With　complex　two-dimensional　structure,　offline　handwritten　mathematical　expressions　is　difficult　to　recognize　due　to　the　variable　scale　of　their　symbols　and　the　various　transformation　of　their　writing　styles.　This　paper　proposed　a　mutual　learning　model　based　on　multi-scale　feature　fusion.　Firstly,　to　enhance　the　model　for　extracting　fine-grained　information　from　expressions　and　comprehending　semantic　information　of　global　two-dimensional　structures,　multi-scale　feature　fusion　was　introduced　in　the　encoding　stage.　Secondly,　paired　handwritten　and　printed　mathematical　expressions　were　introduced　for　training　the　mutual　learning　model,　which　includes　decoder　loss　and　context　matching　loss　to　learn　LaTeX　grammar　as　well　as　semantic　invariance　between　handwritten　and　printed　mathematical　expressions　respectively　to　improve　the　robustness　of　the　model　to　different　writing　styles.　Experimental　validation　was　performed　on　the　CROHME　2014/2016/2019　dataset.　After　introducing　the　multi-scale　feature　fusion　mechanism,　the　expression　correctness　rate　reaches　55.　25%,　52.　31%,　53.　72%,　respectively.　After　introducing　the　mutual　learning　mechanism,　the　expression　correct　rate　reaches　55.　43%,　53.　53%,　53.　79%,　respectively.　The　expression　correctness　rate　reaches　58.　88%,　55.　10%,　57.　05%　after　introducing　both　mechanisms　at　the　same　time.　It　is　proved　experimentally　that　the　proposed　method　can　effectively　extract　the　features　in　formulas　at　different　scales　and　overcome　the　problems　of　different　handwriting　styles　and　small　amount　of　data　by　mutual　learning　mechanism.　In　addition,　the　experimental　results　on　the　HME100K　dataset　verified　the　effectiveness　of　the　proposed　model.　©　2024　South　China　University　of　Technology.　All　rights　reserved.