Vivid memories of learning multiplication facts? Did you learn a song for every fact? Use the nines finger trick? Times tests; public competitive games and visible displays of who has and who has not masters groups of facts? Is the thought of this giving you sweaty palms? I bet this **conventional approach** to learning times tables has led you to doubt your own mathematical ability?

The results reveal, however, that many of those "learned" math facts slip away from short-term memory after a break from lessons. For most learners, sheer willpower and complete dedication is needed to get those facts into rote memory and unfortunately, it doesn't make the knowledge stick!

Mastering the basic multiplication facts is a major stumbling block for many school children (National Mathematics Advisory Panel, 2008). Regrettably, if basic multiplication facts are not learned during the primary school years, it is highly unlikely they will be practised in a structured manner in secondary school (Steel & Funnell, 2001). Children need to be fluent with multiplication times tables in order to access much of the Maths curriculum. Without fluency and quick recall of multiplication times tables facts, maths becomes unconnected and confusing. Sounds of ‘I can’t do Maths’ may ring out around our classrooms as children feel a spiral of failure and frustration (Ginsburg and Baroody, 1990).

Multiplication times tables are too important to be left to chance. A clear, systematic approach is needed across school in order to support all children to recall times tables facts, both quickly and reliably.

Practice undoubtedly plays an important role in fostering combination mastery, but it is not necessarily the key factor or even the most important factor.

**SO, WHY CAN'T KIDS REMEMBER THEIR MULTIPLICATION FACTS?**

**There are many reasons but for me THIS is one of the most compelling:**

The **conventional approach** makes learning the basic multiplication facts unduly difficult and anxiety provoking. The focus on speed and memorising individual facts "**robs children of mathematical proficiency**. For example, it discourages looking for patterns and relationships (conceptual learning), **deflects efforts to reason out answers** (strategic mathematical thinking), and **undermines interest in mathematics and confidence in mathematical ability** (a productive disposition). Indeed, such an approach even undermines computational fluency and **creates the very symptoms of learning difficulties.** "

Other reasons include...

2. Unlike their more successful peers, kids who haven't mastered their multiplication facts might just have had **inadequate educational opportunities or/ and ineffectiveness of practice.**** **

3. Not enough opportunity to **BUILD** **number sense**.

Weak number sense and consequent poor mathematics achievement/ attainment all too often begin with **inadequate informal knowledge**. Preschoolers’ informal knowledge can differ significantly [e.g., Dowker, 2005; Baroody et al., 2006a; National Mathematics Advisory Panel, 2008]. Gaps in everyday knowledge can interfere with understanding formal instruction or engaging in mathematical thinking (e.g., devising problem-solving strategies, reasoning logically about problems) and this greatly delays or hampers the learning of school mathematics [Baroody, 1987, 1996, 1999b; Jordan et al., 2003; Canobi, 2004].

4. Kids won't understand times tables until they've mastered **addition**... In order to be successful with maths, kids must understand that maths is sequential. It's like a basic law of the universe, the same laws that govern gravity and Einstein's theory of relativity. If your child knows how to add numbers together one by one, then adding them quickly in groups (such as times tables) will be easy for them. When kids can successfully multiply, they understand that instead of counting each number by itself (1 + 2 + 3 + 4) they can simply multiply, or "fast add."

5. An **over reliance** on relatively slow **counting strategies** [Mazzocco et al., 2008].

6. learners have not had the opportunity to achieve **AUTOMATICITY**** **(retrieving facts them from long-term memory without conscious effort or attention).

It is not enough that pupils simply “learn” their multiplication facts—they must be committed to memory, just as letter sounds must be memorised in development of phonics automaticity (Willingham, 2009). **Automaticity** is a different type of knowledge; it is based on memory retrieval. Learning starts with understanding of concepts, to be sure, but **memory skills must develop simultaneously**.

To move a fact (or skill) from short-term to long-term memory requires “overlearning”—not just getting an item right, but getting it right repeatedly (Willingham, 2004). And retaining the memory for a long interval requires spacing out additional practice after initial mastery - emphasising the importance of regular review of learned material (Rohrer, Taylor, Pashler, Wixted, & Cepeda, 2005). You can read more about this here and here.

**HOW TO HELP KIDS LEARN THIER MULTIPLICATION FACTS...**

If you’re bamboozled by how you can help your child remember those all-important tables (and yes, they are important! More on that later…) and you’re looking for more effective ways to boost your child's confidence, understanding and achieve mastery of multiplication facts then **READ ON**!

This BLOG packs so much information that you'll want to read it... twice! It's helped countless teachers and parents to help their children** MASTER MULTIPLICATION. **

I've transformed the latest advice of the world's best researchers of mathematics education into practical and easy to replicate maths fact fluency **ideas** to help your kids master those multiplication facts!

**MASTERING MULTIPLICATION** was designed to help kids master their multiplication facts in a **meaningful, connected** way.

**Pedagogically perfect because unlike other resources it builds on what the learner already knows and helps learners build** a rich and well-interconnected web of factual, strategic (procedural), and conceptual knowledge.

