One of our students came in a few weeks later than the rest. It was immediately noticeable that she did not understand multiplication. In the morning they have a multiplication quiz, daily. We have moved on to two-digit multiplication and 4 by 1 digit multiplication with carrying numbers. Without the knowledge of one-digit multiplication, it is pretty unlikely that she would be able to do any of the further multiplication. Within the first few days, we gave her multiplication cards to bring home and practice. A few days later she came back with a note from her mother expressing her concern that the homework was way too difficult for her daughter. This homework was two-digit multiplication. She also stated that she (the mother) wasn't even able to do it, so therefore the assignment was left incomplete. My teacher and I discussed this and realized that it is pretty difficult to pull her to the side of math each day and explain everything separately, so we began to brainstorm what we could do. Ultimately what we decided is that since she is performing below grade level in math, and now we have moved onto finding common denominators of fractions, among other topics that involve multiplication, she really will need to try very hard in class and at home to catch up and understand what we are teaching. So I figured that we can pre-assess her multiplication facts knowledge with times tables 1-12 in order to see where she is. Then I will highlight the facts she knows, so we can focus on the others. Finally, I prepared a sheet explaining how she can practice math facts. For example, multiplying by two, she can just count by twos to get to the number. For nines, she can use the 10-finger rule, where you put the finger down that you are multiplying and so on for 0-12. My plan is to have her focus on two times tables per week, or depending on how she progresses, maybe more, so that she can soon be able to recall the answers fairly quickly. We will also be focusing on how anything times 0 is 0, anything times 1 is that number and some other rules that apply, and make multiplying easier.
It is important to notice the areas in which the students are having difficulties at the beginning stages. For example, something like multiplication, if you don't see that the student is struggling with this, then it will go on throughout the future units and the student will continue to suffer because he/she has not been given/has not asked for the extra help. Not only noticing it, but acting upon it and figuring out how to assist the child in order to improve his/her skills so that the student can keep up and not feel frustrated at school. The thing with math is that the facts and topics you learn, most likely will relate to future units, therefore if some understanding is lacking from the beginning it is important to catch it early in order to prevent the student from falling way behind
I can understand what is happening here because from the first day it was very obvious that she had never learned one-digit multiplication. Or maybe she slightly learned it, but it was not engrained in her mind and she lacks the understanding of why/how it works. It was fairly simple to find a solution as well. Unfortunately, there is not much time in the school-day schedule to have one-on-one tutoring so a majority of this work (times-tables) will need to be done at home. What I plan on doing is introducing the whole concept and plan to her in a systematic manner that does not make it seem overwhelming. We will create the plan together so she has input and makes the plan reasonable/achievable for herself. I hope to have her understanding the multiplication facts for 0-12 by the end of October (we have a week break in the middle). I will also go through some of the rules and tricks with her and meet with her a few times a week to make sure she is working on it at home and see if she has any questions or confusions.
I think this is a case of responsibility on the teacher's and on the students' part to realize when some understanding/knowledge is missing. Not only do the teachers need to be aware of what the student does not understand/how the teacher can help the student, but the student also needs to realize that he/she does not understand and he/she has a responsibility to ask for help. It is also representative of individualizing instruction to make sure that each student is getting what they need out of the lessons. I am really excited to institute this extra instruction for my student and I can't wait to see the benefits that it has.
This sounds like a challenge; however, also keep in mind that until she masters the times tables, her lack of understanding may shut her down for the mathematical instruction that you present in class, depending on the characteristics of the task. My point, therefore, is to call your attention to the fact that it is possible to design your math instruction in a way that either a) assumes / requires students to have certain knowledge to be successful or b) allows multiple entry points into the activity such that students are able to think about the mathematical "big idea" in question with whatever knowledge they currently have.
ReplyDeleteIt is unlikely that this student will be able to learn the times table as quickly as you would like. As a result, it is important to keep her in mind (along with the other students who may not have fully mastered their times tables) as you design your mathematical tasks. Specifically, make sure that you are clear as to what "big idea" you want your students to think about; from there, "differentiate" the instruction so that there are multiple entry points into the activity. Over time, as this student explores the content and engages in mathematical thinking with the knowledge / understandings she has, she will not only strengthen her mathematical understanding but also become more comfortable with the formal times tables.