Reading over these articles reminded me a lot of what we worked on in class last week. The equation shown on the first page of Baroody and Bartel’s article “5-3=3-5” reminded me of the problem we worked on last week. There were discrepancies between 9+3=12+3=15. When doing fast work, I would think this is fine… but when teaching, we need to be very careful with how we represent this… because 9+3 does not equal 12+3…. But if you are simply adding several numbers together, it saves time and it is more convenient. I need to remember when teaching to do the full problems, with all the details, and not leave anything out because my future students could possibly become confused and learn these basics wrong.
“The degree of a student’s understanding is determined by the number, accuracy, and strength of connections.” (Hiebert and Carpenter 1992) This article discusses linking the aspects of knowledge that are accurate and strong to comprehension of the problem. Making connections is discussed as understandings between two pieces of information. Math doesn’t need to be simply equations applied to the problems on one worksheet, and applied or thought of in other circumstances.
Some suggestions they gave to help the students make connections with math so that they use it in other circumstances rather than just one time on a test is through concept maps. This helps them to see when the concept can be used and what it applies to, rather than simply knowing the equation, but not
Math in America is taught poorly in the sense that students have received equations and only use them during that time. What I mean is that students are usually not able to use their background knowledge on equations they have already learned, and other cases they can apply them too. They simply memorize the equation without understanding the complexity of it, and scenarios when it is used. They memorize the equation for that test or exam, and do not use it again. As a teacher we need to teach them equations and help them make a connection on which scenarios to apply it to in everyday life. Taking math outside the classroom….. Giving them math facts in lessons that incorporate when to use it, other than just in the book. I liked the concept map on fractions and decimals, and when to use it. It helped students choose when it is time to use each, and scenarios where is more beneficial for them to use either one. Students are not only memorizing math terms, but also learning when to use them. That way students will use mathematical terms/equations they have learned in the past and are able to still use them today.
I am surprised that this article only discussed concept maps as a tool to helping the student differentiate real life scenarios on which equation to use. I liked the concept, but I would like to see more examples of how I can incorporate this into my lesson plans to help my students understand the complexity of the equation, and not just memorizing what numbers to plug in, and where. Rose and Lauren, do you have any ideas on how we can help students to remember the equations to apply to everyday life?
Gabe, you brought up an excellent topic and one I found very interseting as well. I loved that the article directly related to what we did in class last week. At first I thought the problems of 9+3=12+3=15 was fine until I really thought about what I was showing. The article made my understand a lot more clear on the topic. Yes, 9+3 does give us the solution 12, however 9+3 is not the same as 12+3, which is what the problems is actually stating. I think its really important for us as future teachers to make ourselves very clear in the math that we teach. Math is a difficult subject for many students, and we need to make sure we are being extremely clear on how and why a problem is solved the way that is it. I know how to do a lot of math, but sometimes I dont know when to do equations unless they tell me what they want. This doesn't show good mastery of the math, it simply shows I memorized something, instead of learning it. I dont want students to walk away from school feeling like this.
ReplyDeleteRose and Gabe, I agree that we need to do a much better job of helping students connect everyday examples to the math we are teaching them. i think this is true for all grades. In addition, we need toincorporate students' prior knowledge into math lesson plans, just as we need to in all other subject areas. I think our class discussion last week showed how our school system has failed so many of us.... Most of the class thought what you two thought, that it is ok to write 9+3=12+3=15. I would have also said this is correct, if it was not for me remembering that I learned that this is incorrect in math 201. Something as simple as this is not known by college level students...This to me is evidence that our primary school teachers have failed us and countless others. I am sure that many teachers write equations in this fashion, which ingrain misconceptions in students' mind, sometimes for life. I think two ways we can help change this failing school system is by ALWAYS modeling the correct way of doing things, and identifying any misconceptions students have and helping them relearn the correct things. Also, I think by allowing for as many class discussions that are student lead is a great way of identifying misconceptions, and allowing the student and their peers to help correct the misconception, instead of immediately correcting it as the teacher. Kids constanly hear what they need to do differently from their teachers, so it is more meaningful to them when they discover it on their own, or by the help of a peer. In addition to help debunk misconceptions, classroom discussions help the teacher get an understanding of what students' prior knowledge on the content is, and from there, where the next lessons should develop from and end up at. This way, you are helping to avoid going over material they already know, and thus would grow bored of, and getting a feel for what the next best thing for them to learn is. This is also much more meaningful than simply doing math worksheets and applying dusconnected equations that they are likely to forget, or not know how to use in the future. When the lesson is grounded in their experiences and lives, students will be much more willing to listen, learn, and remember things from that lesson.
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