I saw this activity on a twitter page https://twitter.com/letsplaymath and thought it has some interesting potential for high school math students. The activity published by Math Forum asks participants to create expressions for whole numbers 1-100 using only the digits 2, 0, 1, and 5, in any order*, with the operations +, -, x, ÷, ^ (raised to a power), sqrt (square root), ! (factorial), and !! (double factorial). Grouping symbols may also be used, and multi-digit numbers such as 20, 210, .02 may be used this year. *The order 2, 0, 1, 5 is preferred.
For Algebra 1, Geometry, and Algebra 2 – it would be a great review for basic operations practice. There are so many ways to extend this activity. On example could be that every odd number has to use a negative integer in the expresseion. For upper level math, it would be interesting to see what they could do with the additional operations that they have used – like the log of a number etc.
Think about the conversations this could start if students were encouraged to share their responses and then asked if could they come up with different way for the same value. Just the thought of this makes me smile.
Students could also be asked if they could come up with a strategy of attack when thinking of different number sets…like even numbers or multiples of 10 etc..
How about asking students before they start – to predict the numbers will be the hardest to find a combination that will work and then reflect afterwards if they were correct. Wow think of the thinking! (I am really smiling now with that “evil” smile a math teacher has when they are thinking about making student think 🙂 )
The original directions and worksheets can be found at the link http://mathforum.org/yeargameWorksheets/2015/2015.worksheet.html . Happy New Year!
Use models in math? In high school level courses?? Isn’t that something only elementary teachers need to use??? High school students do not need models and there are not any models to use with high school topics anyway…this has been a reflection of my thoughts until recently. Boy have I made a lot of mistakes as a teacher – it is amazing that my students have been as successful as they have. During most of my teaching career I used models (Algebra Tiles mainly) as an afterthought in Algebra 1 because they had to be “shown” for the state standardized test. My students always complained about the algebra tiles and said that they were too “easy” and that they did need not them – they knew the math so why use the tiles. Duhhhh if I show them the tiles after I taught the standard algorithm they why would they use the tiles…which my students always felt were for “dummies”. I know that I encourage that thought now looking back on it.
Now my thinking has evolved…I have discovered models and how they give students an avenue to communicate and understand the concepts that we ask them to do. I have learned that our students (all students) need to experience most mathematical concepts through models first before they experience the standard algorithm. Students can make many more connections through the use of models and truly understand why the standard algorithm works. It is amazing that using models leads students to a true understanding.
I wanted to share this epiphany with everyone that I work with but how do I start???? Most teachers (high school anyway) that I know do not think that models are needed to help students conceptualize the math that they are teaching. I understand where they are coming from because like I said 2 years ago I was with them. So I decided to start with a group that I work with (or teach) bi monthly – instructional coaches. I started with the Junior High standards that addressed using models to teach and we discussed how important it was to make connections to how students learn specific topics so that students would see that what was being taught is not new – they have seen it before – it is just in a different format. So while I was working with the high school math instructional coaches, I used the practice sheet below for them to see how a linear equation can be solved in several different ways and using models can be used to differentiate so that teachers can reach all students… (you can download here…Modeling to solve equations practice)
This activity went over really well but now how do we get this knowledge to spread throughout the district? That is a question that the coaches and I will need to answer. What I was very pleased with was the fact that by showing the different forms shown while working this activity really showed how different learners might need different tools in order to make connections and gain a true understanding of the topic. Now I need to work on next steps and would love any input from others. I started with solving this set of linear equations but I have plans to continue this with other functions.
Yesterday I was reminded why we are all on what it feels like a crazy rat race…
Sometimes it is easy to forget this…with grades due, parents to call, lessons to plan, and all of the other deadlines that we experience day in and day out. I really appreciated being reminded of that. We are in the education profession to make a difference in a student’s life. The person that reminded me was speaking to a group of teachers and he started with “I was going to tell you what a great job you are doing but I have changed my mind. Instead let’s talk about what your job really is…Your job is to make a difference for students.” He was so right. Teachers and educational leaders need to be reminded of this sometimes, especially when everything gets hectic – It is easy to lose sight of what is important and to get caught up in the day-to-day demands.
“Education is the key to unlocking the world, a passport to freedom.” – Oprah Winfrey. This is the difference that we make every day as teachers and educational leaders. We are improving the future of our student’s lives by increasing their knowledge and chances for higher education – whether it is college or some type of professional certification. An education is the best way to insure that our students have a fighting chance at being a successful adult (however they define that). Horace Mann stated, “Education then, beyond all other devices of human origin, is the great equalizer of the conditions of men, the balance-wheel of the social machinery.“
So remember this when you when you wonder why you are working so hard – there is a reason for planning that lesson or taking the time to write the extra feedback beyond trying to get our students to pass that test. There is a bigger picture – remember that and do what you do best – make a difference.
Educators are a part of a greater plan and make the difference in our student’s lives.
