When I started teaching 6th grade 22 years ago (Oh my goodness that was a long time ago!) I came across this cute little trick to multiplication. It was called Lattice Multiplication. If you are unfamiliar with the trick, you can google it. Yes, I taught it to my students for a couple of years. Yes, it was nice to finally have a way for some students to always get a multiplication problem correct. But that was back when I thought that correct answers was all that mattered.
After reading research and books regarding mathematical understanding I have a different opinion about Lattice Multiplication. John Van de Walle stated in one of his books that “Correct answers do not mean understanding”.
Does Lattice Multiplication teach anything about place value? No. Does it involve place value? Of course it does; that’s what makes it work. But unfortunately very few students can explain mathematically why it works. Therefore, let’s just not show it to students.
More or Less?
When providing comparison problems for your students be sure to make a concerted effort to use both ‘more’ and ‘less’. We typically forget about ‘less’.
Here’s an example.
Macey had 6 A’s this quarter on her report card. Aaron had 2 less A’s. How many A’s did Aaron have?
Mathematical discussions have taken place in many classrooms for many years. However, the book titled “Number Talks: Helping Children Build Mental Math and Computation Strategies” by Sherry Parish has greatly influenced my thinking. Number Talks is a specific time set aside within a classroom when students mentally solve problems and then share their strategies with their peers. The book itself provides ideas on how to get started and also includes a DVD that shows Number Talks at several different grade levels. In the book the teacher can also read about different strategies students may use when solving problems mentally. Some of those strategies are Make a Ten, Friendly Numbers, Compensation, Near Doubles, etc. Special strings of problems are also provided in the book. A string is a set of problems used to highlight the relationships between problems. Pages of strings are provided for certain grade bands. However, if your students are in an upper elementary grade and Number Talks are new to them, they may not be ready for the strings provided for that grade band. It may be necessary to use some of the K-2 strings first. As a teacher you may decide not to use all of the strings for a particular strategy but I would recommend that you not randomly choose strings. Be intentional about the strategy strings that you choose. If you want more information or clarity please feel free to ask. There are a lot of resources regarding Number Talks on the internet. http://schoolwires.henry.k12.ga.us/domain/3791 is one of those sites. I have been told that there are many YouTube videos available also.
I have been asked several questions regarding number talks and would like to address them below.
- Can I teach the strategy before I give a string so that the students know what to do? I say ‘no’. If after several days of working on similar strings no one in your class has shared the desired strategy, then I think it would be appropriate for you to share a strategy that you “saw a student use once”. You may wonder how this is different. If you share a strategy first then the students will be more likely to try to follow your lead and not try to solve the problem with a strategy that makes the most sense to them.
- Is it Ok to tell the students what strategy to use? When a student shares a strategy I do believe that it is Ok for you to ask the class to try to solve the next problem using “Marcia’s strategy”. But I would not require that students use a particular strategy all of the time.
- My students try to come up with the most obscure way of solving a problem, what do I do? Many students simply want to share their ideas with others. However, you want to give everyone an opportunity to participate during Number Talks at least once a week. Some of these students can be satisfied by simply sharing their strategy with an ‘elbow partner’. Before you call on someone to share in front of the class, tell the students to discuss their solution and strategy with their ‘elbow partner’. This way everyone can talk.
- Don’t we want our students to be efficient? Yes! But you can’t force a child there until he/she is mathematically ready. So in the meantime, spend time asking them to compare strategies used to solve the same problem. Then talk about efficiency.
- The next is not a question but something that a teacher shared with me this past week. During a curriculum night with parents, she conducted a Number Talk. She said that parents were amazed and very excited to know that their children were talking about mathematics in such a way. I think this was a great idea, so I suggest that you try it sometime.
This is a question for you? Does anyone know of a rubric for assessing Number Talks? Teachers are looking for a way to periodically ‘give a grade’ for student understanding displayed through Number Talks. If you have such a tool will you please share it with us? Thank you.
Well, that’s all for this post right now. I’ll address any additional comments or questions in further posts.