I agree with the comments thus far - and also teach a range of multiplication models for students. It is interesting that the lattice model is identified as a means for differentiated instruction - I suggest that it is only differentiated because of the over-reliance on the traditional (vertical algorithm). Perhaps in an alternate universe students are taught the (vertical algorithm) as an alternative to the lattice method which is their traditional algorithm. In any event, the algorithms should only be used as a procedure once conceptual understanding of multiplication has been attained.

In differentiated instruction teacher is the professional who decides according to his students' readiness level, learning profile etc. which is the best way for these specific students to learn. Thus any changes and adaptations we make in the way to suit better to our students' need can and may be consider as differentiated instruction.  In this specific case if I understand right teachers provide student's with a strategy on multiplication which it is closer to students' learning and working abilities. My only concern is that in mixed ability classrooms this strategy should be provided only to students that really find it difficult to work on the curriculum level.

Yes, if any deliberately selected strategy is used with certain students who apparently need it and not with others, then you are differentiating instruction.  If it is used with almost all the students, then, by definition, it is not.  I also agree with Stavroula that this particular strategy should be provided only for those who really struggle with the standard approach and would add that, for some of those struggling students, the lattice approach actually adds confusion.  It reminds me of the Vermont dairy farmer riding on a train through Texas with a rancher.  As they rounded a curve, they had a quick glimpse of a huge herd of cattle.  The farmer (who owned 6 milking cows) was stunned  and wondered aloud how many cattle there had been.  The Texas rancher replied "6,437 head."  "How could you count them so fast?" asked the farmer.  "It's easy if you know the trick," explained the rancher.  "Just count the legs and divide by 4."

Stavroula and John thank you. In my opinion we should challenge all students by teaching such solutions just to know that there are different ways to solve problems. But  another difficult  way (or of the same difficulty) leads to failure thus I don't consider it as differentiated instruction.  From my experience I  agree with John that is confusing for children with learning disabilities.

I am interested to hear some of you say that providing an alternative strategy for multiplication should only be used if the student is having difficulty with the traditional algorithm. My experience teaching children and adults learning to teach mathematics to children is that many were moved far too quickly to the formal algorithm. Even though many can use the algorithm they still (even as adults)  do not understand the conceptual ideas behind it. For example the big ideas about place value. I would (and do) use the Lattice method as well as the array algorithm with my students (young and old). My experience is that students move towards a more efficient method of coming to an answer once the previous method become redundant. The student begins to take short cuts and before you know it is using one of the formal algorithms. I would argue that the array algorithm is actually as quick as the traditional algorithm and is easier for students as it hunks together the operations.  

Brenda thanks . I agree with this approach.

I agree with the comments thus far - and also teach a range of multiplication models for students. It is interesting that the lattice model is identified as a means for differentiated instruction - I suggest that it is only differentiated because of the over-reliance on the traditional (vertical algorithm). Perhaps in an alternate universe students are taught the (vertical algorithm) as an alternative to the lattice method which is their traditional algorithm. In any event, the algorithms should only be used as a procedure once conceptual understanding of multiplication has been attained.

I agree Kevin. I  always teach the array method as well which is a formal algorithm, just not the traditional algorithm that most of us grew up learning.

I am a newcomer with this question but gladly I learn.

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