Earlier this week I received an update from Dan Meyer’s Blog. This particular post was about the electronic platforms and how they sometimes hinder the pedagogical choices of teachers. The link to the blog is http://blog.mrmeyer.com/?p=17917&utm_source=feedburner&utm_medium=email&utm_campaign=Feed%3A+dydan1+%28dy%2Fdan+posts+%2B+lessons%29. (This has been continued with two more updated posts on entitled “Dashboards are Hard #1 & #2. )
When I read this post, I had to reply. I had just experienced a very frustrating class with my developmental math college students where I often have a choice to teach in the same manner/order as the computer program they are required to use (by the college) or I can do what I know is best which has caused problems for my students in the past. I believe in teaching concepts – not slivers (section by section) but if I do this then my students are not prepared to use the computer program that they are required to use. It is very frustrating – the college insists that I continue to perpetuate the kind of instruction that has assisted these students to be in my class in the first place.
Later that day I received an article from the NY Times, http://www.nytimes.com/2013/09/03/science/applying-new-rigor-in-studying-education.html?_r=0 which said that research has found that the choice of instructional materials — textbooks, curriculum guides, homework, quizzes — can affect achievement as profoundly as teachers themselves; a poor choice of materials is at least as bad as a terrible teacher, and a good choice can help offset a bad teacher’s deficiencies. At first this surprised me and then I realized that the instructional materials included electronic platforms and the yes, a bad resource does effect my effectiveness as a teacher. Just as I knew from my work with curriculum that good resources help teachers be more successful – especially struggling teachers.
So what a quandry here…do I stop teaching these students that I have a true place in my heart for because the resources that the college demands of me to use make me question my integrity as a teacher. I do understand one of the reasons why districts and colleges require specific resources to be used. This practice has several purposes; one of which is to try to raise the level of effectiveness of teachers and another would be to try to regulate the curriculum that is taught. I will continue to try to work around the system that I am required to use so I can do what I feel is best for my students.
This does give me a lot to think about since my state is starting procedures for a math resource adoption. It only reinforces to me the importance of educating our teachers on the standards and research based pedagogical practices to ensure that my district adopts resources that support our teachers in using best practices and in teaching to the level and the target of our state’s standards.
Ok – so I am very new to the world of blogging. I have been reading several blogs over the last 2-3 years but I never thought that I had anything to say that was important enough to take the time to blog. This summer I decided that I need an outlet to write my thoughts so I could think them through and develop them for when I am teaching and working with coaches and teachers.
So I started this blog and have been winging it …and was about to drop it because I am back to the thought that maybe I do not have enough to say to keep up a blog. Then today I ran across this Exploring the MathTwitterBlogosphere (through Dan Meyer’s Blog – dy/dan <firstname.lastname@example.org>) which promises 8 weeks of fun missions and prompts. Hmmm…with a title and promise like that who can turn it down. I think I will try it and see what I will learn. If you are like me and interested in learning more maybe you should try it too.
Here is the link: http://exploremtbos.wordpress.com/ – It begins on October 6th
Technology geared for math teachers – this will be a first…looking forward to seeing what it will bring.
I found this picture and at first thought that it was cool.
Something about it kept bothering me though – it stayed on my mind. After I thought more about it, I realized what was bothering me…is this really what I wanted from my students? Do I want them to just “do” math? Or do I want them to understand the math? To make connections from the math? To be able to apply the math in new situations? Do I want to my students to question? To problem solve?
I know the answer to these questions. I want my students to do more than “Just do the math”. I want my students to do more than to mimic my steps in solving – I want them to be able to understand, apply, and justify while problem solving.
When I was meeting with a group of teachers recently, I discussed with them about the traits we would want our students to show in our math classes. These traits included:
- Flexible thinking
- Problem solving
- Learning from mistakes
- Making connections
- Verbalizing thoughts
And while I was discussing these traits, I made the observation – “Aren’t these the traits that our students/our children need to be successful in life?” So really aren’t we teaching our students to be successful in life – if we are teaching mathematics correctly in our classes? Math class is so much more than math class…or least it should be.
The struggle is how do we as math teachers do this – Now that we know this should be our goal and not the goal of teaching students just do the math.
Knowing that there is not just one answer because there is not just one student – I am looking forward to continuing my journey toward excellence in teaching math for all students.
This summer I have begun reading several blogs and in one of them the writer said – you should blog because you need to write. This resonated within me. I am at a point in my career where I am seeing so many connections between what I know about math and I what I don’t know that I feel the need to write them down to help me process them. I was taught in a traditional math class where I learned to mimic the steps that were shown to me. I understood why the steps worked but I didn’t see the beauty of the math – the connections between everything we do. I am a good teacher – at least that is what my students tell me but with this new knowledge I am gaining daily I realize that I could have and should have given so much more to my students. My goal for this blog is to discuss the changes that should be made in order to reach all students in secondary math classes.
Every math teacher I know works hard and wants success for their students. The lack of success comes from the lack of knowledge not the lack of trying. There is not a magic pill to bridge the gap in making math accessible and there not just one way or one strategy – if there was this wouldn’t be an issue. Hopefully this blog will help others while it helps me. ~A