Students in these situations can learn new skills from the peers their and partnered with in these groups. The skills they gain from cooperative learning experiences can greatly benefit the students in their future careers.
        The cooperative learning strategy can be used in every subject area and would be great in many occasions in math. It provides for students excelling in the subject to be teacher to those at a lower level. Students who are struggling are be paired with those who have mastered the concept being taught and together they can work with and learn from each other to find the correct answers for the problems given. It also provides those with different skills to come together to display their varied skills. For example, if you are assigning students to make math posters, you would pair a student skilled in math, a student skilled in art, and a student skilled in reading to work together to create the poster so all would be able to learn new skills from one another.
       After being in the classroom to see this strategy used, I find it very useful.  The following video is an example that shows that this is a useful tool in the classroom to more fully engage students in learning. It shows fifth grade students working out the problems and together they have to decide whether their answers are correct. This kind of work should be used as an alternative to the teacher reading off the answers to students. Video: Students Explain Benefits of Reaching Consensus
        I enjoyed watching the students speak for themselves on the benefits of this kind of activity vs. having the teacher read off the answers. It shows that students really enjoy learning and they were glad to tell the teacher what activity helped them learn more. Most students are very social and this is just another way to get them to discuss school topics with other students. It was nice to see students working together toward the same goal and to see their joy upon reaching that goal. It is important to remember that You, as the teacher, are in charge of your students learning. It is up to you to choose activities that will provide for optimal learning. 

1512-Week 2

The National Council of Teachers of Mathematics’ publication, Principles & Standards for School Mathematics is a great resource. This week we are looking specifically at Ch. 3: Standards for School Math: Data Analysis and Probability. This section is about getting students to formulate questions that can be answered by data. It also discusses using data wisely.

Teaching students to “READ” the data is very important. There is lots misuse of data (statistics) as a way to sway public opinion. This connects to topics like reading the media, like television advertisements. One example would be analyzing infomercial adds…”only 4 easy payments of $19.95 plus shipping.” Teaching that simple math to find out that the item is really $85. Or “one in ten use this product” to find out that 1/10=only 10%.

With these standards in place, increasing in sophistication across the grades by the end of high school students should have a sound knowledge of elementary statistics. Work in data analysis and probability offers a natural way for students to connect math with other subjects and with experiences in their daily lives. The reasoning skills they develop will also serve them in work and in life in the future. Student in the primary grades start with easy topics to connect to students. These topics could be what kinds of pet students have or favorite kinds of pizza and show it with the use of tally sheets or charts. Students later grow to topics such as recycling or conservation in the middle grades. With these first steps, it leads students to being able to compare other data from books, newspapers, and the Internet. 

1510-Week 2

Raising the Stakes Standards
        Mathematics is a highly interconnected subject. It is important for teachers and curriculum directors to look at the standards from several consecutive years when designing a curriculum for a particular year. Math standards increase as you go to higher grades- the higher the grade the more standards there are to cover. The standards cover Numbers and Operations, Algebra, Geometry and Measurement.

The purpose of the MN Math Standards are:

• To set the expectations for achievement in mathematics for K-12 students in Minnesota - requirements for graduation from high school.
• To align state tests to.
• A guide for school districts in designing mathematics curricula.

        One issue the U.S. is facing is that they are trying to replace those retiring in science and engineering but falling behind the need says the TAMS Report (2007). It also discusses that all concerns about national math performance are on the gaps:

• U.S. and Foreign gap
• Race, gender, and S.E.S. gap
• Talent gap

        There are many areas on which we could improve, but this is a gradual process. It can not happen immediately as many would like. With the push for higher standards, comes a push from teachers to students to achieve higher scores on state tests, which brings a whole lot of pressure for those students. 

        One area in which students struggle with is place value. Many students have trouble with this concept through the 4th grade. To help with understanding this topic it has been shown that by studying other cultures numeric system helps with the understanding place values. There are also many other aids such as visuals (i.e. cartoons as above), manipulatives (i.e. base-ten blocks) and songs (below) to help students learn this concept. Teachers are trying anything to get their students learning and loving math!

1512-Week 1

Understandable, Comprehensible, Coherent Curriculum
      The topic of National Standards is a Hot button issue and has been debated for years. The article "A Coherent Curriculum" is a great read for any future or current teacher. This article makes some very good points about curriculum. The article brings up some very important issues that the U.S. should address right now.

     There are gaps between U.S students and those in other countries in the overall ranking in math and science. By not having a coherent curriculum, the performance of US students was average or lower than those in other countries with more coherent curriculums (or national standards). In their examination of what is taught, they looked at “intended” content and “enacted” content. Intended content is what was intended for teachers to teach (i.e. the national, state, or district standards). Enacted content is what teachers actually taught. Intended content is replicated in U.S. textbooks. In the U.S., most teachers “follow” the textbook. Strengths and weaknesses in the intended content can be found in this study. The intended content in the U.S., relative to others in the world, is not focused, highly repetitive, not very demanding, and incoherent. Teachers are covering a wide variety of topics briefly and not going in-depth, therefore, "a mile wide and an inch deep" is fitting to the curriculum of the U.S.

      The article made a good point about how the U.S. has long list of what should be taught and we have market-driven textbooks. Many have widely different opinions about what should be taught therefore the U.S. has broad national standards, more specific state standards, and local districts are left to decide their own as well. All this variation keeps the students of the U.S. at an average or below level compared to other countries.

1510-Week 1

Overwhelmed by Math
       I find teaching math hard. When you have so many different algorithms or ways to teach a concept, its hard to decide which would be most beneficial to the students. I have been subbing in a school for the last 2 years that uses Everyday Mathematics. The different algorithms that are taught through this text got me!! I did’t understand some of them, which made it hard to help struggling students understand it. I understand the efficient and internationally known standard algorithms. In the past that was the typical method teacher would go by. 
      After being exposed to the videos below, it got me thinking. It was an eye-opener. I relieved that these "other" algorithms and methods of teaching math are all able to be taught effectively, it is just up to the teacher to back the method they are teaching. If a teacher doesn't believe in the method they are to teach, students are likely to feel as hostile to it as the person teaching it. 
      The first video is on math texts. The video hostess does not think that Everyday Mathematics is a great text for teaching math. I now have weird feelings about that text and don't know whether it is good or not, but the professor in the other videos makes a great point that you can't really teach something you don't back or you will have little success in the classroom. I can say when having to do harder math problems, recently, I am a little dependent on the calculator, but it is up to our school community (parents and teacher) to teach students that they can do these simple problems in their head rather then relying on the use of a calculator to tell them the answer. With dedication, we can teach math independence.

Math Education: An Inconvenient Truth

Math Education: A response to "An Inconvenient Truth" Part1
Math Education: A response to "An Inconvenient Truth" Part2 

Getting Our Kids On Top Of The World

Getting our kids on top of the world…in academics that is! Studies have shown that are kids are average of falling below. Our country is lacking of a coherent curriculum for our students. The problem is deciding what is best for our kids to learn. You would think we would learn anything from looking at those countries whose children are excelling in their academics far better than ours!?

In other countries, they have higher, specific National Standards. They don’t let every school decide for themselves what is best for their students! Many teach from a textbook. These books come from a market-driven society. There is no telling which ones offer the best lessons until tested and may not be the best for every group of students.

They also focus on fewer topics in-depth. If you are covering a topic in Math, like fractions and you are only spending a week on the subject chances are there are a few kids who will not understand. Practice makes perfect right? When going in depth on a topic it gives the slower students time to gain that understanding.