**A more connected, meaningful ways to Master Multiplication... **

However, if you really want to help your learner, I would say this: **The most important single factor influencing learning is what the learner already knows**. Ascertain this and teach them accordingly. **This famous quotation from David Ausubel in 1968 points out one of the fundaments for constructivism as theory of learning and knowledge, and states a still common held teaching approach**. The first one found to investigate **"what the learner already knows"**

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**WHAT WE ALREADY KNOW DETERMINES WHAT, HOW, AND HOW WELL WE LEARN.**

In other words: **prior knowledge**. According to Ausubell, new things that we want or need to learn need to be connected to what we already know. The knowledge we already have is stored as schemata (also known as schemas) in our long - term memory. Schemata are basically mental frameworks in which we can integrate new information. They’re like the clothing rack in the hall where there are ‘hooks’ that we can use to hang new information. Without these hooks, we have nothing to which we can connect the new information.

Kirschner, Sweller, and Clark (2006) explain why this is. If the learner doesn’t have the basic ‘hooks’ (i.e., relevant prior knowledge) to hang the more complex information on, then they’ll start swimming using trial and error and then drown very quickly as they don’t know how to do it effectively. In other words, the foundational knowledge that the learner needs to do the more complex stuff, first need to be made *explicit *to the learner and the instruction used needs to accommodate this.

When MASTERING MULTIPLICATION you need to understand what your learners prior knowledge is. Try this: Mastering Multiplication Self Assessment

**This one - to - one interview is an 'inter view' where the adult listens to learn and probes deeply into children’s thinking. ****A wonderful opportunity to find out what your learners knows using effective questioning to ascertain previous knowledge. **

Heick’s (2021) posting on Why questions are more important than answers included encouragement to teachers to constantly practice their strategies to better ensure that students reveal their thinking. You can read more about this here

Few know about the richness and importance of Ausubel's assimilation theory of meaningful learning and retention, which holds many more instruction-altering insights. You can read more about this HERE. One of the main reasons why this theory is so important is because it focuses on the end goal teachers are after: teachers don't want students to memorise distinct ideas; teachers want students to develop vast bodies of knowledge in the subjects they are taught. Ausubel explains that the only way to achieve this is through supporting students **to learn ***meaningfully.*

As general rules of thumb, practice is useful if its primary purpose is to provide students an opportunity to discover patterns or relations or to ensure reasoning strategies become automatic (once a child has discovered patterns and relations).

**FOCUS ON LEARNERS MASTERY OF A FEW FACTS AT A TIME: INCREMENTAL REHEARSAL - AND SPACED PRACTICE (more on that to come).**

**Focusing on structure**, rather than memorising individual facts by rote, makes the learning, retention, and transfer of any large body of factual knowledge more likely [Katona, 1967].

As with any worthwhile knowledge, **meaningful memorisation** of basic combinations can reduce the amount of time and practice needed to achieve mastery, maintain efficiency (e.g., reduce forgetting and retrieval errors), and facilitate application of extant knowledge to unknown or unpracticed combinations [Baroody, 1985; Carpenter et al., 1989].

Here are some meaningful ways to use **MASTERING MULTIPLICATION**:

**Based on a wealth of research by cognitive scientists, there are some powerful teaching strategies that transform students’ long-term learning:**

**RETRIEVAL **
**SPACED RETREIVAL **
**INTERLEAVED PRACTICE**

**I've written a BLOG on these too which is linked here.**

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If you'd like the opportunity to try out this resource for FREE (yes, thats right, for absolutely nothing!) click the image below:

If you like what you see then why not check out our complete range of MASTERING MULTIPLICATION.

## Here are some references and resources that might be of interest to you...

Ausubel, D. P. (1968). *Educational Psychology: A Cognitive View*. New York, NY: Holt, Rinehart and Winston.

Ausubel's Meaningful Learning Revisited

Bjork, E. L., & Bjork, R. A. (2011). Making things hard on yourself, but in a good way: Creating desirable difficulties to enhance learning. In M. A. Gernsbacher, R. W. Pew, L. M. Hough, J. R. Pomerantz (Eds.), *Psychology and the real world: Essays illustrating fundamental contributions to society*, *(*pp 56-64). New York, NY: Worth Publishers.

Kirschner, P. A., Sweller, J., & Clark, R. E. (2006). Why minimal guidance during instruction does not work: An analysis of the failure of constructivist, discovery, problem-based, experiential, and inquiry-based teaching. *Educational Psychologist*, *41*(2), 75-86.

Krapohl, E., Rimfeld, K., Shakeshaft, N.G., Trzaskowski, M., McMillan, A. & Plomin, R. (2014). The high heritability of educational achievement reflects many genetically influenced traits, not just intelligence. *Proceedings of the National Academy of Sciences, 111*(42), 15273-15278.

Shakeshaft, N.G., Trzaskowski, M., McMillan, A., Rimfeld, K., Krapohl, E., Haworth, C.M.*,* & Plomin, R. (2013). Strong genetic influence on a UK nationwide test of educational achievement at the end of compulsory education at age 16. *PloS one*, *8*(12), e80341.

Simonsmeier, B. A., Flaig, M., Deiglmayr, A., Schalk, L., & Schneider, M. (2018). Domain-Specific Prior Knowledge and Learning: A Meta-Analysis. *Research Synthesis 2018, Trier, Germany*. Retrieved from https://www.researchgate.net/publication/323358056_Domain-Specific_Prior_Knowledge_and_Learning_A_Meta-Analysis

Stein, M. K., & Smith, M. S. (1998). Mathematical tasks as a framework for reflection: From research to practice. *Mathematics Teaching in the Middle School*, *3*(4), 268-275.

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